1
11
0
3
1
1
2
7
1
0
1
0
1
0
0
0
0
2
0
0
1
6
1
0
3
0
1
0
1
4
11
0
0
6
0
1
0
1
8
1
3
1
2
0
2
6
0
0
0
0
0
0
0
0
25
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
3
0
0
0
0
0
0
0
5
2
4
1
0
0
13
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
0
1
1
0
2
0
2
0
12
0
2
0
0
0
1
3
0
1
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
1
0
0
3
0
2
0
0
0
2
0
0
0
8
3
0
0
1
10
0
4
0
1
0
1
0
0
0
4
1
0
3
0
1
1
0
2
0
0
0
0
2
19
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
10
0
0
6
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
79
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
3
7
1
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
6
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
26
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
2
4
0
8
1
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
4
0
0
0
0
0
7
0
2
0
0
0
3
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
3
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
1
5
0
1
0
0
2
0
0
1
0
4
0
0
4
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
5
0
8
2
2
0
0
0
3
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
30
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
4
0
0
2
1
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
11
0
0
0
1
0
2
0
4
0
0
1
0
1
0
1
7
2
0
2
0
1
1
4
1
1
0
0
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
23
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
3
3
5
0
2
0
0
0
0
1
2
4
0
0
0
0
2
0
0
9
0
2
0
9
0
0
0
0
0
0
0
0
0
6
0
6
5
3
1
9
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
1
0
1
0
3
2
0
0
0
2
15
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
9
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
2
1
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
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
0
1
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
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
8
0
1
0
0
0
0
0
0
0
2
1
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
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
2
0
0
1
0
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
1
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
0
0
0
3
1
0
15
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
3
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
0
0
0
0
5
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
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
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
1
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
0
0
0
0
0
0
0
0
0
1
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
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
28
1
0
1
0
0
5
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
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
0
0
0
0
0
0
0
0
0
0
0
0
2
4
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
0
0
1
0
0
0
2
0
0
0
0
0
0
1
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
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
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
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
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
0
0
0
0
0
0
0
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
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
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
0
2
1
0
1
0
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
1
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
1
2
4
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
1
0
0
1
0
3
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
1
0
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
1
0
1
0
0
2
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
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
15
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
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
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
1
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
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
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
2
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
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
6
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
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
0
1
0
1
0
2
0
0
0
4
0
0
1
0
0
1
0
2
0
0
0
1
0
0
6
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
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
1
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
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
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
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
1
0
0
0
0
0
1
0
0
0
3
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
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
5
0
0
1
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
6
0
0
0
1
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
6
0
0
1
0
0
0
2
0
0
0
0
0
1
5
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
2
0
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
1
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
4
0
1
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
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
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
1
2
0
0
2
0
4
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
1
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
1
0
0
0
0
0
3
0
0
0
1
0
2
8
2
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
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
3
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
0
0
0
0
0
1
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
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
10
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
1
0
5
0
0
1
0
0
0
1
0
7
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
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
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
5
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
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
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
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
3
0
0
0
0
4
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
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
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
0
0
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
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
1
0
0
2
0
0
0
0
4
0
5
0
0
0
0
0
0
0
1
0
0
