8
1
2
1
1
1
1
1
1
4
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
6
2
1
1
1
1
1
3
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
2
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
3
1
2
1
1
1
1
1
1
2
1
1
3
2
1
1
4
1
1
12
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
8
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
3
1
7
1
1
1
1
1
1
4
1
1
1
1
1
1
23
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
9
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
3
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
6
3
2
1
1
10
1
1
1
1
1
3
1
1
1
1
1
1
1
2
2
3
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
4
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
3
10
1
1
1
1
1
1
1
1
1
1
1
1
2
1
6
1
3
1
1
1
2
1
2
1
4
4
1
1
1
1
1
1
3
1
1
1
1
1
2
1
3
1
1
1
5
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
5
2
1
1
1
2
1
1
1
1
2
1
1
1
5
1
1
2
1
1
1
2
1
1
1
1
3
8
1
1
1
13
1
1
2
1
1
1
2
1
2
1
1
1
1
3
1
1
1
5
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
10
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
5
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
4
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
8
1
1
1
2
1
1
1
1
1
1
1
14
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
4
3
2
5
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
11
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
3
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
13
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
48
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
3
1
1
9
1
3
1
1
3
14
1
1
1
1
3
1
1
1
1
1
1
2
6
9
1
1
1
2
2
1
1
1
2
1
10
1
1
1
1
4
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
7
1
2
1
7
1
2
11
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
3
1
12
1
1
1
1
1
1
1
4
2
2
1
1
2
2
1
2
1
4
1
1
1
2
1
1
2
1
1
1
10
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
1
1
5
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
11
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
4
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
4
1
1
1
2
1
1
2
1
1
1
1
2
1
1
10
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
6
3
1
1
1
1
1
1
1
4
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
8
1
1
1
3
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
9
3
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
19
1
1
1
1
1
1
1
1
1
12
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
5
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
8
1
1
3
1
1
1
1
1
4
1
1
1
1
1
2
10
3
1
7
1
1
1
1
1
1
1
14
1
1
1
11
1
1
27
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
6
1
1
1
1
1
1
1
1
1
1
1
4
3
1
1
1
1
1
1
1
1
1
12
2
3
2
1
2
1
1
1
2
9
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
12
1
1
1
1
1
1
1
1
1
28
6
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
5
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
3
1
1
3
1
1
1
1
2
1
1
1
1
5
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
5
1
1
1
4
1
2
1
1
1
1
1
4
1
1
1
1
2
2
2
1
1
2
1
3
1
1
2
1
2
1
1
1
1
1
1
1
2
4
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
4
1
4
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
32
1
1
3
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
4
3
1
1
8
1
1
1
4
14
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
3
1
2
2
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
2
4
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
6
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
6
4
2
1
1
1
6
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
18
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
4
1
1
1
1
1
1
3
5
2
1
1
1
1
1
4
3
2
1
1
1
2
1
1
3
2
1
1
2
1
1
9
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
4
1
6
1
1
1
1
1
1
2
1
1
12
15
1
1
3
1
2
1
1
2
2
1
1
1
5
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
6
3
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
3
2
1
2
1
4
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
21
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
3
2
1
1
5
1
7
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
23
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
4
133
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
3
1
1
3
3
1
1
1
7
4
1
1
1
2
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
5
2
1
1
1
1
1
1
55
1
1
1
2
13
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
3
1
1
1
4
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
2
1
1
1
1
6
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
3
1
2
1
1
2
1
1
1
19
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
7
41
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
8
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
4
1
7
1
1
4
1
1
1
1
1
1
1
1
11
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
10
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
2
1
6
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
7
1
1
1
2
15
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
4
2
12
2
1
1
1
1
1
2
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
4
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
4
1
1
1
1
1
1
2
1
1
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
2
1
1
1
2
1
1
3
1
2
1
1
1
2
9
1
2
1
2
5
1
4
1
1
26
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
6
1
1
1
1
1
1
6
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
3
2
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
4
2
1
1
1
16
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
6
3
1
7
1
1
1
1
1
1
9
1
3
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
34
1
1
1
1
1
4
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
6
1
1
12
1
2
1
1
1
1
1
1
2
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
6
3
1
1
1
1
2
2
2
1
1
1
8
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
3
1
2
1
1
1
1
2
5
1
4
1
1
1
1
1
9
1
1
2
1
2
1
4
1
1
1
7
1
1
1
1
5
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
6
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
13
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
2
1
1
13
1
1
1
1
14
1
1
7
2
1
1
11
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
7
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
6
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
4
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
6
3
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
7
1
1
1
1
1
1
5
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
7
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
3
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
4
1
3
2
1
1
2
2
1
1
1
1
1
1
1
3
1
1
2
1
3
2
1
6
1
1
1
1
1
1
116
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
2
3
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
2
1
1
1
1
1
1
1
3
10
1
1
1
9
1
1
1
1
1
1
1
2
1
1
1
25
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
2
1
1
1
4
5
1
1
1
1
7
1
1
1
1
2
1
1
2
1
1
1
1
1
1
16
1
1
1
1
1
1
1
11
1
2
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
8
1
1
2
1
1
1
1
4
3
1
1
1
1
2
1
1
2
1
1
6
1
1
1
1
1
1
2
1
2
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
2
4
2
1
1
2
1
1
1
2
1
1
4
1
1
4
1
1
1
1
1
1
1
1
3
1
1
8
1
1
1
1
1
1
1
2
1
1
1
1
90
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
5
2
1
1
1
1
5
1
1
1
2
1
1
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
2
1
1
1
1
2
1
1
1
1
6
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
7
1
1
1
1
12
4
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
8
1
2
1
1
1
1
2
1
1
3
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
9
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
4
1
3
1
1
1
1
1
1
3
7
1
1
2
1
1
1
1
1
1
1
1
165
2
1
1
3
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
4
1
1
1
1
1
2
2
1
1
15
1
2
1
1
9
1
1
1
1
9
1
1
1
8
5
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
12
1
8
1
1
1
1
1
1
2
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
3
1
1
1
2
2
1
1
1
1
3
1
1
2
1
2
1
1
1
2
3
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
1
2
1
1
1
1
1
1
14
3
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
4
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
4
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
3
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
3
1
3
1
1
5
1
1
4
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
3
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
5
1
1
1
4
1
1
1
4
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
1
4
1
1
1
3
1
1
2
1
1
1
4
1
1
1
1
1
2
1
1
12
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
13
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
7
1
2
1
1
2
1
1
1
1
1
6
1
1
1
1
7
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
9
1
1
1
1
3
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
88
1
1
1
1
3
1
13
1
1
1
7
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
4
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
2
2
1
2
2
27
1
2
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
2
1
1
1
6
1
1
1
1
1
1
1
1
1
1
2
3
2
2
1
1
2
2
1
1
2
1
1
8
1
2
4
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
8
3
1
1
1
2
2
1
1
13
1
1
1
4
2
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
11
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
6
1
1
1
1
2
1
1
1
1
1
4
3
1
2
1
1
7
1
1
1
1
2
1
3
1
2
1
1
1
1
2
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
2
1
1
1
1
1
2
12
2
1
1
2
6
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
2
2
1
1
1
1
1
14
1
1
2
1
1
2
4
1
1
1
1
1
3
1
1
1
1
7
1
2
1
1
1
8
2
4
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
4
1
1
2
1
1
4
1
1
1
1
1
1
2
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
24
1
1
1
1
5
2
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
3
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
6
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
2
1
1
25
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
3
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
4
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
8
1
1
2
2
1
1
1
2
4
1
1
1
1
1
1
3
7
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
3
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
8
3
1
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
1
1
9
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
9
1
2
1
8
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
6
1
1
1
1
3
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
1
1
1
1
4
2
2
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
1
1
1
7
1
4
1
1
1
1
2
4
1
1
1
1
1
3
1
1
1
2
1
1
5
2
1
1
1
1
7
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
2
1
7
3
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
4
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
8
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
6
1
1
1
1
1
1
24
2
2
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
16
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
2
1
5
2
1
1
3
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
3
1
1
1
1
1
1
7
1
2
1
1
1
1
1
1
1
1
2
1
5
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
56
5
1
1
5
2
1
1
1
9
1
1
1
1
1
5
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
1
12
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
3
2
2
1
1
2
1
2
1
13
1
1
1
1
3
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
8
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
3
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
3
2
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
7
1
1
1
1
1
1
3
1
1
1
1
1
1
1
14
1
1
1
1
1
1
1
1
2
1
4
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
4
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
2
3
1
1
1
1
2
4
3
1
1
1
1
1
2
2
1
56
1
2
65