1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
6
2
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
2
1
1
1
1
2
5
4
1
1
1
2
1
1
1
5
2
1
1
1
1
2
13
1
1
1
7
1
1
16
4
1
1
5
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
2
9
1
2
3
1
2
2
2
5
1
1
1
1
2
1
1
3
1
9
4
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
4
1
1
1
2
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
2
1
1
3
1
1
1
2
1
1
1
4
1
1
1
1
3
1
1
5
1
1
1
1
3
1
1
1
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
4
5
1
1
1
2
1
1
1
1
1
1
2
4
1
2
1
5
5
1
1
1
1
2
1
1
1
1
1
4
1
4
1
2
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
6
1
1
1
1
1
1
1
113
1
1
5
1
1
2
1
1
1
1
3
1
2
5
1
1
1
1
2
1
1
1
1
2
1
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
1
2
1
1
1
1
1
1
1
7
1
1
1
2
1
1
2
1
2
1
7
1
1
1
1
2
1
4
1
1
3
1
1
2
1
1
1
1
3
2
1
1
3
1
3
1
2
1
1
1
1
1
1
2
2
2
19
1
2
1
1
1
3
2
1
1
2
1
10
1
4
1
1
1
3
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
4
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
3
3
1
1
1
1
1
1
2
1
1
1
2
13
1
2
1
2
5
1
1
1
1
1
1
4
1
2
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
2
1
2
9
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
10
1
1
1
1
1
2
1
1
1
3
1
3
1
12
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
3
2
2
1
2
3
1
1
1
1
1
2
2
1
1
1
2
5
4
2
1
1
1
1
1
3
1
1
1
2
1
1
2
4
5
2
2
1
2
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
1
1
1
2
1
1
1
5
1
2
1
1
2
3
1
1
1
1
1
1
3
1
5
2
2
1
1
1
1
1
3
1
5
7
1
1
1
1
1
1
1
2
5
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
4
2
3
2
1
1
1
1
1
1
1
1
9
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
3
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
3
1
3
5
1
1
2
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
2
2
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
7
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
9
1
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
11
10
1
1
1
2
1
1
1
4
1
5
3
1
3
1
1
1
2
7
2
4
1
1
1
1
1
1
1
1
2
3
1
2
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
2
1
1
1
1
3
1
1
1
1
2
1
1
3
1
1
1
1
1
4
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
4
1
1
7
1
3
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
11
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
6
1
1
1
1
11
1
1
1
1
1
1
2
6
1
1
3
1
1
1
3
1
2
1
1
1
1
1
2
1
1
1
1
1
3
1
2
1
1
9
1
1
2
1
1
1
1
2
1
1
1
5
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
5
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
14
8
1
1
1
3
1
1
1
2
1
2
1
1
1
1
1
3
1
1
4
2
1
2
3
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
3
2
2
1
1
1
1
1
3
1
5
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
4
1
1
2
3
1
1
3
1
2
1
2
1
3
1
1
1
1
6
8
1
1
3
1
1
34
2
2
1
1
1
1
2
1
5
1
15
1
4
2
2
1
1
3
3
1
1
1
1
6
1
2
1
1
1
1
1
8
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
3
1
1
3
1
1
3
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
3
2
4
2
3
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
7
1
1
5
6
1
1
3
1
1
1
1
12
1
1
2
2
1
1
2
9
8
1
2
1
4
1
1
2
1
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
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
4
3
1
1
1
2
1
1
1
1
4
1
1
2
1
1
8
10
1
1
1
10
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
3
1
1
1
1
1
2
1
2
2
5
1
1
1
1
1
3
2
3
1
1
1
1
1
1
1
1
1
6
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
4
1
1
1
1
1
1
1
1
4
1
7
2
1
1
1
1
1
1
2
1
1
1
4
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
6
2
1
1
1
1
2
8
4
2
2
1
5
2
1
1
5
2
9
1
1
1
1
1
2
17
2
1
1
1
1
1
1
1
3
2
1
1
2
1
1
9
1
1
1
1
1
1
2
5
4
6
1
9
1
1
8
12
3
1
1
1
1
7
1
1
2
1
1
3
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
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
2
1
1
1
1
3
1
1
2
4
1
2
3
1
1
3
1
1
1
1
1
1
1
8
1
1
1
3
1
1
1
1
2
1
1
1
1
1
4
1
1
1
1
2
1
5
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
6
3
2
1
1
5
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
5
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
8
1
1
3
1
1
2
1
2
1
3
2
1
2
9
1
4
1
2
1
6
1
1
2
8085
159
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
5
1
1
1
1
2
1
1
1
2
1
3
1
1
4
1
2
1
1
1
1
2
1
1
2
1
1
1
4
1
2
1
2
1
4
1
1
2
1
2
1
2
1
1
2
1
5
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
2
1
1
1
1
1
2
1
1
1
2
2
2
1
4
1
1
1
1
1
1
1
1
1
1
2
2
6
1
1
1
1
5
2
1
1
1
1
1
1
2
2
2
2
3
2
2
1
1
4
1
1
1
4
1
1
2
1
1
1
3
9
1
1
1
1
1
1
1
1
1
3
3
1
1
1
1
1
3
1
5
1
2
1
4
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
68
1
1
1
1
1
3
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
2
1
1
1
2
1
1
1
1
3
1
1
2
8
3
2
3
1
1
1
1
1
2
5
2
1
1
1
1
1
4
1
1
5
1
1
1
2
7
1
1
1
1
3
2
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
6
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
8
3
1
2
1
1
1
1
1
1
5
2
1
6
3
1
1
1
1
1
1
1
1
3
1
2
1
1
2
1
4
1
1
3
12
3
2
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
22
1
1
1
1
1
1
3
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
2
1
1
2
1
1
1
1
1
1
5
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
6
1
1
4
1
2
1
1
1
10
1
1
1
3
1
1
1
1
2
2
1
2
3
1
1
1
1
1
4
1
1
2
1
1
1
1
1
2
1
2
4
2
9
1
4
1
2
1
1
1
1
1
8
1
1
1
1
1
1
1
2
1
1
6
3
1
1
1
1
1
2
1
3
1
11
2
1
1
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
2
2
1
26
1
5
1
2
1
13
1
1
3
1
2
1
1
5
3
2
1
1
1
2
1
1
2
1
1
2
1
1
3
7
5
1
1
2
8
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
2
1
1
1
4
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
3
2
2
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
1
1
1
1
1
2
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
3
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
3
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
3
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
3
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
3
3
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
3
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
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
3
1
1
2
1
2
1
1
1
61
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
1
1
2
1
1
1
1
1
1
1
3
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
1
1
1
1
2
1
1
1
2
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
12
2
1
1
1
1
1
2
1
1
2
1
1
1
1
3
1
1
2
2
1
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
3
1
1
1
1
1
1
530
2
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
2
1
1
1
1
1
1
1
2
15
1
1
1
1
1
3
1
2
3
1
1
1
1
1
1
2
3
2
2
2
1
1
1
1
2
1
3
2
2
1
2
1
1
1
1
1
1
2
4
6
4
2
3
1
1
1
1
1
1
1
4
4
1
2
1
1
1
1
1
1
3
2
1
5
1
1
2
1
2
1
1
1
7
8
4
1
2
1
2
1
4
1
2
1
3
4
3
2
4
2
1
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
3
2
1
1
1
2
2
3
1
1
1
2
1
8
1
2
1
1
1
2
2
1
1
1
4
2
1
2
1
3
1
3
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
3
1
4
3
1
8
1
1
1
1
1
1
3
1
1
2
1
15
1
1
1
1
2
1
1
1
3
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
7
1
2
1
1
33
1
5
1
2
1
1
1
1
1
1
2
2
2
2
1
4
1
2
1
2
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
4
7
1
1
1
1
2
4
2
9
1
1
4
2
2
1
2
1
1
1
1
1
3
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
12
3
2
1
1
1
1
1
1
1
1
10
5
2
2
1
1
1
2
11
1
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
4
2
1
1
1
1
1
2
1
1
1
3
1
1
1
11
2
2
1
1
5
2
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
28
2
1
2
1
1
8
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
3
1
1
1
2
1
2
1
1
1
2
1
10
7
1
2
1
1
1
2
1
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
1
6
1
2
1
6
1
6
1
2
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
2
1
1
1
1
1
1
1
1
1
3
1
1
2
1
2
1
2
1
3
2
1
8
2
1
1
1
1
1
1
1
14
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
6
1
1
1
1
1
2
2
3
18
1
1
2
2
2
1
2
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
6
1
1
1
1
2
5
1
1
2
3
2
2
1
9
1
1
1
3
4
11
1
2
1
1
1
1
2
1
1
5
2
1
1
28
9
1
1
1
1
1
2
1
3
1
1
9
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
2
3
3
1
1
1
1
1
1
1
1
1
1
9
5
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
13
1
1
2
3
4
2
1
1
2
4
2
2
1
1
1
1
1
15
2
1
3
5
2
6
5
3
1
1
1
1
7
1
1
2
2
4
4
1
1
2
1
1
1
2
1
3
1
4
2
2
1
1
1
1
1
10
1
1
1
1
1
2
5
1
1
2
1
1
1
23
2
2
1
1
1
2
2
1
2
1
2
1
2
2
1
1
2
1
1
2
2
9
3
1
2
2
1
1
1
1
1
2
2
2
2
1
1
4
10
76
2
1
6
1
5
2
1
1
1
1
3
3
3
9
1
1
1
1
2
1
2
1
3
1
1
1
1
2
2
1
1
1
4
2
1
1
1
1
12
2
1
2
1
1
1
3
1
1
1
4
4
1
2
1
1
3
1
2
2
1
1
1
1
1
1
1
232
1
1
2
3
2
1
1
2
1
1
1
6
9
6
3
1
1
6
1
1
1
1
2
3
2
1
14
3
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
5