1
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
1
0
2
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
2
0
0
0
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
2
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
1
0
1
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
0
0
0
0
0
0
0
0
1
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
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
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
2
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
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
9
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
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
5
4
0
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
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
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
3
1
0
0
0
0
3
2
0
0
2
1
1
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
6
2
6
6
2
5
1
0
3
0
0
5
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
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
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
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
19
0
0
0
0
0
0
0
0
0
0
0
0
8
4
0
7
0
0
0
0
0
1
1
0
1
0
1
1
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
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
1
0
0
0
0
1
1
1
1
1
0
1
2
0
1
0
1
0
0
2
2
1
21
0
0
0
0
0
0
21
0
0
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
0
3
1
0
0
0
3
0
6
0
0
1
0
0
0
1
0
0
1
1
0
0
0
3
1
1
1
1
0
0
0
0
0
0
3
1
3
3
0
0
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
3
0
3
1
1
2
0
1
0
2
2
2
4
2
1
0
2
0
0
2
1
3
3
1
0
9
0
0
0
9
1
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
0
0
0
0
0
0
0
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
0
0
0
1
0
0
4
2
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
3
9
2
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
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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
1
0
0
2
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
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
3
1
0
0
0
0
0
1
1
1
1
1
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
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
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
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
4
1
1
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
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
3
0
0
0
0
0
1
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
3
1
1
0
1
2
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
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
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
0
2
3
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
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
1
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
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
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
