1
3
2
1
1
6238
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
2
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
2
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
13
1
2
1
3
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
2
1
1
3
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
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
6
1
1
1
7
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
2
2
1
2
1
1
3
1
1
1
1
4
2
1
4
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
3
2
1
1
1
1
1
1
1
1
110
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
2
5
1
1
3
3
3
1
1
1
1
3
1
2
1
2
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
3
15
1
4
1
1
1
1
2
1
4
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
4
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
3
1
2
1
2
2
1
1
1
1
1
1
1
1
1
3
3
1
3
1
1
1
1
1
3
1
1
4
2
1
2
1
3
1
1
1
1
2
2
4
1
1
1
1
3
1
2
1
1
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
2
1
1
1
1
1
1
1
5
2
3
1
4
2
1
1
1
8
1
1
2
1
1
1
4
2
2
1
1
1
1
1
1
1
1
3
1
1
3
1
1
1
2
1
1
1
5
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
3
1
2
1
2
1
1
1
1
1
1
1
1
1
1
12
1
1
1
3
2
1
1
5
1
1
1
1
1
1
1
1
1
2
1
1
1
1
4
1
1
1
8
1
1
1
1
1
1
1
1
2
2
6
1
1
4
1
1
1
1
1
1
2
1
1
1
6
1
1
1
1
1
1
10
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
2
1
3
1
2
2
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
4
4
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
9
3
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
19
1
1
1
1
1
1
1
20
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
10
1
1
1
1
1
1
1
1
1
1
2
1
2
1
6
2
7
1
1
4
1
1
3
2
1
2
8
1
1
1
1
1
2
1
1
4
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
25
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
4
1
1
1
1
1
6
1
1
1
1
1
1
2
2
1
5
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
3
8
2
1
2
1
22
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
5
1
1
1
1
1
1
3
1
1
1
1
1
1
5
1
2
2
1
3
8
1
1
5
1
1
1
1
1
1
3
1
1
3
1
1
1
1
2
4
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
2
4
9
1
1
1
1
1
1
1
1
5
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
5
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
3
6
9
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
9
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
4
4
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
3
1
2
1
7
1
4
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
1
1
1
2
1
1
1
1
9
2
1
1
3
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
1
1
1
1
1
1
1
2
1
1
3
1
1
1
9
1
1
1
1
1
1
10
1
5
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
26
1
1
1
2
1
1
1
1
17
2
1
1
1
1
1
1
2
1
1
1
1
19
1
2
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
4
2
1
1
1
1
1
3
3
1
3
1
5
1
1
1
1
4
1
1
2
1
3
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
10
1
2
6
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
7
2
1
1
1
1
1
10
1
1
1
4
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
2
1
3
2
1
2
1
1
7
10
1
1
2
1
1
1
1
1
5
1
1
4
1
1
1
1
1
2
3
3
4
1
1
4
1
3
1
1
1
8
1
1
1
1
2
3
1
1
9
1
1
2
1
1
1
2
1
1
1
3
1
1
2
1
1
1
1
1
1
3
1
1
2
1
5
3
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
7
1
1
1
1
1
1
2
1
1
1
1
1
2
6
1
1
3
2
1
1
1
2
3
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
2
1
1
1
1
1
3
1
1
1
12
6
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
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
7
2
3
2
1
1
1
1
2
1
1
1
1
1
2
1
4
1
1
1
1
1
2
1
1
1
1
1
1
1
1
8
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
1
1
1
1
2
1
1
1
5
4
1
1
1
1
1
7
1
1
1
1
1
2
1
3
2
1
1
5
1
10
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
4
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
3
1
1
2
1
1
1
15
1
5
1
1
1
2
1
1
2
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
3
1
3
2
2
1
1
1
1
1
9
1
1
1
1
1
1
1
7
1
3
2
1
2
1
1
5
1
1
5
1
1
1
1
2
1
1
1
1
7
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
5
12
1
2
1
1
1
1
1
2
41
1
1
3
1
1
2
1
1
1
1
1
19
2
5
1
1
1
6
1
1
1
1
3
1
1
1
1
1
4
1
1
1
4
1
1
1
2
1
1
16
1
1
1
1
2
1
3
3
1
1
1
1
1
1
1
2
1
1
1
1
2
1
3
1
1
1
1
1
1
3
3
1
2
1
1
1
2
2
1
1
10
1
1
1
1
2
1
1
1
1
1
8
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
4
1
1
1
3
1
1
7
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
11
1
1
11
3
2
1
1
1
4
1
1
1
1
11
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
2
2
1
10
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
3
1
1
9
1
1
4
1
1
1
1
1
1
2
1
1
1
1
2
3
2
25
1
2
8
1
2
1
1
1
1
19
1
1
1
1
1
1
3
1
2
1
1
2
1
1
1
4
1
1
5
3
1
4
1
2
1
1
1
1
1
1
27
1
1
2
1
1
1
1
1
1
3
1
7
1
2
3
1
1
1
1
1
1
2
4
1
3
1
3
2
3
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
4
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
3
1
2
1
1
1
1
1
4
1
1
3
1
1
1
5
1
2
1
1
1
3
4
1
2
2
1
1
1
1
2
1
1
1
1
3
1
3
1
1
1
2
3
1
1
1
7
1
1
15
1
1
1
3
2
1
1
1
1
2
1
2
1
2
1
4
1
1
1
1
1
1
1
1
1
1
2
4
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
3
1
4
1
1
1
2
1
1
1
2
2
3
1
1
1
2
1
1
3
1
3
1
1
1
1
1
1
3
2
8
1
14
1
1
1
1
1
1
8
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
5
1
1
1
1
1
1
2
7
2
1
1
5
1
2
1
1
7
1
3
2
1
1
1
1
6
1
1
1
1
1
1
2
2
3
1
1
2
1
1
1
1
1
4
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
6
5
1
1
1
1
12
1
1
7
8
1
8
11
1
10
1
1
23
1
1
3
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
53
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
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
3
1
1
1
1
1
1
2
10
1
1
1
1
1
1
2
2
1
1
1
3
1
2
1
1
2
1
1
1
2
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
3
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
4
1
1
1
1
2
1
13
1
1
1
1
1
1
2
1
1
4
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
3
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
3
1
3
1
1
1
2
28
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
8
1
2
1
2
1
3
1
1
1
1
10
1
1
1
1
1
11
1
1
3
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
2
1
9
1
1
2
1
1
1
2
1
2
1
5
1
2
2
5
3
1
2
2
1
4
1
1
2
3
1
1
1
1
2
2
1
1
2
1
3
1
2
1
8
2
1
1
1
1
18
1
5
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
4
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
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
4
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
15
1
1
1
1
1
1
1
9
1
1
1
1
3
1
1
1
1
1
2
1
1
1
9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
3
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
7
1
2
1
1
1
1
1
1
1
4
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
3
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
2
2
1
1
1
3
1
3
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
3
3
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
4
1
1
4
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
2
1
1
1
3
3
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
14
1
1
14
2
1
1
1
1
1
1
1
2
2
1
1
1
3
1
1
1
2
2
1
3
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
3
1
2
1
3
3
2
2
1
1
1
1
1
4
3
2
2
1
3
2
1
1
1
1
2
1
3
1
1
1
1
2
1
4
7
1
1
1
1
1
1
4
1
1
1
3
16
1
1
5
3
1
1
1
4
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
3
1
2
1
1
1
3
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
2
1
1
2
7
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
5
1
1
3
3
1
1
1
1
1
2
1
2
1
1
1
1
6
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
10
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
5
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
2
1
1
2
1
1
1
1
1
6
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
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
1
1
1
1
1
1
1
2
1
1
6
1
1
1
2
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
17
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
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
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
2
1
1
1
1
1
1
5
1
2
5
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
6
1
1
1
4
2
1
1
1
1
1
1
2
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
4
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
20
1
1
1
1
1
1
1
2
1
1
1
1
3
1
8
1
2
1
7
1
1
2
1
1
1
1
2
7
1
1
1
1
1
1
1
9
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
1
4
1
1
1
1
1
3
1
2
1
1
2
1
1
1
7
3
1
1
1
15
1
4
1
1
1
1
1
1
1
4
1
3
2
1
13
1
1
1
1
1
1
1
1
8
1
1
2
1
1
1
1
3
2
1
1
1
1
1
16
1
1
2
3
1
1
1
1
1
1
1
5
1
4
1
1
1
1
2
1
1
1
1
2
3
4
1
1
1
1
2
1
1
1
4
1
1
1
2
25
1
1
1
1
1
3
1
1
1
1
4
1
2
1
1
2
2
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
5
2
1
2
1
1
1
1
1
1
15
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
3
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
3
1
1
1
1
1
1
2
1
1
4
1
8
2
1
1
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
6
1
5
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
12
1
1
1
1
1
1
1
1
1
3
1
2
1
2
8
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
3
1
1
1
1
1
5
9
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
1
1
1
1
1
4
2
1
1
1
4
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
4
1
1
1
4
1
6
3
1
1
6
1
1
1
1
2
2
3
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
23
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
3
1
2
1
5
1
1
5
2
3
1
1
1
1
4
1
1
1
3
1
2
6
1
1
1
3
1
1
1
1
1
1
1
1
15
1
1
1
2
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
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
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
4
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
6
7
1
1
2
1
5
1
1
2
1
1
1
1
1
3
1
1
1
1
2
1
1
3
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
6
2
1
1
1
1
5
1
1
1
1
1
1
1
7
1
1
1
1
2
8
1
1
1
1
1
1
1
1
5
2
1
1
1
1
1
4
1
1
2
1
1
1
1
1
1
5
1
6
1
1
1
1
17
1
1
1
1
1
1
1
1
1
1
3
1
3
2
1
4
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
3
1
1
1
1
2
1
1
2
8
1
1
1
1
1
1
2
2
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
3
1
1
1
1
1
1
1
1
2
1
6
1
1
1
1
1
1
1
1
2
1
1
1
14
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
4
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
5
2
2
1
2
1
1
6
1
1
5
1
1
1
1
1
1
1
1
1
1
1
7
1
4
1
1
5
1
3
1
1
1
1
1
1
6
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
10
1
1
9
3
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
3
1
3
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
2
4
1
1
3
1
2
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
7
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
12
1
1
1
2
1
1
1
1
1
3
1
1
1
3
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
6
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
4
1
1
1
1
1
2
1
1
1
1
1
1
2
15
2
1
1
1
3
7
1
3
1
6
1
1
1
1
1
1
1
1
2
1
36
1
1
2
11
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
3
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
13
1
1
1
1
1
1
1
1
1
1
4
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
2
1
1
1
1
2
1
3
2
8
1
1
1
3
4
1
1
18
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
4
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
5
1
1
2
1
2
3
1
1
1
1
1
1
2
1
1
1
1
3
1
5
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
4
2
2
1
2
3
1
5
1
1
1
2
1
1
1
2
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
3
8
2
1
2
1
2
1
1
1
1
1
1
1
2
1
4
1
3
1
1
1
1
1
1
2
1
1
2
11
1
1
4
1
2
1
1
1
2
1
1
1
1
1
2
6
3
1
1
3
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
9
2
1
2
1
3
1
8
3
1
1
1
1
3
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
6
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
37
1
7
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
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
2
1
1
1
1
1
13
1
1
1
1
1
1
1
1
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
1
1
1
1
2
1
1
3
1
1
1
1
1
2
1
5
1
1
1
1
1
1
1
12
2
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
5
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
6
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
2
1
1
6
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
4
2
1
1
1
1
5
1
27
1
1
1
2
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
3
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
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
3
1
1
1
2
1
2
1
1
1
1
1
1
1
1
11
4
1
1
5
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
5
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
6
1
1
2
1
1
1
1
2
1
2
4
1
2
1
3
2
1
1
1
1
2
1
2
1
1
3
1
1
15
1
4
3
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
12
1
1
1
3
1
7
1
1
1
1
1
1
1
1
1
2
2
4
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
5
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
3
1
21
1
11
2
1
1
1
1
1
1
4
5
1
1
1
1
1
1
1
4
1
1
3
1
2
1
1
1
12
1
3
1
2
1
1
2
1
1
1
4
3
4
1
1
1
1
1
1
1
1
1
1
1
3
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
4
1
2
3
1
1
2
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
1
1
2
1
1
1
2
1
2
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
1
1
1
1
1
2
1
1
1
1
2
1
1
4
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
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
10
1
1
1
1
2
1
1
1
1
1
1
1
1
12
41
2
1
2
1
1
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
3
10
1
1
1
1
1
1
1
1
1
12
1
2
2
3
1
1
1
1
1
2
1
1
1
3
2
2
1
1
1
1
5
1
1
1
3
1
2
10
1
11
1
1
1
1
1
1
1
1
1
1
3
1
1
567
1
13
1
1
1
3
13
2
12
1
1
1
1
4
1
2
2
2
1
4
1
1
10
1
1
2
2
7
1
1
1
1
1
1
1
1
1
1
1
1
2
1
8
1
1
2
1
5
2
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
4
3
1
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
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
3
1
1
1
3
3
1
1
3
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
3
1
1
1
1
10
1
1
2
2
5
32
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
3
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
1
1
4
1
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
2
1
1
1
3
1
1
1
1
2
1
1
1
1
3
2
1
2
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
3
2
1
1
1
1
2
1
1
1
1
4
1
1
1
1
2
1
1
1
4
2
3
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
5
1
1
1
1
2
1
1
18
1
2
1
3
1
1
1
2
1
1
1
1
2
7
1
1
1
10
2
2
1
1
1
1
1
1
1
2
1
1
1
3
1
3
1
1
1
16
1
24
5
1
1
7
8
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
4
23
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
7
1
2
1
3
1
1
1
1
18
8
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
6
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
11
1
1
1
1
2
1
3
1
1
1
1
1
7
1
12
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
4
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
3
2
4
1
1
1
10
1
1
1
1
1
1
2
1
1
1
1
1
1
3
10
1
1
1
2
1
4
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
3
1
3
1
15
1
1
1
5
1
1
1
1
1
1
1
1
1
3
2
4
1
1
1
1
83
1
1
11
1
1
1
1
1
2
12
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
4
1
3
1
1
1
2
1
11
3
1
1
1
1
1
6
1
1
1
1
1
1
1
1
2
1
1
1
1
6
1
1
1
1
1
1
1
6
1
4
1
1
1
1
7
1
2
1
1
1
2
2
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
30
4
1
1
1
1
1
1
1
1
1
1
9
1
1
1
1
2
1
3
1
3
1
1
1
1
1
1
1
1
1
2
3
2
1
1
33
1
1
1
1
1
1
1
3
4
1
1
1
1
4
1
1
3
1
1
25
1
6
1
1
1
1
3
1
2
1
1
1
1
1
1
4
2
1
1
3
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
3
1
2
2
1
4
1
3
1
1
16
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
12
2
1
1
3
1
1
5
1
1
4
1
6
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
7
1
2
1
2
8
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
6
8
2
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
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
1
1
1
12
2
2
1
1
7
5
1
4
1
2
1
16
1
2
2
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
12
1
1
1
2
1
1
1
1
2
2
2
2
1
1
4
1
2
1
1
3
1
1
1
1
1
1
3
1
2
1
1
1
3
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9
5
3
2
1
1
1
4
1
1
1
1
1
1
1
1
3
1
1
1
1
1
5
1
1
2
1
1
1
1
2
1
2
1
4
1
1
1
1
1
1
1
16
1
1
1
1
1
1
1
2
1
8
1
1
1
1
3
1
1
1
3
1
1
1
3
1
1
1
1
7
3
2
1
1
1
1
1
1
1
1
1
1
15
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
4
1
1
20
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
6
11
1
5
2
11
1
1
1
2
1
1
1
1
1
1
2
1
1
1
5
3
4
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
9
2
2
1
1
3
2
1
1
1
1
1
2
1
1
1
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
5
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
2
1
1
3
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
2
1
2
4
1
1
2
1
1
1
1
1
1
1
1
3
4
1
1
1
9
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
76
3
1
3
1
2
1
2
1
2
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
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
6
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
5
1
1
3
1
1
1
2
1
2
1
1
10
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
4
1
1
2
1
1
1
2
1
1
1
1
1
18
1
1
1
1
24
1
2
10
3
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
8
3
1
6
1
1
1
1
1
2
15
1
1
9
1
1
1
1
2
1
1
1
1
13
1
1
1
3
1
1
1
5
1
1
2
8
11
1
1
1
15
1
2
1
8
10
1
1
1
2
1
4
1
1
1
2
1
1
10
1
1
3
1
1
1
1
6
1
1
3
3
1
1
4
1
1
1
1
1
3
5
1
2
1
1
2
1
3
1
6
1
2
1
3
1
2
1
1
1
1
2
2
2
1
1
11
5
1
1
1
1
1
8
1
1
28
1
1
1
2
1
1
1
1
1
1
3
1
23
1
6
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
12
1
1
1
6
1
1
1
1
1
1
3
2
2
1
1
1
1
1
2
2
1
4
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
4
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
5
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
1
3
1
1
1
1
1
1
1
1
6
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
3
1
1
2
1
1
2
1
2
1
6
2
1
1
1
3
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
2
1
1
1
1
1
4
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
11
1
8
1
1
6
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
1
2
1
1
1
1
1
1
2
3
3
1
1
2
2
3
4
1
1
5
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
4
3
3
1
1
2
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
3
1
1
2
1
1
1
2
1
1
1
6
1
1
1
5
1
1
1
1
4
1
1
1
1
1
1
1
1
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
4
4
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
5
2
3
1
1
1
1
3
1
1
1
1
1
9
1
2
2
1
1
2
4
1
2
1
1
2
1
1
1
1
6
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
6
1
1
3
1
2
1
7
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
6
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
2
1
1
1
1
1
1
1
2
1
34
9
1
1
1
2
1
1
1
4
1
1
2
1
1
3
1
1
2
1
1
1
2
1
1
1
2
9
1
1
6
1
5
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
2
1
1
3
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
3
1
1
1
1
1
3
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
20
12
1
1
1
1
1
6
1
1
1
2
1
1
1
1
1
1
1
1
1
13
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
5
1
1
1
7
1
3
1
1
1
1
1
1
5
3
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
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
3
1
3
1
1
1
1
1
53
5
1
1
1
1
1
1
3
1
1
1
1
3
5
1
2
1
1
3
3
2
1
1
1
5
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
3
1
2
1
1
1
1
1
3
1
2
1
1
3
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
2
1
1
1
1
3
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
3
1
1
3
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
89
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
11
7
1
1
1
1
1
1
1
2
4
1
1
1
2
35
1
2
1
2
2
1
1
1
6
1
1
1
5
1
2
1
1
1
1
32
2
1
1
1
1
1
4
1
1
1
1
1
1
1
3
1
1
1
5
1
1
4
3
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
5
1
3
2
1
9
1
1
1
1
2
1
1
1
3
7
1
1
1
1
1
2
1
1
23
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
2
2
5
1
2
1
1
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
1
22
1
1
1
1
1
1
1
1
3
2
2
2
1
14
1
1
1
1
3
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
2
3
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
5
5
1
1
1
3
2
2
3
3
1
1
1
1
1
1
1
1
1
1
1
1
19
1
2
1
1
1
4
1
1
1
1
1
1
3
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
4
1
1
2
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
2
1
1
1
1
1
1
1
1
1
3
4
1
2
1
2
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
10
1
2
1
1
1
1
1
2
2
1
3
1
1
1
2
1
1
1
1
2
2
1
1
1
5
1
1
1
2
1
2
1
1
1
1
2
1
2
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
1
1
1
1
1
1
9
1
1
1
1
1
4
1
10
1
1
1
4
1
1
2
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
1
1
2
1
1
1
1
2
16
1
1
1
1
4
1
1
1
1
1
2
3
1
2
1
1
2
1
3
1
1
1
1
4
1
1
1
1
1
4
1
1
1
1
1
1
1
3
2
2
1
1
1
1
1
2
1
1
1
1
1
1
3
1
3
2
1
1
1
2
1
1
1
1
2
4
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
3
6
1
1
2
1
1
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
3
1
7
1
2
1
4
1
1
10
1
1
5
1
2
1
1
1
1
1
1
12
1
1
1
1
2
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
5
1
1
1
1
1
4
1
1
1
1
1
2
7
1
1
3
1
1
1
1
1
4
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
2
3
1
1
1
1
1
61
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
13
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
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
2
3
1
1
1
1
2
1
1
1
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
4
1
1
1
1
5
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
3
1
1
1
1
14
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
3
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
14
1
1
2
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
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
13
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
4
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
17
1
15
1
1
1
1
1
1
1
1
1
1
1
1
1
6
2
1
1
1
2
1
1
3
1
1
1
1
2
1
1
3
1
1
8
1
2
1
1
1
1
5
2
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
1
1
1
1
1
1
1
1
3
1
1
2
1
1
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
8
1
1
1
1
2
1
5
1
1
1
1
1
1
1
8
13
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
2
1
1
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
4
1
2
1
1
1
2
2
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
2
1
3
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
2
1
2
11
6
1
2
1
1
1
1
1
1
1
5
5
1
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
9
1
2
1
1
1
1
1
1
1
1
1
26
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
14
1
1
1
2
1
1
1
1
1
1
25
1
1
1
2
2
1
1
2
3
1
1
1
12
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
22
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
6
1
1
2
1
2
1
1
1
3
1
1
3
1
2
1
1
1
1
2
1
4
2
10
1
1
1
1
3
1
1
1
2
1
1
1
6
1
1
18
2
1
16
1
1
1
1
1
4
1
1
1
1
1
1
1
5
1
1
3
1
1
1
1
1
1
1
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
2
1
1
1
1
1
10
1
1
1
2
1
1
1
1
1
2
6
4
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
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
2
1
2
1
2
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
19
3
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
5
1
4
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
2
2
1
1
1
1
2
1
1
3
2
4
1
3
1
2
3
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
5
1
7
1
1
1
1
1
1
10
3
1
3
1
2
1
1
1
2
1
1
2
1
8
1
1
1
2
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
3
1
1
1
1
1
3
3
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
6
1
1
3
7
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
2
1
9
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
3
1
2
1
2
1
1
1
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
4
1
1
2
9
1
5
1
1
1
9
2
1
1
1
1
5
3
1
1
2
1
1
3
1
1
2
1
1
13
1
1
2
6
1
1
4
1
1
4
2
1
6
4
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
6
1
1
1
1
1
1
2
2
1
50
1
1
1
3
1
1
2
1
1
1
2
1
6
1
8
2
3
2
2
1
1
1
1
2
1
1
1
6
1
1
1
2
1
1
7
1
1
1
1
1
1
3
2
3
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
4
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
6
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
4
1
1
1
3
1
1
1
3
3
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
31
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
6
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
1
7
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
10
1
1
14
1
1
1
1
1
2
6
1
1
1
1
1
1
1
2
1
3
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
1
1
2
1
1
6
3
1
1
1
4
1
1
4
1
1
1
2
1
2
1
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
4
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
6
2
1
2
1
1
1
1
1
1
1
2
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
9
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
4
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
4
7
9
17
1
1
1
1
2
1
1
1
1
1
1
1
4
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
4
2
1
1
6
1
1
1
1
3
1
2
3
4
1
2
2
1
1
1
3
1
1
3
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
6
2
1
2
1
1
2
1
1
1
1
3
13
2
2
3
11
1
1
2
1
1
1
1
4
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
8
1
7
1
5
2
1
6
1
6
1
1
1
1
1
1
1
1
1
6
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
5
1
1
1
1
1
4
2
1
10
1
2
3
1
1
5
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
7
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
5
9
1
1
1
1
8
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
1
2
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
17
1
4
1
2
1
1
1
1
2
1
1
1
2
1
3
1
1
1
7
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
16
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
3
2
2
1
1
2
7
1
1
1
1
1
1
1
1
1
1
3
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
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
3
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
3
1
1
1
1
1
1
2
1
2
1
2
1
1
1
3
1
1
1
1
5
2
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
7
8
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
1
3
1
3
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
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
8
2
1
3
1
1
2
1
1
1
1
1
1
1
1
7
1
22
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
2
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
14
16
1
2
1
1
1
1
1
1
1
1
3
1
2
1
2
1
1
1
1
1
3
1
1
1
1
3
10
1
1
1
2
1
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
4
1
1
5
1
1
1
1
1
3
1
1
1
1
1
2
2
3
1
1
1
2
1
1
8
4
3
1
1
1
1
1
1
1
1
3
1
1
1
4
8
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
3
1
2
1
1
3
1
1
1
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
1
2
1
13
1
1
1
13
1
1
1
1
1
1
1
1
4
1
2
1
1
1
3
2
1
1
4
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
2
2
5
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
2
1
1
1
1
3
1
2
1
1
1
1
2
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
2
2
1
4
1
2
1
1
1
1
2
1
1
1
10
2
2
1
1
4
2
1
1
1
1
1
1
1
40
2
1
1
1
1
1
2
1
4
6
3
1
2
1
4
1
4
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
4
1
2
6
1
4
1
1
2
1
1
1
5
1
1
1
3
1
1
3
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
2
1
3
21
1
2
1
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
14
1
1
1
1
2
1
1
1
1
1
2
1
1
1
5
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
3
1
5
1
6
1
3
1
2
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
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
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
2
1
1
9
1
1
10
1
1
1
1
1
4
1
3
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
11
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
17
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
2
1
1
4
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
2
3
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
10
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
4
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
2
1
7
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
2
1
1
1
3
1
21
1
1
5
1
1
4
2
1
1
1
2
1
2
1
3
2
1
3
1
1
1
1
1
1
2
1
6
2
2
1
1
3
2
1
1
8
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
21
1
1
1
1
2
2
1
1
1
1
1
1
1
1
4
4
1
1
1
2
10
1
1
3
1
1
4
1
3
1
1
1
1
1
1
1
3
1
1
2
18
1
1
1
2
4
1
1
2
1
1
5
1
1
3
1
2
1
1
5
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
1
4
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
4
1
3
14
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
7
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
3
1
4
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
3
1
1
1
3
2
1
1
2
1
1
1
1
3
1
2
2
1
1
2
5
1
1
3
4
2
3
1
3
1
1
3
1
3
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
3
2
1
1
1
9
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
2
1
1
1
1
3
1
1
1
4
2
2
1
2
1
1
1
5
1
1
4
1
4
2
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
9
5
1
1
2
1
4
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
3
3
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
3
1
4
1
1
1
1
1
1
2
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
2
4
1
1
1
6
1
1
1
1
1
1
1
1
2
4
2
1
2
1
1
2
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
4
1
2
1
1
1
1
1
2
1
1
1
1
1
8
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
2
1
1
8
1
1
1
1
1
5
1
1
1
1
1
6
8
1
1
1
1
1
1
1
1
1
1
1
4
1
4
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
7
6
5
1
3
1
6
1
2
2
1
1
1
1
2
1
1
6
1
1
1
2
2
1
1
1
1
17
2
2
1
17
1
7
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
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
1
1
5
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
3
1
1
1
1
1
2
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
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
37
1
2
1
1
1
1
1
1
2
1
3
1
1
1
4
1
1
1
1
1
5
1
1
1
1
3
2
1
1
1
1
3
1
1
2
1
1
4
1
1
3
14
2
5
1
1
3
1
2
1
1
1
1
1
1
1
1
10
1
1
4
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
2
1
1
4
2
5
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
3
1
1
1
1
1
1
1
2
1
5
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
9
3
1
1
1
1
4
8
1
1
1
1
1
31
1
1
1
1
1
1
12
27
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
5
1
1
1
3
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
2
2
1
1
4
1
1
3
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
12
1
2
2
1
1
1
1
1
1
1
1
13
9
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
2
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
2
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
2
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
5
1
1
1
1
3
1
1
2
2
1
13
1
1
2
11
1
6
1
22
1
1
1
1
1
1
1
1
7
1
2
1
1
3
1
1
5
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
19
2
1
1
1
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
2
1
1
4
3
1
1
1
1
1
1
1
10
1
2
1
1
1
1
1
5
1
1
1
2
5
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
3
3
1
1
1
1
1
2
3
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
3
1
1
1
1
1
4
1
1
1
1
1
3
1
2
1
1
3
1
1
1
3
1
1
1
1
5
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
2
1
1
1
2
1
3
1
2
7
1
1
1
1
1
1
1
3
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
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
6
1
1
2
1
7
1
1
1
1
1
1
1
1
1
1
1
3
1
1
3
3
1
1
1
1
1
4
6
1
1
2
1
1
5
1
1
1
1
17
1
1
1
2
4
2
1
1
1
1
1
1
1
10
7
1
1
1
1
1
1
6
1
1
16
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
75
1
1
1
1
1
1
13
1
1
1
21
1
1
4
6
1
2
1
2
1
4
1
2
1
1
2
2
9
1
35
1
1
1
1
1
1
1
3
1
13
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
7
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
5
1
1
1
2
1
1
1
1
1
1
2
1
4
1
5
1
2
1
1
2
1
1
1
2
32
1
1
1
3
1
1
1
1
1
1
2
4
1
1
3
1
2
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
1
4
1
1
2
1
1
1
2
1
2
1
4
23
1
2
1
1
1
2
1
1
2
2
5
1
1
3
1
2
1
1
1
1
2
1
1
7
2
1
6
2
1
1
3
1
1
1
1
1
1
4
2
1
1
1
3
36
2
1
1
1
1
2
2
5
1
4
1
7
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
16
1
1
2
1
2
2
1
6
1
2
1
2
1
2
5
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
3
1
9
7
1
1
1
1
3
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
3
1
5
1
1
3
1
1
1
1
1
1
1
1
1
3
1
5
1
1
2
1
2
1
3
1
1
6
1
2
6
1
1
1
1
1
1
1
1
1
1
2
13
3
2
1
1
3
2
1
1
1
1
1
1
1
1
6
1
1
1
1
1
4
1
1
1
1
1
1
1
1
7
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
8
1
6
1
1
1
1
6
3
1
1
1
3
3
1
1
1
1
1
1
1
6
1
3
5
1
1
1
4
1
1
1
3
1
2
1
2
1
1
3
1
1
3
1
3
1
1
1
1
1
1
2
1
2
4
1
1
2
2
1
1
1
1
3
1
4
1
1
9
1
1
1
4
1
1
7
1
1
5
1
1
2
1
1
1
1
2
3
9
1
1
1
1
1
1
1
1
1
4
1
2
1
5
2
1
1
1
1
1
1
2
1
2
1
8
2
4
1
1
4
1
1
1
1
1
1
3
2
1
1
3
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
4
1
1
3
1
1
2
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
11
1
1
4
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
7
2
1
1
1
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
1
1
3
1
1
4
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
4
1
1
1
1
4
1
1
1
1
1
2
2
1
1
3
4
1
1
1
1
1
3
1
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
2
2
2
2
1
2
1
1
1
4
10
1
1
2
1
1
16
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
6
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
7
1
1
1
3
1
1
1
1
1
1
6
1
1
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
1
1
2
1
2
1
1
3
1
1
1
3
1
4
1
3
3
1
1
1
1
4
1
1
7
2
2
1
1
1
2
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
23
4
1
1
1
1
1
1
1
1
1
1
20
15
1
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
3
1
2
3
1
1
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
1
1
2
1
5
1
1
5
1
1
1
8
2
1
1
1
1
1
6
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
1
1
2
2
4
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
3
1
3
1
1
1
1
1
1
4
2
1
1
1
1
1
1
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
2
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
10
1
6
1
2
1
1
2
5
1
1
1
1
1
1
1
8
1
1
1
1
10
2
1
4
1
2
6
1
2
1
1
1
2
1
1
1
1
1
7
1
1
1
1
2
7
1
1
2
1
1
4
1
1
3
1
2
1
1
1
1
1
1
3
1
2
1
1
16
1
1
6
1
1
3
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
4
1
1
2
1
1
2
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
2
1
1
1
1
1
1
1
1
1
1
2
1
1
7
1
1
1
1
2
1
1
2
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
5
1
1
1
4
1
1
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
5
1
2
1
3
1
1
20
1
2
1
4
3
1
3
1
1
1
2
3
1
1
1
1
1
1
1
1
1
3
1
1
1
3
1
3
1
1
1
2
2
1
4
1
1
1
1
1
1
1
3
1
1
1
1
1
2
7
1
3
1
1
1
9
1
1
2
1
1
3
7
1
1
1
1
1
2
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
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
2
3
1
1
1
2
9
1
1
1
1
2
1
2
4
2
1
1
1
6
1
1
1
3
1
1
1
11
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
5
1
1
1
10
1
1
1
3
1
1
1
1
3
1
1
1
8
7
2
1
61
1
1
6
5
1
1
1
1
1
1
1
22
1
1
1
4
1
5
1
1
1
1
3
1
1
1
1
3
1
23
2
1
3
2
1
1
1
3
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
7
2
1
1
2
1
1
1
1
3
1
1
1
1
4
1
1
1
1
14
8
1
1
1
2
1
1
1
1
1
1
1
4
17
2
2
1
1
1
2
1
1
1
1
1
4
12
1
2
1
2
1
1
1
1
1
1
3
1
3
1
1
1
3
1
1
1
14
1
1
1
2
1
1
1
1
1
1
4
5
3
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
8
1
1
1
9
1
1
1
1
1
1
1
20
1
1
1
1
1
2
1
1
1
4
1
1
1
2
1
1
1
1
7
7
3
1
1
1
1
2
2
1
1
1
1
3
1
1
1
1
1
4
1
1
12
1
6
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
5
1
5
3
1
5
3
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
4
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
16
1
1
2
1
1
4
1
1
1
1
1
1
1
6
3
11
1
1
1
1
1
1
1
3
1
19
1
1
2
1
1
1
2
2
9
1
1
1
3
1
1
1
3
1
2
5
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
4
2
3
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
2
1
1
1
1
3
1
1
1
1
1
17
2
1
1
1
1
1
1
1
17
1
2
1
1
1
1
1
1
2
4
1
3
1
2
3
2
1
1
1
2
3
2
3
1
1
2
2
1
1
2
1
3
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
4
1
1
1
1
2
1
1
1
1
1
9
3
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
7
1
6
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
2
1
1
1
1
1
1
5
3
1
1
1
2
1
1
1
1
1
1
1
1
4
1
1
4
1
1
38
2
1
1
1
1
22
1
2
1
1
1
1
17
1
1
1
1
1
1
1
1
1
1
3
1
16
2
1
1
1
1
1
2
1
2
1
3
1
1
3
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
8
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
1
2
1
1
2
1
1
1
1
1
1
5
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
3
13
1
1
1
1
1
1
3
1
1
3
2
36
1
1
1
1
1
1
1
1
3
9
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
4
2
1
1
1
2
1
1
1
1
1
1
3
1
2
1
13
1
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
1
11
2
1
1
1
1
1
1
1
1
1
1
1
1
2
8
1
1
1
1
1
1
4
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
3
1
3
4
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
12
1
3
7
1
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
2
2
1
5
1
1
2
1
8
3
1
1
1
1
1
1
2
1
1
2
1
1
2
3
1
1
1
1
1
2
1
1
2
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
2
1
1
1
1
1
15
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
4
1
10
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
3
8
1
1
1
1
1
1
1
4
1
1
1
2
1
1
1
1
1
1
1
2
6
1
1
1
5
1
1
1
3
1
1
1
7
1
1
1
1
1
1
1
2
1
2
1
1
1
2
21
1
1
1
1
5
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
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
16
2
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
2
1
2
2
3
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
2
1
1
4
27
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
3
1
1
1
1
1
2
3
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
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
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
12
1
3
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
8
6
4
2
1
1
1
1
1
1
1
6
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
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
6
1
1
1
1
2
3
2
6
1
2
2
1
1
1
1
1
1
2
2
2
5
8
1
4
1
1
2
1
3
1
1
1
1
1
2
2
2
1
1
1
1
1
1
3
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
4
5
1
2
1
1
1
1
1
1
1
1
16
1
1
1
1
1
1
1
1
1
2
1
6
1
6
2
1
1
1
1
1
1
1
1
5
7
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
20
4
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
2
1
1
1
3
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
5
1
1
1
1
10
2
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
2
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
3
2
1
3
60
1
2
2
1
1
1
1
1
1
3
7
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
6
1
2
1
1
3
1
1
1
1
1
3
1
1
1
1
2
2
1
18
1
1
1
1
1
2
1
4
1
1
1
1
1
2
3
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
11
2
10
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
1
3
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
7
1
1
3
1
3
5
2
1
1
1
1
1
2
2
1
1
1
1
1
1
3
1
1
2
1
2
1
1
1
1
16
1
33
7
1
2
2
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
3
2
1
4
1
1
1
5
1
1
2
1
22
1
1
3
1
1
7
1
1
1
1
1
4
1
1
1
2
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
1
1
14
4
1
1
1
1
1
7
1
1
4
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
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
6
3
1
1
1
1
1
1
8
1
1
1
1
2
5
1
1
1
3
2
1
1
1
3
1
18
1
2
1
1
2
2
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
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
41
1
1
15
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
4
5
1
1
1
1
1
2
1
1
1
1
1
1
13
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
6
1
3
1
1
1
2
1
1
1
1
1
1
2
2
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
4
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
9
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
4
1
1
1
1
1
1
6
1
1
1
2
1
1
1
1
1
1
1
4
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
4
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
6
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
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
9
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
3
8
1
1
1
4
4
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
1
1
23
1
1
1
4
2
1
1
2
7
1
1
1
1
1
1
1
1
1
7
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
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
3
1
1
1
4
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
19
1
5
1
1
1
2
2
1
3
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
2
2
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
5
5
1
2
1
2
1
1
5
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
7
2
8
1
1
1
1
1
2
2
2
4
2
1
1
1
1
1
1
2
3
4
3
1
3
1
1
1
1
1
2
1
15
1
3
1
1
1
1
2
2
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
20
1
1
1
1
1
1
1
1
1
1
1
2
1
6
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
3
1
1
1
1
1
1
1
1
1
2
10
2
1
1
1
3
1
1
1
1
2
1
1
6
3
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
1
2
1
1
1
15
1
4
1
1
1
3
1
1
1
2
1
1
1
4
1
1
2
1
3
1
1
1
2
4
1
1
1
1
2
1
1
1
2
2
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
1
8
1
2
2
1
1
1
1
2
2
1
4
1
1
8
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
14
1
1
4
1
1
7
2
1
6
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
8
1
1
1
8
24
2
1
1
1
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
9
1
1
1
1
1
1
2
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
3
1
7
1
1
1
2
1
2
1
1
1
1
2
1
1
3
2
2
1
1
1
1
5
1
25
1
1
2
1
2
1
1
5
1
2
1
1
2
1
1
1
1
1
3
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
8
2
1
1
1
1
1
1
1
1
1
6
1
4
1
2
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
12
1
2
9
4
1
3
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
5
3
1
1
1
1
4
1
2
4
1
1
1
1
5
1
1
1
2
1
1
1
1
1
5
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
2
1
3
1
2
1
1
1
1
1
2
4
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
1
2
4
5
1
1
1
1
1
1
1
1
2
1
1
1
2
8
1
2
1
1
1
2
1
1
1
5
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
7
1
2
4
1
2
1
1
1
1
2
3
1
1
1
1
1
1
1
4
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
5
1
1
5
1
2
1
1
5
1
3
2
1
1
1
2
1
1
5
3
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
2
1
1
2
1
1
5
1
1
3
1
1
2
1
8
1
2
1
1
1
1
1
2
8
3
1
2
1
1
1
1
3
1
2
1
1
1
1
10
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
4
1
1
2
2
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
3
1
1
1
1
1
4
1
1
1
1
1
1
1
3
1
1
1
1
4
1
1
1
1
3
1
1
13
1
1
1
2
1
1
3
1
1
9
7
5
1
3
1
1
1
1
1
1
1
1
1
1
1
3
1
2
3
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
2
3
1
4
2
1
1
1
1
1
2
1
1
1
1
5
1
1
1
1
2
1
13
4
1
1
1
7
1
4
1
1
1
1
2
4
1
1
1
2
2
2
1
1
1
1
2
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
2
1
1
5
3
1
2
1
1
1
1
4
1
1
1
2
3
2
1
2
1
1
1
3
1
1
2
1
1
2
6
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
6
1
1
2
2
1
4
1
1
1
1
1
1
1
6
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
3
2
1
1
1
1
3
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
3
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
6
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
2
1
13
1
1
3
1
1
2
1
1
1
5
2
1
2
6
1
8
7
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
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
3
1
1
1
2
1
1
1
1
8
1
1
1
2
8
1
1
1
1
1
1
1
1
1
1
1
2
1
5
1
1
2
1
1
1
2
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
3
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
19
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
1
9
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
9
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
3
2
1
1
2
1
4
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
17
1
1
1
1
1
1
1
1
4
1
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
1
1
10
1
2
2
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
6
6
1
2
1
9
1
1
16
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
4
1
2
1
1
1
1
5
1
1
1
5
3
1
1
1
1
6
1
2
1
1
1
2
1
1
1
3
2
1
3
18
1
1
1
1
2
1
1
1
4
1
1
1
2
1
1
1
1
1
1
9
1
1
1
2
5
1
2
1
2
1
1
1
2
1
5
2
1
2
1
1
21
1
1
1
1
1
1
1
1
3
1
3
1
1
3
1
1
1
7
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
11
1
1
2
1
1
1
1
1
1
1
14
2
1
2
1
2
11
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
1
1
2
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
10
1
1
1
1
1
1
1
1
1
2
1
1
4
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
15
3
1
1
1
1
1
2
1
1
1
1
1
7
1
1
1
1
5
3
4
1
1
1
6
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
4
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
3
1
1
1
1
1
5
1
1
1
1
1
2
1
1
15
1
8
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
5
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
7
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
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
3
1
1
1
1
1
2
1
1
1
14
3
2
1
12
1
1
1
1
17
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
24
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
8
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
8
1
3
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
26
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
9
1
1
1
1
2
1
1
1
1
1
1
3
1
1
18
1
1
1
1
1
1
1
1
7
1
1
1
1
2
1
1
1
1
3
1
1
1
4
1
1
5
2
1
1
1
1
1
1
1
1
1
1
2
3
1
1
12
1
1
2
4
1
1
19
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
21
1
3
1
2
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
8
2
1
3
1
1
1
2
1
2
2
1
1
1
2
6
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
3
1
1
1
1
2
1
1
3
5
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
2
1
3
6
1
1
1
1
2
2
5
6
11
1
1
1
1
5
5
1
1
1
3
2
1
3
21
1
1
1
1
1
1
1
2
1
1
6
1
1
1
2
1
2
2
1
1
1
1
2
3
3
1
1
1
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
1
2
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
2
1
1
1
3
2
5
1
1
2
1
1
3
1
2
1
1
1
1
6
3
1
1
2
1
1
1
2
1
1
1
1
1
1
4
2
1
1
7
2
1
3
1
1
1
5
1
2
4
1
1
1
2
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
6
1
1
2
1
1
1
4
1
4
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
3
8
1
1
1
1
1
3
5
1
7
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
2
1
7
1
1
5
3
2
33
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
6
6
2
2
13
2
1
1
1
1
1
1
1
1
1
8
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
4
1
1
1
1
1
1
4
1
1
1
1
1
6
1
1
1
1
1
1
1
1
13
29
1
1
1
2
1
1
1
1
8
1
1
3
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
3
1
1
1
3
1
1
1
1
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
5
1
1
3
1
2
3
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
3
1
1
4
1
1
1
1
1
1
2
1
1
1
1
2
2
1
3
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
14
2
1
1
1
3
1
1
1
1
1
2
1
1
1
2
3
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
3
1
1
1
1
1
3
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
3
1
1
1
1
1
1
2
1
1
3
3
1
1
4
1
1
5
1
1
1
1
1
2
1
1
1
7
1
1
1
1
1
1
1
3
1
1
1
1
5
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
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
4
1
1
1
1
1
1
1
2
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
3
1
1
2
54
1
1
1
23
5
2
4
1
2
1
2
1
3
1
2
16
6
1
1
1
1
1
1
1
4
1
1
1
1
1
1
3
1
3
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
1
3
1
1
1
1
1
1
2
1
1
2
1
1
2
3
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
4
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
10
3
1
12
1
1
1
1
1
1
2
1
13
1
1
2
6
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
4
1
8
2
4
1
2
1
2
4
1
2
2
1
1
2
2
1
1
1
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
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
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
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
7
1
3
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
4
1
8
1
1
1
1
1
1
2
1
3
1
1
1
2
2
2
1
1
3
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
6
7
2
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
2
1
3
1
2
1
1
2
3
1
1
1
1
1
1
2
2
1
1
8
1
1
1
2
4
1
9
2
4
1
1
9
1
5
1
1
1
1
1
6
1
2
2
7
1
1
1
1
1
1
1
9
1
1
2
1
1
1
1
1
1
9
1
3
1
1
1
3
1
2
2
3
1
2
1
2
2
1
1
2
1
1
1
1
1
10
21
1
10
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
3
2
1
1
1
1
1
6
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
3
1
2
1
6
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
3
1
1
1
1
2
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
4
24
2
1
1
1
3
2
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
2
2
1
1
1
1
1
1
1
3
1
1
1
5
1
1
1
1
1
1
8
1
1
1
1
2
1
1
1
1
1
1
1
9
2
1
5
1
1
1
1
1
1
1
2
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
2
1
1
1
5
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
8
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
31
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
3
2
2
1
1
1
2
2
1
1
1
1
3
3
2
2
1
1
1
1
1
1
5
1
1
4
2
3
9
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
6
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
4
2
1
1
2
2
1
4
1
1
2
2
2
1
1
4
1
2
1
3
2
1
2
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
3
1
1
10
3
1
3
1
2
2
1
1
1
1
1
1
1
3
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
4
1
1
1
1
1
1
2
1
1
1
4
1
1
1
3
3
1
1
1
1
1
1
2
1
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
3
1
1
2
1
1
2
3
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
5
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
3
1
1
1
1
1
1
3
6
1
3
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
4
6
2
1
1
1
1
3
1
1
1
1
12
1
2
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
5
2
1
1
2
1
1
3
1
1
1
2
1
1
1
1
1
7
1
1
1
2
6
1
1
1
1
2
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
2
2
1
1
1
1
1
1
1
25
1
2
17
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
3
1
2
1
1
1
1
4
1
1
1
1
2
1
1
1
4
1
1
2
1
3
3
1
1
3
1
1
1
1
1
4
1
1
1
5
1
1
1
2
3
1
1
1
4
4
1
1
2
1
1
1
1
1
2
1
1
1
12
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
29
12
1
1
1
1
1
1
1
1
1
2
1
4
3
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
10
1
1
1
5
2
1
1
16
1
3
1
1
1
1
2
1
4
1
3
4
1
1
1
1
32
6
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
15
1
1
1
1
1
1
1
1
2
1
1
1
1
1
13
1
1
3
1
1
1
1
1
1
5
1
1
1
1
3
5
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
3
1
2
1
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
4
3
1
1
1
1
2
1
1
3
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
9
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
2
1
4
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
2
1
1
1
1
1
1
8
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
2
3
1
8
1
1
3
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
15
2
9
1
2
3
3
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
104
1
1
1
1
2
1
1
1
1
2
1
2
1
1
6
3
1
1
1
1
4
1
1
2
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
4
1
2
3
2
1
1
1
1
2
1
3
1
1
1
1
1
4
2
1
1
1
1
3
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
1
1
1
2
3
3
30
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
2
1
1
1
1
5
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
5
1
1
1
1
1
3
1
1
1
2
2
1
1
1
1
2
1
1
5
1
1
1
2
1
1
6
1
4
1
3
1
1
1
1
1
1
1
2
1
1
1
1
4
1
2
1
4
2
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
3
1
1
1
7
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
4
2
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
4
1
1
2
1
1
1
7
1
1
1
1
1
8
1
1
1
1
23
1
1
1
1
1
5
1
1
1
6
1
1
2
1
1
2
25
1
1
1
1
1
32
14
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
19
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
2
5
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
2
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
2
1
1
3
3
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
4
2
1
2
1
1
1
1
1
9
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
13
3
1
1
1
1
1
2
1
1
2
1
1
1
1
3
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
8
1
1
1
1
22
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
2
1
1
1
1
6
1
1
1
1
2
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
3
1
5
1
1
1
2
1
1
1
1
1
2
1
1
1
10
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
9
1
23
1
2
1
1
1
1
1
2
1
2
1
3
16
1
1
1
1
1
1
2
1
1
1
1
13
1
4
1
1
1
1
11
1
4
2
1
1
2
28
1
1
1
1
1
1
2
1
1
3
1
1
2
1
3
1
1
1
1
3
1
1
1
1
5
1
1
1
2
1
1
3
1
3
1
1
1
2
1
1
1
2
1
3
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
4
1
10
1
1
1
1
1
1
3
6
1
1
1
1
1
1
1
1
2
1
1
1
1
7
2
1
3
1
2
2
1
11
1
1
1
1
1
1
4
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
20
1
2
2
1
1
2
1
1
1
1
6
1
1
1
1
2
8
2
1
1
1
1
1
1
2
3
1
1
1
1
1
1
2
1
2
1
1
1
5
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
1
1
1
1
4
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
3
1
1
1
1
1
1
1
1
3
1
5
1
1
2
1
1
1
1
1
1
22
1
1
4
1
1
8
1
1
1
1
1
1
3
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
3
1
1
1
1
1
1
2
2
1
5
1
1
1
1
2
6
1
2
3
1
1
8
4
2
1
1
2
4
1
5
1
1
1
7
1
1
1
1
1
1
1
4
1
1
1
1
6
1
1
6
1
2
1
2
1
5
1
2
1
1
1
1
1
3
1
2
1
1
8
1
1
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
26
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
6
1
1
1
1
3
3
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
3
1
2
1
3
6
1
1
1
2
1
1
1
4
3
1
3
1
1
1
5
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
2
1
1
1
1
2
5
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
5
2
1
1
1
5
1
1
1
1
1
1
3
3
1
1
1
1
1
1
1
2
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
1
1
1
2
1
2
2
1
1
17
1
1
1
2
1
1
3
1
1
1
5
1
1
1
10
2
18
1
1
1
1
1
1
2
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
8
13
1
1
1
1
1
1
1
1
5
1
1
1
5
1
1
1
1
2
1
1
2
1
1
1
1
1
1
8
1
1
1
2
1
2
1
1
1
20
1
1
1
1
1
4
1
1
1
1
1
1
1
1
6
1
4
1
1
1
1
1
5
1
1
1
2
6
1
1
1
3
1
4
1
1
1
1
1
1
1
2
1
1
1
6
1
1
4
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
2
1
7
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
6
1
1
1
1
1
3
1
1
1
5
1
2
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
3
1
1
7
1
1
1
2
1
1
2
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
2
1
1
1
17
5
1
1
2
1
1
2
1
1
1
1
1
1
16
1
1
3
20
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
2
16
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
5
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
5
1
1
1
2
1
8
2
1
12
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
4
2
1
2
1
1
1
4
1
1
2
1
1
2
1
1
1
1
3
1
1
1
2
5
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
2
1
1
1
1
11
1
1
1
1
3
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
2
12
1
11
1
2
1
1
1
1
1
2
1
1
14
1
1
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
12
1
2
1
1
1
1
2
1
3
14
5
1
3
1
2
1
1
2
1
2
1
1
1
1
1
1
1
4
8
1
4
2
1
2
2
4
1
1
1
1
1
5
1
1
2
2
1
2
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
3
4
6
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
3
1
1
3
1
1
1
1
1
1
8
1
1
1
1
4
2
1
1
1
1
9
1
3
1
1
1
1
1
1
1
1
1
1
1
1
9
6
2
6
1
1
1
1
1
1
1
1
4
3
3
1
1
1
1
1
1
5
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
3
4
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
6
1
2
11
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
2
1
1
1
1
1
2
2
3
3
1
1
1
1
2
1
1
17
1
1
6
1
1
1
1
1
2
1
16
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
4
2
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
4
1
4
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
7
1
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
9
1
1
1
1
6
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
5
1
1
3
2
1
1
1
1
2
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
5
1
1
1
1
1
1
2
1
3
1
1
1
1
3
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
5
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
5
1
1
1
3
1
2
2
2
1
4
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
8
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
3
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
5
1
1
1
2
4
1
1
2
1
1
1
1
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
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
1
1
1
1
1
1
1
1
2
2
5
1
4
1
1
1
2
1
1
1
1
1
4
1
2
1
1
1
1
1
3
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
14
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
4
10
1
1
1
2
8
1
1
1
2
4
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
6
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
4
1
1
2
1
1
1
2
1
2
1
1
1
1
1
11
1
1
1
5
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
22
1
1
1
4
1
1
1
1
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
3
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
1
1
1
1
3
1
4
1
5
1
1
1
1
4
2
5
1
1
1
1
1
1
1
4
3
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
4
1
1
1
1
2
3
1
4
1
1
1
1
1
2
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
1
4
1
4
1
1
1
2
6
1
1
4
1
12
1
1
2
1
2
2
1
1
4
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
4
2
1
4
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
3
2
3
1
1
1
1
1
1
1
1
3
1
3
7
3
1
1
4
1
1
1
3
3
1
1
1
3
1
7
1
1
1
2
1
1
1
1
1
1
1
8
1
1
4
1
1
1
1
2
1
11
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
3
1
2
4
1
1
5
5
1
2
2
1
1
1
3
2
1
1
1
3
8
1
2
1
1
1
1
3
1
8
5
1
2
1
1
1
1
1
7
1
1
1
1
1
1
5
1
2
1
4
1
1
3
1
1
1
1
4
1
1
1
2
1
1
1
1
3
1
1
22
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
4
2
1
2
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
6
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
50
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
19
2
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
3
1
2
1
1
2
1
1
1
1
1
3
1
1
3
1
1
2
1
1
1
15
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
2
1
8
2
1
1
14
1
1
1
1
1
1
1
4
1
1
2
1
1
12
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
4
2
2
25
2
2
1
1
1
1
1
1
1
2
3
20
2
1
4
1
1
6
2
1
5
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
1
1
1
3
1
1
1
1
2
2
1
9
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
4
7
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
1
2
1
1
1
1
1
6
1
1
1
1
2
2
1
8
1
1
3
1
1
17
1
1
1
1
11
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
6
1
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
4
1
2
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
1
2
1
2
3
1
1
1
2
1
1
1
1
48
1
1
1
1
1
1
1
1
1
2
1
2
1
1
4
1
1
1
2
1
1
8
2
1
1
1
3
1
1
1
4
1
5
1
1
1
1
2
1
1
1
1
1
1
2
4
1
1
1
1
4
3
1
4
1
1
2
2
1
1
1
1
1
1
3
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
1
1
2
1
4
1
2
1
1
2
1
1
3
1
1
1
1
1
1
1
9
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
4
1
2
1
1
8
1
1
1
2
1
6
2
1
3
1
1
1
1
1
1
1
1
1
1
1
5
2
1
1
1
1
1
1
1
2
1
1
1
1
2
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
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
14
1
1
1
1
1
2
1
1
2
4
1
6
1
1
1
1
1
1
1
1
1
22
1
1
1
1
1
1
1
4
1
1
2
5
4
1
1
1
2
1
1
1
2
1
1
3
1
1
4
1
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
5
2
1
1
10
1
1
1
3
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
4
1
2
2
2
1
1
1
1
1
1
1
20
35
1
1
3
4
1
1
1
1
1
1
2
1
1
2
1
1
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
35
1
1
1
1
1
1
1
1
1
1
1
1
2
18
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
1
3
1
1
1
1
5
1
3
3
1
7
1
1
1
1
1
3
2
1
1
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
34
1
1
1
1
4
2
2
1
1
2
1
1
1
1
1
4
2
1
1
1
1
2
1
2
4
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
2
4
1
1
1
2
1
1
1
1
1
1
3
1
1
2
1
1
3
1
1
1
1
1
1
5
2
1
6
1
4
1
1
1
3
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
1
1
1
1
1
1
2
1
1
2
4
1
3
2
21
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
6
1
5
1
1
3
1
1
1
1
1
4
3
1
1
1
1
2
1
1
1
5
1
1
1
1
2
1
5
3
2
4
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
4
1
2
1
3
1
1
1
1
1
1
1
2
1
1
8
2
1
21
1
1
1
1
1
1
1
1
2
1
1
1
5
1
1
1
1
1
5
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
17
1
3
1
2
1
1
1
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
5
1
2
1
4
1
20
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
8
6
3
1
1
1
1
1
1
3
1
1
1
1
65
1
1
1
1
1
1
1
1
1
1
1
2
2
1
5
16
1
1
1
1
1
1
1
1
1
80
1
1
1
4
1
1
1
1
3
2
1
3
1
4
1
1
5
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
5
1
9
1
2
1
1
1
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
2
1
1
1
1
3
2
1
1
6
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
4
1
1
1
1
5
2
2
3
1
1
2
6
1
1
1
1
2
1
1
1
1
2
1
1
1
1
9
1
1
1
3
1
6
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
4
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
5
1
1
1
1
1
2
2
1
1
1
1
1
1
1
8
1
1
1
1
1
2
1
2
1
1
1
8
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
2
1
2
1
1
6
1
1
1
1
1
1
4
1
1
1
4
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
7
1
2
1
3
1
1
2
1
1
1
1
1
1
1
2
2
1
7
1
2
1
1
2
1
1
8
1
1
2
1
1
1
1
1
7
2
1
1
1
1
1
1
2
1
1
4
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
2
3
1
1
6
9
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
8
1
1
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
4
6
3
18
1
1
1
1
1
1
1
1
1
2
3
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
3
1
1
1
2
3
3
1
1
1
6
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
5
1
2
3
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
2
4
4
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
6
3
1
1
2
7
1
1
1
1
1
1
1
2
1
2
1
1
1
3
3
1
1
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
16
1
1
1
1
1
1
1
2
2
1
2
1
1
8
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
2
1
1
1
8
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
2
1
1
1
4
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
8
1
1
1
1
1
1
1
6
1
2
1
1
3
1
1
4
1
1
3
2
1
1
5
1
1
1
1
1
2
2
1
11
1
4
1
4
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
2
2
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
3
2
1
1
1
1
1
1
1
1
1
1
1
1
11
3
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
6
1
1
1
2
1
3
1
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
4
1
1
3
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
5
1
1
2
1
1
1
1
2
1
1
1
2
1
1
5
1
2
1
1
1
1
2
4
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
11
1
2
1
2
2
3
1
1
2
1
1
1
4
3
1
1
1
2
2
1
1
3
2
1
1
3
1
1
1
1
1
2
1
1
1
2
5
1
1
1
2
4
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
4
1
1
1
1
1
1
1
1
1
1
6
3
1
1
1
1
1
1
1
6
2
1
2
1
1
4
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
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
7
1
4
1
2
1
3
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
26
2
21
1
3
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
5
2
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
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
2
10
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
10
1
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
2
1
1
1
1
1
11
1
2
1
1
4
1
4
1
4
4
1
1
3
1
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
1
1
2
148
1
1
4
1
5
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
21
1
1
6
1
1
1
1
1
1
1
7
1
1
1
1
4
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
3
1
1
1
1
1
1
1
3
1
2
1
1
1
3
1
4
1
1
1
1
1
1
1
1
1
1
5
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
19
1
2
1
1
1
1
7
1
1
1
1
2
1
1
57
8
1
1
1
1
3
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
11
1
1
1
1
1
2
1
3
1
2
1
3
1
1
1
1
1
2
1
2
4
1
1
1
2
1
1
1
1
1
2
2
1
5
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
18
1
1
1
2
3
2
1
1
1
1
1
1
3
1
7
1
1
1
1
2
19
3
1
3
1
1
1
1
1
2
1
1
5
1
1
2
1
1
2
1
1
3
1
1
1
1
1
1
4
1
5
1
1
1
1
1
1
2
1
5
6
2
1
1
3
2
1
1
4
2
1
1
1
1
2
1
1
3
2
1
2
1
1
1
1
1
1
3
1
5
1
1
1
1
11
2
2
2
1
1
1
6
1
1
1
1
2
1
7
1
1
1
1
1
1
1
1
1
1
2
1
2
3
1
4
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
6
1
4
1
1
35
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
4
1
7
2
5
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
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
9
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
17
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
3
3
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
1
1
1
4
1
3
10
1
1
1
1
1
1
1
6
1
1
2
1
1
2
1
1
2
2
2
1
11
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
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
10
1
11
2
1
1
1
1
1
4
1
1
1
1
1
1
1
17
1
1
1
1
2
7
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
3
1
1
4
1
1
5
2
1
1
8
3
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
5
1
2
1
1
1
1
1
1
1
3
1
9
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
1
1
2
1
1
1
2
1
3
1
1
2
1
1
2
1
3
1
1
1
1
1
1
3
2
1
1
5
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
1
1
1
2
3
2
1
1
1
1
1
2
1
1
3
1
2
1
1
1
2
1
1
1
1
1
15
1
1
2
17
2
1
1
34
1
1
1
24
1
1
1
2
4
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
16
1
1
1
1
1
22
1
1
1
1
4
12
2
1
3
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
21
1
1
1
1
2
1
1
1
1
1
23
2
1
1
1
1
2
1
1
2
2
1
4
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
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
11
1
2
1
1
38
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
3
2
1
1
2
1
2
1
1
2
2
8
11
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
17
1
1
1
1
2
3
1
1
1
1
2
3
2
1
2
1
1
5
3
1
1
3
1
10
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
3
1
3
1
1
1
2
1
2
1
4
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
4
4
1
1
1
1
1
1
1
1
1
1
1
6
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
6
1
1
1
3
1
1
1
1
1
1
1
1
1
4
1
3
1
2
2
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
3
1
1
1
3
1
1
1
1
3
1
1
4
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
4
1
6
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
2
1
7
1
1
1
31
7
8
1
5
1
1
1
1
1
1
2
1
1
1
1
51
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
4
1
1
1
1
12
2
1
2
1
1
1
1
2
10
1
1
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
10
1
1
1
1
2
2
3
3
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
6
2
1
1
1
2
1
5
7
1
1
1
1
7
1
3
2
1
1
1
1
2
1
4
1
1
1
1
1
1
2
1
1
6
1
1
1
1
1
1
1
1
1
3
6
1
1
3
1
1
3
1
1
1
9
1
1
1
1
1
2
1
1
3
3
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
4
1
2
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
13
1
1
1
1
6
1
1
1
1
1
21
14
1
1
5
2
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
1
1
4
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
5
1
1
1
1
1
1
24
1
1
1
1
1
1
1
1
3
2
1
2
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
2
1
1
1
1
1
1
1
1
3
3
1
1
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
2
1
1
1
2
1
1
3
2
1
6
1
3
1
2
1
1
1
1
1
1
1
1
17
2
1
2
1
1
1
1
1
1
1
5
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
32
1
1
3
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
4
1
2
6
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
4
1
1
1
1
2
4
1
2
1
1
1
1
1
1
1
2
1
1
1
12
1
1
1
1
1
1
1
1
1
2
4
1
2
1
1
1
1
1
1
1
1
1
1
1
1
5
3
1
1
3
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
20
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
4
1
2
1
1
7
32
1
1
1
1
1
1
4
1
1
1
1
1
1
3
1
1
1
5
2
1
2
1
1
1
1
1
1
2
1
1
1
3
1
7
2
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
1
1
1
1
1
1
4
4
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
26
3
1
2
2
1
1
2
1
1
1
1
3
1
1
1
6
1
4
1
4
2
1
2
1
1
2
1
1
1
1
5
4
1
4
1
1
2
2
1
1
2
1
1
1
1
4
1
1
1
41
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
9
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
2
1
1
1
2
1
1
4
1
1
2
1
2
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
9
1
1
2
1
1
1
2
1
1
1
1
1
1
5
1
1
3
1
1
1
1
8
4
1
1
1
1
1
1
4
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
8
1
5
1
1
1
1
2
2
1
1
1
2
1
1
3
1
1
1
3
1
1
3
1
1
4
1
1
6
1
1
1
1
1
5
1
3
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
3
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
1
14
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
5
1
1
1
1
1
1
1
4
1
1
1
1
1
1
8
1
10
1
106
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
14
1
1
1
2
1
2
1
1
3
2
2
3
6
1
1
1
1
1
1
2
1
2
1
3
2
1
4
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
11
1
1
2
2
1
1
1
1
1
1
1
15
5
4
1
1
1
1
1
1
1
1
1
1
6
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
2
1
1
1
1
7
2
2
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
3
2
1
1
1
1
1
1
1
1
1
1
1
13
1
1
1
1
7
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
4
1
1
1
1
2
1
2
3
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
27
1
1
1
4
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
7
1
1
1
1
1
3
1
3
2
1
1
1
1
1
1
2
2
1
1
1
1
10
1
2
1
1
2
1
3
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
3
1
6
1
1
1
1
1
1
7
1
1
1
1
1
1
2
1
1
1
1
11
1
1
3
5
4
2
1
1
1
1
2
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
1
1
1
1
1
2
1
3
3
1
68
3
2
1
1
2
6
4
1
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
3
1
1
1
1
1
1
3
2
1
1
1
1
1
1
3
2
3
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
7
1
1
1
1
1
1
1
1
3
1
1
1
1
4
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
2
1
1
5
2
1
1
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
1
2
1
3
1
1
1
1
4
2
2
2
1
1
48
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
4
3
1
1
1
2
2
1
1
1
2
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
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
3
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
2
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
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
15
1
1
1
1
2
1
1
1
1
1
1
1
1
1
10
3
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
5
1
3
1
1
4
1
1
1
6
1
1
3
1
1
4
5
1
1
1
2
2
1
1
2
1
1
1
1
1
4
1
10
5
5
1
1
8
1
4
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
5
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
3
5
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
3
1
1
1
1
1
2
6
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
1
1
1
1
1
1
2
1
2
1
1
1
1
4
1
1
1
1
1
1
1
2
2
3
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
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
5
1
4
1
1
1
3
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
4
1
1
2
1
1
1
1
3
13
2
1
1
1
1
2
1
1
1
1
3
1
1
1
6
1
1
1
2
3
1
8
1
1
2
2
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
25
1
1
1
2
1
1
2
1
2
1
7
1
3
1
1
1
1
1
1
1
13
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
3
2
1
1
4
4
2
1
1
1
1
1
2
4
32
1
2
2
1
3
2
1
1
1
1
1
1
1
1