2
1
0
0
0
2
1
0
1
0
0
0
5
4
3
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
0
2
1
0
0
0
2
1
0
1
0
3
2
1
0
0
2
1
0
0
0
7
6
5
4
3
2
1
0
0
4
3
2
1
0
0
3
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
3
2
1
0
0
0
0
0
1
0
0
3
2
1
0
1
0
2
1
0
0
1
0
1
0
0
3
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
4
3
2
1
0
0
1
0
0
0
3
2
1
0
2
1
0
0
0
3
2
1
0
0
2
1
0
0
0
0
1
0
1
0
3
2
1
0
4
3
2
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
4
3
2
1
0
0
0
0
0
0
0
3
2
1
0
0
6
5
4
3
2
1
0
0
0
2
1
0
4
3
2
1
0
0
2
1
0
2
1
0
2
1
0
2
1
0
2
1
0
1
0
0
1
0
0
4
3
2
1
0
0
0
2
1
0
10
9
8
7
6
5
4
3
2
1
0
0
1
0
0
0
3
2
1
0
1
0
0
0
0
0
1
0
5
4
3
2
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
1
0
0
2
1
0
1
0
3
2
1
0
1
0
1
0
0
1
0
0
5
4
3
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
5
4
3
2
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
5
4
3
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
3
2
1
0
0
4
3
2
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
3
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
4
3
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
4
3
2
1
0
2
1
0
0
0
2
1
0
0
5
4
3
2
1
0
0
4
3
2
1
0
0
1
0
0
4
3
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
1
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
2
1
0
1
0
6
5
4
3
2
1
0
6
5
4
3
2
1
0
0
1
0
0
0
3
2
1
0
0
1
0
1
0
3
2
1
0
5
4
3
2
1
0
1
0
0
0
1
0
1
0
0
5
4
3
2
1
0
2
1
0
0
0
4
3
2
1
0
1
0
1
0
1
0
3
2
1
0
0
1
0
2
1
0
1
0
1
0
0
2
1
0
4
3
2
1
0
3
2
1
0
0
0
1
0
4
3
2
1
0
1
0
0
2
1
0
0
1
0
0
3
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
4
3
2
1
0
1
0
0
5
4
3
2
1
0
0
2
1
0
0
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
1
0
2
1
0
0
6
5
4
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
6
5
4
3
2
1
0
0
4
3
2
1
0
0
4
3
2
1
0
0
0
0
2
1
0
4
3
2
1
0
1
0
1
0
2
1
0
0
3
2
1
0
1
0
0
0
0
0
0
1
0
0
0
8
7
6
5
4
3
2
1
0
2
1
0
0
1
0
1
0
1
0
1
0
2
1
0
0
1
0
0
5
4
3
2
1
0
2
1
0
4
3
2
1
0
2
1
0
0
2
1
0
2
1
0
0
3
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
0
1
0
2
1
0
4
3
2
1
0
4
3
2
1
0
3
2
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
5
4
3
2
1
0
0
4
3
2
1
0
0
0
0
6
5
4
3
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
6
5
4
3
2
1
0
0
0
2
1
0
3
2
1
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
3
2
1
0
2
1
0
2
1
0
1
0
0
0
1
0
2
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
3
2
1
0
1
0
2
1
0
2
1
0
0
0
0
3
2
1
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
2
1
0
0
5
4
3
2
1
0
0
2
1
0
1
0
2
1
0
1
0
1
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
6
5
4
3
2
1
0
1
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
5
4
3
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
4
3
2
1
0
0
0
1
0
2
1
0
0
0
3
2
1
0
1
0
3
2
1
0
1
0
4
3
2
1
0
0
0
2
1
0
1
0
1
0
2
1
0
3
2
1
0
2
1
0
0
6
5
4
3
2
1
0
2
1
0
0
0
0
2
1
0
1
0
4
3
2
1
0
0
3
2
1
0
0
0
2
1
0
0
5
4
3
2
1
0
1
0
0
6
5
4
3
2
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
3
2
1
0
0
0
0
0
1
0
5
4
3
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
3
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
3
2
1
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
4
3
2
1
0
3
2
1
0
0
0
0
2
1
0
3
2
1
0
2
1
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
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
1
0
2
1
0
0
1
0
3
2
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
4
3
2
1
0
0
0
11
10
9
8
7
6
5
4
3
2
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
3
2
1
0
3
2
1
0
0
1
0
3
2
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
3
2
1
0
2
1
0
2
1
0
0
1
0
0
2
1
0
1
0
0
4
3
2
1
0
1
0
1
0
0
0
3
2
1
0
0
1
0
3
2
1
0
1
0
3
2
1
0
2
1
0
0
4
3
2
1
0
0
1
0
11
10
9
8
7
6
5
4
3
2
1
0
0
0
0
0
5
4
3
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
3
2
1
0
4
3
2
1
0
4
3
2
1
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
2
1
0
1
0
0
3
2
1
0
0
0
6
5
4
3
2
1
0
1
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
4
3
2
1
0
0
1
0
0
0
0
3
2
1
0
0
0
5
4
3
2
1
0
2
1
0
2
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
2
1
0
0
1
0
1
0
2
1
0
1
0
1
0
4
3
2
1
0
0
1
0
0
1
0
2
1
0
6
5
4
3
2
1
0
1
0
2
1
0
1
0
0
3
2
1
0
2
1
0
0
1
0
1
0
2
1
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
0
1
0
1
0
1
0
6
5
4
3
2
1
0
1
0
1
0
0
1
0
0
3
2
1
0
0
0
0
3
2
1
0
0
0
1
0
4
3
2
1
0
6
5
4
3
2
1
0
0
0
0
1
0
4
3
2
1
0
1
0
1
0
0
8
7
6
5
4
3
2
1
0
2
1
0
0
0
2
1
0
0
0
0
4
3
2
1
0
0
1
0
1
0
0
3
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
3
2
1
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
4
3
2
1
0
0
0
8
7
6
5
4
3
2
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
3
2
1
0
0
0
0
2
1
0
3
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
4
3
2
1
0
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
3
2
1
0
3
2
1
0
0
1
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
0
4
3
2
1
0
2
1
0
0
0
0
0
1
0
2
1
0
3
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
3
2
1
0
0
3
2
1
0
2
1
0
0
0
0
1
0
3
2
1
0
3
2
1
0
1
0
1
0
1
0
2
1
0
2
1
0
2
1
0
2
1
0
2
1
0
3
2
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
4
3
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
6
5
4
3
2
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
3
2
1
0
0
0
2
1
0
0
6
5
4
3
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
0
0
4
3
2
1
0
3
2
1
0
0
4
3
2
1
0
0
1
0
0
1
0
1
0
0
1
0
4
3
2
1
0
3
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
3
2
1
0
1
0
0
1
0
0
2
1
0
0
1
0
2
1
0
7
6
5
4
3
2
1
0
0
0
4
3
2
1
0
3
2
1
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
3
2
1
0
0
0
0
0
0
1
0
1
0
1
0
3
2
1
0
1
0
3
2
1
0
2
1
0
0
0
3
2
1
0
3
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
5
4
3
2
1
0
0
0
0
1
0
4
3
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
9
8
7
6
5
4
3
2
1
0
0
4
3
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
3
2
1
0
1
0
0
1
0
1
0
4
3
2
1
0
0
0
2
1
0
5
4
3
2
1
0
0
0
0
4
3
2
1
0
5
4
3
2
1
0
0
1
0
0
7
6
5
4
3
2
1
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
2
1
0
2
1
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
0
2
1
0
3
2
1
0
4
3
2
1
0
2
1
0
1
0
0
2
1
0
1
0
0
0
5
4
3
2
1
0
2
1
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
3
2
1
0
2
1
0
3
2
1
0
0
0
0
0
0
3
2
1
0
3
2
1
0
3
2
1
0
1
0
0
1
0
0
3
2
1
0
1
0
2
1
0
0
0
0
6
5
4
3
2
1
0
2
1
0
1
0
2
1
0
0
2
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
3
2
1
0
1
0
1
0
3
2
1
0
0
0
0
2
1
0
7
6
5
4
3
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
5
4
3
2
1
0
0
4
3
2
1
0
2
1
0
1
0
5
4
3
2
1
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
2
1
0
4
3
2
1
0
0
0
1
0
0
0
2
1
0
0
5
4
3
2
1
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
3
2
1
0
1
0
0
1
0
4
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
1
0
5
4
3
2
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
4
3
2
1
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
3
2
1
0
0
1
0
4
3
2
1
0
1
0
0
1
0
0
1
0
0
0
7
6
5
4
3
2
1
0
0
2
1
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
1
0
3
2
1
0
0
0
3
2
1
0
0
3
2
1
0
0
0
0
0
0
0
4
3
2
1
0
1
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
2
1
0
1
0
1
0
1
0
2
1
0
0
5
4
3
2
1
0
10
9
8
7
6
5
4
3
2
1
0
3
2
1
0
0
0
3
2
1
0
0
3
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
3
2
1
0
2
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
3
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
3
2
1
0
1
0
0
0
0
3
2
1
0
3
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
4
3
2
1
0
4
3
2
1
0
0
0
0
1
0
1
0
0
0
3
2
1
0
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
3
2
1
0
1
0
1
0
0
0
1
0
3
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
2
1
0
2
1
0
0
6
5
4
3
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
3
2
1
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
3
2
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
2
1
0
0
0
1
0
4
3
2
1
0
7
6
5
4
3
2
1
0
2
1
0
3
2
1
0
4
3
2
1
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
3
2
1
0
1
0
0
1
0
0
3
2
1
0
0
0
2
1
0
7
6
5
4
3
2
1
0
0
0
0
3
2
1
0
0
0
3
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
3
2
1
0
0
0
0
0
5
4
3
2
1
0
0
0
3
2
1
0
4
3
2
1
0
2
1
0
0
1
0
0
0
1
0
2
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
3
2
1
0
0
3
2
1
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
2
1
0
4
3
2
1
0
0
1
0
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
2
1
0
2
1
0
2
1
0
0
0
3
2
1
0
8
7
6
5
4
3
2
1
0
1
0
2
1
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
5
4
3
2
1
0
0
0
0
2
1
0
0
1
0
0
7
6
5
4
3
2
1
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
5
4
3
2
1
0
3
2
1
0
1
0
0
1
0
3
2
1
0
0
0
1
0
1
0
0
3
2
1
0
5
4
3
2
1
0
1
0
0
0
1
0
1
0
6
5
4
3
2
1
0
2
1
0
0
0
0
3
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
3
2
1
0
1
0
2
1
0
2
1
0
1
0
1
0
1
0
0
0
1
0
5
4
3
2
1
0
1
0
5
4
3
2
1
0
0
1
0
1
0
1
0
2
1
0
2
1
0
0
3
2
1
0
0
0
3
2
1
0
0
0
1
0
0
0
0
1
0
0
3
2
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
4
3
2
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
2
1
0
3
2
1
0
0
3
2
1
0
2
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
2
1
0
0
5
4
3
2
1
0
3
2
1
0
0
0
0
0
3
2
1
0
0
3
2
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
0
1
0
4
3
2
1
0
0
0
0
3
2
1
0
1
0
4
3
2
1
0
0
2
1
0
0
4
3
2
1
0
0
2
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
0
6
5
4
3
2
1
0
4
3
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
4
3
2
1
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
3
2
1
0
3
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
3
2
1
0
0
2
1
0
3
2
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
0
5
4
3
2
1
0
1
0
3
2
1
0
0
1
0
0
2
1
0
0
1
0
2
1
0
5
4
3
2
1
0
0
2
1
0
8
7
6
5
4
3
2
1
0
0
0
0
0
0
2
1
0
4
3
2
1
0
0
1
0
2
1
0
0
1
0
2
1
0
3
2
1
0
0
1
0
0
3
2
1
0
0
0
8
7
6
5
4
3
2
1
0
0
1
0
2
1
0
3
2
1
0
2
1
0
0
0
1
0
0
1
0
0
1
0
4
3
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
6
5
4
3
2
1
0
1
0
1
0
4
3
2
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
4
3
2
1
0
0
0
0
0
2
1
0
0
0
3
2
1
0
1
0
1
0
0
4
3
2
1
0
2
1
0
2
1
0
2
1
0
1
0
1
0
0
0
0
3
2
1
0
0
1
0
0
0
6
5
4
3
2
1
0
3
2
1
0
1
0
2
1
0
6
5
4
3
2
1
0
0
0
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
2
1
0
0
0
0
5
4
3
2
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
1
0
0
4
3
2
1
0
0
4
3
2
1
0
0
1
0
1
0
0
3
2
1
0
4
3
2
1
0
1
0
1
0
0
1
0
1
0
0
0
3
2
1
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
6
5
4
3
2
1
0
4
3
2
1
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
3
2
1
0
0
0
1
0
0
0
3
2
1
0
0
5
4
3
2
1
0
4
3
2
1
0
0
0
1
0
0
0
3
2
1
0
0
1
0
1
0
0
2
1
0
2
1
0
0
0
4
3
2
1
0
0
0
1
0
0
0
0
3
2
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
4
3
2
1
0
0
1
0
2
1
0
3
2
1
0
0
1
0
0
4
3
2
1
0
4
3
2
1
0
1
0
0
0
4
3
2
1
0
0
0
0
1
0
1
0
10148