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
0
0
3
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
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
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
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
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
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
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
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
0
3
0
0
3
4
1
2
0
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
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
11
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
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
1
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
1
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
0
0
0
0
0
0
4
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
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
2
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
0
0
1
0
0
0
0
0
0
0
0
0
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
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
8
1
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
16
0
0
0
0
0
0
0
2
1
0
1
0
4
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
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
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
12
0
0
0
0
0
0
12
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
1
0
3
0
0
0
2
1
0
1
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
4
2
1
1
0
0
0
0
0
3
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
3
1
1
0
1
0
1
0
0
1
1
0
0
2
0
1
0
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
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
11
4
0
0
0
1
1
1
1
0
0
0
0
1
1
0
2
0
1
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
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
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
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
0
0
0
0
0
1
1
1
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
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
3
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
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
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
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
1
0
0
0
0
1
0
1
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
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
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
1
0
1
0
1
1
1
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
2
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
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
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
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
1
0
0
1
1
1
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
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
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
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
1
0
0
1
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
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
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
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
