0
0
0
0
10
8
6
0
0
0
5
0
0
0
11
0
0
0
10
0
0
0
3
12
0
0
9
10
6
0
5
3
0
0
0
0
4
0
9
0
0
1
8
0
8
11
12
0
0
12
0
0
8
9
0
2
0
4
0
0
6
5
12
10
0
0
0
0
0
0
0
0
9
0
7
0
5
0
0
0
0
11
0
0
0
0
0
0
0
5
0
7
5
1
3
0
0
0
0
0
7
0
0
0
0
0
0
7
0
0
0
0
0
0
10
0
0
0
6
10
0
7
9
0
0
0
0
0
0
0
3
11
6
0
0
0
0
0
0
6
8
0
6
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
4
0
0
0
11
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
4
0
0
11
7
0
0
0
10
7
0
0
0
0
0
4
0
0
0
0
7
0
3
0
0
10
0
6
0
9
0
4
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
3
9
3
0
0
12
12
0
9
8
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
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
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
0
1
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
1
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
1
0
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
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
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
1
1
0
1
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
1
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
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
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
1
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
1
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
0
0
0
0
1
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
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
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
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
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
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
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
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
1
0
1
0
1
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
1
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
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
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
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
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
1
0
0
0
0
0
0
1
1
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
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
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
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
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
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
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
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
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
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
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
0
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
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
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
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
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
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
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
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
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
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
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
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
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
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
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
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
1
0
0
1
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
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
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
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
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
0
1
0
0
1
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
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
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
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
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
1
1
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
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
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
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
0
1
0
1
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
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
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
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
1
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
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
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
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
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
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
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
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
1
1
0
0
0
0
1
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
0
1
0
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
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
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
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
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
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
1
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
1
1
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
0
0
0
1
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
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
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
1
1
0
1
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
0
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
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
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
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
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
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
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
0
0
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
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
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
1
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
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
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
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
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
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
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
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
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
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
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
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
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
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
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
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
1
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
1
0
0
0
1
1
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
1
0
0
1
1
1
0
0
1
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
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
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
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
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
1
0
1
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
0
0
0
1
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
1
1
1
0
1
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
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
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
1
0
0
1
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
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
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
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
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
1
1
1
1
1
0
0
0
0
1
0
0
1
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
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
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
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
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
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
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
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
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
1
1
1
1
0
1
0
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
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
0
0
1
1
0
0
1
1
0
0
0
0
1
0
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
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
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
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
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
1
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
1
0
1
0
1
0
0
0
0
1
0
0
1
1
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
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
0
0
1
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
1
1
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
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
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
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
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
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
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
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
0
1
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
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
1
0
1
0
1
1
0
0
1
1
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
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
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
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
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
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
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
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
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
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
0
0
1
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
1
1
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
1
1
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
0
0
1
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
1
1
0
1
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
1
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
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
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
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
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
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
1
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
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
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
0
1
1
1
0
1
0
1
0
0
0
0
0
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
0
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
1
1
0
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
1
0
1
0
0
0
0
0
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
1
1
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
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
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
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
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
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
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
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
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
1
0
1
1
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
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
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
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
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
1
0
1
0
1
0
1
0
0
0
0
0
1
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
1
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
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
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
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
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
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
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
1
0
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
1
0
1
0
0
0
0
1
1
0
1
1
1
1
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
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
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
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
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
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
1
0
0
0
1
0
1
1
1
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
1
0
0
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
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
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
1
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
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
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
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
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
1
0
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
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
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
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
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
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
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
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
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
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
0
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
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
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
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
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
1
0
1
0
0
0
1
0
1
1
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
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
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
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
1
0
0
0
1
1
0
1
1
1
0
1
1
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
0
0
1
0
0
0
0
0
0
1
1
0
1
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
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
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
1
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
0
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
0
0
1
1
0
0
0
1
1
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
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
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
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
1
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
1
1
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
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
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
0
1
0
1
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
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
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
1
1
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
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
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
1
0
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
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
0
0
1
0
0
0
0
1
0
1
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
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
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
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
0
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
1
0
1
0
1
0
0
0
0
0
1
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
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
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
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
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
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
0
0
0
0
1
1
1
0
1
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
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
0
0
0
0
0
0
1
0
1
1
1
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
1
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
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
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
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
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
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
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
1
0
0
1
1
1
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
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
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
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
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
1
1
0
0
0
1
1
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
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
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
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
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
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
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
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
1
1
1
1
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
0
1
0
0
1
0
1
0
0
0
0
1
1
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
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
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
1
0
0
1
0
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
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
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
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
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
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
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
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
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
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
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
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
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
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
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
1
1
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
1
1
1
1
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
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
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
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
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
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
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
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
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
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
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
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
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
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
0
0
0
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
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
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
0
0
0
0
0
0
1
1
1
0
0
1
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
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
0
1
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
1
0
0
0
1
1
1
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
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
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
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
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
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
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
1
1
1
1
0
0
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
1
0
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
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
0
0
1
0
0
0
0
0
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
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
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
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
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
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
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
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
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
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
1
0
1
0
1
0
1
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
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
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
1
1
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
1
0
0
1
0
0
1
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
1
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
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
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
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
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
1
0
0
0
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
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
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
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
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
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
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
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
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
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
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
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
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
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
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
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
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
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
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
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
1
0
0
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
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
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
0
1
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
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
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
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
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
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
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
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
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
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
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
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
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
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
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
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
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
1
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
1
0
0
0
0
0
0
1
1
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
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
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
1
0
0
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
1
1
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
1
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
1
0
0
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
0
1
0
0
0
0
0
0
0
1
1
1
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
0
1
0
1
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
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
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
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
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
1
0
0
1
0
0
0
1
1
1
0
1
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
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
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
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
0
1
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
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
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
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
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
1
0
0
1
1
0
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
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
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
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
1
0
0
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
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
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
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
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
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
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
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
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
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
1
1
0
0
1
0
1
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
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
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
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
1
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
1
1
0
1
0
1
1
1
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
1
1
0
0
1
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
1
0
0
1
0
0
0
1
0
1
1
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
0
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
1
0
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
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
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
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
1
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
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
1
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
1
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
1
0
0
0
1
1
0
1
1
0
0
0
1
1
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
1
1
1
0
0
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
0
0
0
0
0
0
0
0
1
0
1
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
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
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
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
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
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
1
1
0
0
1
0
0
1
0
1
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
1
0
1
0
1
0
1
1
0
1
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
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
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
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
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
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
1
0
0
0
0
1
1
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
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
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
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
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
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
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
1
1
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
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
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
0
0
0
1
1
1
1
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
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
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
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
0
1
1
0
0
0
0
0
1
1
1
1
1
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
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
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
0
0
0
0
0
1
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
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
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
0
0
0
1
0
0
1
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
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
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
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
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
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
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
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
0
0
1
0
0
1
1
1
0
1
0
1
0
1
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
1
1
0
0
0
0
1
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
0
1
1
1
0
0
0
0
0
0
0
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
1
0
0
0
0
1
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
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
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
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
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
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
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
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
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
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
1
0
1
0
1
1
1
0
0
0
1
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
1
0
0
1
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
1
1
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
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
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
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
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
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
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
0
1
0
1
0
0
1
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
0
1
0
0
1
0
0
1
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
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
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
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
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
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
0
1
1
0
0
0
1
1
1
0
1
1
1
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
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
1
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
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
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
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
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
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
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
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
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
1
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
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
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
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
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
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
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
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
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
1
0
1
1
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
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
1
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
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
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
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
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
1
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
1
0
0
0
1
1
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
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
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
1
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
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
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
1
0
0
1
0
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
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
1
1
0
0
0
1
0
1
0
1
0
0
1
0
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
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
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
0
1
0
1
0
1
0
1
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
1
0
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
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
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
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
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
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
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
1
1
1
0
0
0
0
1
0
0
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
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
1
1
1
0
1
1
1
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
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
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
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
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
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
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
1
1
1
1
1
1
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
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
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
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
0
1
0
1
0
0
0
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
1
0
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
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
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
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
0
0
1
0
1
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
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
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
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
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
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
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
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
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
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
1
1
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
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
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
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
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
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
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
1
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
0
0
0
0
1
0
0
0
1
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
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
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
1
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
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
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
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
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
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
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
1
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
0
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
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
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
1
1
1
1
0
0
0
0
0
0
1
0
1
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
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
1
1
0
0
0
0
0
0
0
0
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
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
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
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
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
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
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
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
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
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
1
0
1
1
0
0
0
0
1
0
1
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
1
0
1
1
0
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
1
0
1
1
0
0
0
1
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
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
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
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
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
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
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
1
1
0
0
0
1
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
1
1
0
1
0
0
0
1
1
1
1
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
1
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
1
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
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
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
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
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
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
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
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
1
0
1
1
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
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
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
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
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
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
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
1
1
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
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
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
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
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
1
0
1
0
0
0
0
1
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
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
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
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
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
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
1
1
0
0
0
1
0
1
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
1
0
1
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
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
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
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
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
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
1
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
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
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
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
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
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
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
1
1
0
1
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
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
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
1
1
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
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
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
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
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
0
1
1
1
0
0
1
0
0
1
0
1
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
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
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
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
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
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
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
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
1
1
0
0
0
1
0
0
1
0
0
1
0
1
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
1
1
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
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
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
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
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
1
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
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
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
0
1
0
0
1
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
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
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
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
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
1
0
1
1
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
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
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
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
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
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
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
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
0
0
1
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
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
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
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
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
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
1
0
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
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
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
1
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
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
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
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
1
0
0
0
0
1
1
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
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
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
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
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
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
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
1
1
0
0
0
1
1
0
1
1
1
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
0
1
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
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
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
1
0
0
0
0
0
0
0
1
0
1
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
0
0
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
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
1
0
0
0
1
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
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
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
1
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
1
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
1
0
0
0
0
1
1
1
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
1
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
0
0
1
1
0
0
0
0
1
0
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
0
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
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
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
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
0
0
0
0
1
1
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
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
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
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
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
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
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
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
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
1
1
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
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
1
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
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
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
1
0
0
1
0
1
0
0
1
0
1
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
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
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
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
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
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
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
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
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
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
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
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
0
1
0
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
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
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
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
0
1
1
1
0
1
0
0
0
1
0
1
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
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
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
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
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
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
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
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
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
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
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
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
1
1
1
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
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
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
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
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
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
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
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
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
0
1
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
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
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
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
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
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
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
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
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
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
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
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
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
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
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
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
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
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
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
1
0
1
1
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
1
0
1
0
1
0
0
0
0
0
1
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
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
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
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
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
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
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
0
1
0
1
0
1
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
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
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
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
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
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
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
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
0
1
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
1
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
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
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
1
1
0
1
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
0
1
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
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
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
1
0
0
0
1
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
1
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
1
1
0
0
0
1
0
0
1
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
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
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
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
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
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
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
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
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
1
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
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
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
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
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
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
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
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
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
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
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
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
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
1
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
1
0
1
0
1
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
0
0
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
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
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
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
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
0
1
0
1
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
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
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
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
0
1
0
0
1
1
1
0
1
0
0
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
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
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
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
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
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
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
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
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
1
1
0
1
0
1
1
1
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
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
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
1
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
1
0
0
0
0
0
1
1
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
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
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
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
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
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
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
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
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
0
1
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
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
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
1
0
0
0
0
0
1
0
1
0
1
0
0
0
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
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
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
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
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
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
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
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
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
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
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
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
1
0
1
0
0
1
0
0
0
0
1
1
1
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
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
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
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
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
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
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
1
0
0
1
0
0
1
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
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
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
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
0
1
0
1
0
0
0
0
1
0
0
0
1
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
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
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
0
1
0
0
1
1
0
1
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
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
1
0
1
0
1
1
0
1
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
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
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
0
0
0
1
0
1
1
1
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
1
1
0
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
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
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
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
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
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
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
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
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
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
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
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
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
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
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
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
0
1
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
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
1
1
0
0
0
0
1
1
0
0
1
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
1
0
1
1
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
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
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
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
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
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
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
1
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
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
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
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
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
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
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
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
1
0
0
1
0
0
1
1
0
1
0
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
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
0
0
1
0
0
0
0
1
0
1
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
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
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
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
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
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
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
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
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
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
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
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
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
1
0
1
0
1
0
0
1
0
0
0
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
0
0
0
0
0
0
1
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
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
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
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
0
0
1
1
1
0
1
0
0
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
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
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
1
1
1
0
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
1
0
0
0
0
0
1
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
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
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
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
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
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
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
0
0
0
0
0
0
1
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
0
0
0
0
1
1
0
0
1
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
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
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
1
0
1
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
1
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
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
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
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
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
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
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
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
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
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
0
1
1
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
1
1
1
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
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
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
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
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
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
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
1
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
1
0
0
1
0
0
0
1
0
1
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
1
1
0
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
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
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
1
0
1
1
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
0
0
1
0
0
0
0
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
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
1
1
0
0
0
0
0
1
1
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
1
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
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
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
0
0
0
0
0
1
0
0
0
1
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
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
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
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
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
0
1
1
1
0
1
1
1
0
0
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
1
0
0
1
1
1
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
1
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
0
1
0
0
0
0
0
1
0
0
0
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
1
0
0
0
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
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
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
1
1
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
1
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
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
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
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
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
1
0
0
1
0
0
1
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
0
1
0
0
1
1
0
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
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
1
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
1
0
0
1
0
0
1
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
1
1
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
0
1
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
0
1
0
0
1
1
1
1
1
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
0
0
0
0
1
0
0
0
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
1
1
0
1
1
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
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
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
0
0
0
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
1
0
1
0
0
1
0
1
0
1
1
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
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
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
1
1
0
1
1
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
0
0
1
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
0
0
1
0
0
0
1
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
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
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
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
1
1
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
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
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
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
0
1
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
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
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
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
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
1
0
0
0
1
1
0
0
0
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
1
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
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
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
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
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
1
1
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
1
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
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
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
0
1
0
0
0
1
1
0
0
1
1
0
1
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
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
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
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
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
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
0
1
0
1
1
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
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
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
1
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
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
1
0
1
0
1
1
0
1
0
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
1
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
1
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
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
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
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
0
1
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
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
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
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
1
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
1
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
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
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
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
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
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
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
0
0
0
1
0
0
0
0
1
0
1
1
1
1
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
1
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
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
0
1
0
0
1
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
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
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
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
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
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
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
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
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
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
1
0
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
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
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
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
1
0
0
0
1
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
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
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
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
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
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
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
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
1
0
0
1
0
0
0
1
0
1
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
1
0
0
1
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
1
0
1
1
1
0
0
0
1
0
0
0
0
1
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
1
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
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
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
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
1
0
0
1
0
0
1
1
0
1
1
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
1
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
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
1
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
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
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
1
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
0
0
1
1
1
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
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
0
0
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
0
0
1
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
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
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
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
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
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
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
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
0
1
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
0
1
0
0
1
1
1
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
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
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
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
1
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
1
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
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
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
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
1
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
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
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
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
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
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
1
0
1
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
1
0
0
0
0
0
0
1
0
0
1
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
1
1
1
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
0
0
0
1
1
0
0
1
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
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
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
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
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
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
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
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
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
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
1
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
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
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
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
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
1
1
1
1
1
0
0
1
0
1
0
1
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
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
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
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
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
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
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
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
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
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
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
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
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
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
1
1
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
0
1
0
1
0
0
1
1
1
0
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
1
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
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
1
0
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
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
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
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
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
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
0
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
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
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
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
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
1
0
1
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
1
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
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
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
1
0
0
1
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
1
0
0
0
0
0
1
0
1
1
1
1
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
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
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
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
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
0
1
1
0
0
0
1
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
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
1
1
1
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
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
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
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
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
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
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
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
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
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
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
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
1
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
1
0
0
0
0
1
1
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
1
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
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
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
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
1
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
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
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
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
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
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
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
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
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
1
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
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
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
0
0
0
0
0
0
1
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
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
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
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
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
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
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
0
0
0
1
0
1
1
0
1
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
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
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
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
0
0
0
1
1
0
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
1
1
1
0
0
0
0
0
0
0
0
1
0
0
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
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
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
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
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
1
1
1
1
0
1
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
1
0
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
1
1
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
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
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
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
1
1
0
0
1
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
1
1
0
0
1
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
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
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
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
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
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
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
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
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
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
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
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
0
0
0
1
0
0
0
1
0
1
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
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
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
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
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
1
0
0
0
1
0
0
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
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
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
0
1
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
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
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
1
0
0
0
0
0
0
0
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
0
0
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
1
0
1
0
0
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
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
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
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
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
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
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
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
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
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
0
0
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
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
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
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
1
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
1
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
0
1
0
0
0
0
0
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
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
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
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
1
0
1
0
0
1
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
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
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
1
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
0
0
1
1
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
1
0
0
0
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
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
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
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
1
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
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
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
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
0
1
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
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
