1
1
1
1
2
2
2
1
1
1
2
1
1
3
1
1
2
1
1
2
3
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
3
1
12
2
1
2
1
3
18
3
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
3
1
2
2
2
2
1
2
2
4
2
2
18
1
1
1
1
1
1
1
1
1
1
4
1
1
3
12
1
3
1
4
2
12
1
18
2
1
1
1
1
1
3
4
2
1
1
1
2
2
2
3
1
3
4
1
2
14
1
3
1
3
1
11
1
2
1
4
6
4
1
1
2
4
3
3
1
1
5
2
1
4
1
1
1
3
2
1
1
2
1
1
3
1
1
1
4
5
1
1
1
1
3
3
2
11
1
2
9
1
20
14
1
3
4
1
1
2
1
1
5
5
1
1
1
29
2
3
1
3
1
28
1
1
1
1
1
1
14
1
3
1
2
15
2
1
2
1
1
1
3
2
1
3
1
15
1
2
1
1
1
1
24
6
1
1
3
1
4
2
1
3
2
1
1
8
1
1
1
1
2
3
1
1
1
1
1
1
8
1
4
2
2
1
1
1
12
2
1
1
2
1
1
1
2
1
1
1
1
21
3
1
1
2
2
1
5
1
2
1
2
5
3
3
3
3
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
7
1
1
4
1
3
1
31
1
1
1
3
2
2
1
1
1
1
1
4
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
3
1
1
2
11
4
1
2
1
2
1
1
1
1
1
3
4
1
1
2
1
1
2
1
1
1
1
1
2
1
1
3
2
1
4
1
2
1
1
2
2
2
1
7
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
1
8
1
1
1
6
3
1
3
1
33
1
1
4
1
4
2
1
2
2
1
1
1
4
2
1
3
1
1
13
1
1
2
1
5
1
1
1
3
2
3
1
19
2
1
2
1
1
1
5
1
1
1
1
2
3
6
1
1
1
1
3
2
1
3
3
3
1
1
1
1
4
1
7
1
3
17
2
1
1
1
1
1
2
2
1
3
3
3
1
2
1
2
3
1
1
1
2
2
1
2
2
1
1
10
1
3
1
1
1
5
3
4
1
22
1
4
1
1
1
1
2
2
2
1
3
1
1
9
1
1
2
2
2
1
5
1
1
2
2
1
1
1
3
1
1
1
3
2
4
2
1
1
2
2
5
3
1
1
1
1
2
1
5
1
2
1
3
3
1
1
1
2
4
3
2
1
7
2
1
1
2
3
2
1
1
3
1
1
5
6
1
3
1
1
1
2
1
2
1
1
1
2
1
6
1
1
2
1
1
6
1
1
1
1
1
1
13
191
1
1
4
1
1
1
1
2
6
7
4
3
1
1
1
1
1
1
1
1
3
2
14
2
2
1
1
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
4
3
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
3
2
1
6
1
2
1
3
2
1
7
1
1
4
2
2
2
2
3
1
1
1
1
3
1
2
1
2
1
3
1
1
2
1
1
1
3
1
1
1
1
1
2
3
1
1
3
3
3
1
1
1
2
4
2
5
3
1
1
2
1
5
1
1
2
1
6
14
3
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
8
1
1
20
5
4
2
9
1
2
1
1
1
2
2
6
5
1
1
1
2
3
1
7
2
1
1
1
1
13
2
1
7
2
1
1
3
4
3
4
1
3
1
1
3
1
1
3
6
1
6
1
1
1
1
1
1
1
11
10
3
7
2
1
1
2
1
1
1
5
1
1
2
1
1
2
1
1
1
1
1
1
8
3
1
2
2
1
2
1
1
1
1
2
1
3
8
4
1
2
1
5
6
5
2
1
2
3
1
1
1
1
23
1
2
1
3
3
2
1
1
1
1
4
1
2
1
1
9
1
1
2
1
7
1
3
1
1
1
1
1
1
1
1
1
1
4
3
1
1
1
1
1
2
6
9
2
1
1
11
1
1
1
5
2
2
1
1
1
1
1
2
1
2
3
1
1
3
1
1
1
6
1
1
4
1
2
3
1
1
1
1
1
3
2
1
1
2
1
1
1
2
2
5
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
2
1
2
1
1
1
1
4
2
1
1
1
1
1
2
2
1
1
4
1
1
1
2
2
1
2
1
1
1
2
1
3
11
1
1
3
1
1
9
3
2
4
2
2
1
1
1
4
1
1
2
1
3
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
2
1
1
1
4
2
2
1
2
1
1
4
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
5
1
1
3
1
1
1
1
2
2
1
1
2
1
1
1
3
2
1
11
3
2
7
2
1
1
1
1
1
2
1
1
1
2
12
2
3
1
1
1
1
1
1
1
1
8
5
3
1
1
1
1
3
5
2
3
1
1
1
1
3
5
1
5
1
11
1
8
1
2
1
1
1
18
1
1
1
1
1
2
1
2
1
3
1
2
2
3
1
1
10
1
2
1
1
1
1
1
2
1
3
2
1
5
2
3
1
1
1
4
1
1
1
7
3
1
2
1
1
2
22
1
1
1
3
1
1
1
2
6
2
1
1
1
1
1
1
12
1
1
1
1
1
1
2
1
2
1
3
2
1
5
5
1
3
4
1
1
1
11
2
4
1
1
1
1
1
4
1
2
3
43
1
2
2
1
1
7
2
1
1
1
1
1
2
1
1
3
1
1
4
1
1
1
1
1
4
1
4
1
6
1
1
4
1
1
1
3
1
1
1
1
1
1
1
2
1
2
1
1
2
3
2
2
1
3
1
1
3
2
1
1
4
1
3
1
4
3
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
3
1
7
4
1
1
5
1
1
1
1
1
3
1
1
1
1
1
3
2
1
9
1
1
1
1
2
2
1
1
43
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
7
2
6
1
28
3
2
1
1
1
1
1
1
1
1
1
1
4
2
1
1
2
2
2
1
1
1
1
2
1
7
1
3
1
1
6
1
5
8
3
1
5
1
1
1
1
1
1
1
1
1
1
2
1
1
3
7
1
2
3
2
2
1
1
1
1
1
1
1
4
2
3
1
1
2
5
1
1
1
1
1
2
1
6
4
1
1
1
14
1
1
1
1
4
1
1
1
1
1
1
3
1
1
7
1
1
1
4
2
1
4
1
1
1
2
3
1
1
1
4
8
1
1
2
1
3
5
1
2
4
1
1
1
1
1
1
1
3
2
1
4
9
1
1
1
3
6
2
2
1
1
1
1
1
1
1
1
1
2
1
4
1
2
1
7
3
2
1
1
1
1
1
1
1
2
2
1
1
2
1
9
3
1
78
1
3
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
4
3
2
1
4
3
1
1
3
7
1
1
1
3
8
2
1
1
10
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
2
2
1
10
1
1
1
1
1
1
1
1
8
1
1
1
2
5
1
6
1
3
1
2
1
1
1
1
1
1
6
1
1
1
1
1
8
1
14
1
1
1
1
1
2
1
1
3
1
2
5
3
1
1
1
2
1
9
6
1
1
2
1
1
1
1
4
8
1
2
14
2
9
1
1
29
1
1
5
1
1
1
2
2
1
1
1
2
1
1
3
1
2
2
1
1
1
1
1
1
10
1
2
1
7
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
2
5
1
1
1
1
1
1
4
1
1
1
2
1
1
1
1
1
1
6
1
1
2
1
1
1
9
1
1
1
3
2
2
1
1
3
1
1
1
1
1
4
4
1
1
1
1
1
1
4
2
2
1
1
1
1
1
1
3
3
1
2
3
1
1
1
1
1
2
1
3
1
1
2
2
1
1
1
2
1
3
1
8
8
1
3
1
1
1
1
1
2
1
1
1
1
1
4
3
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
3
1
1
1
1
6
2
1
8
2
1
12
2
1
1
1
4
2
1
3
1
1
1
4
1
1
2
1
8
2
1
2
1
3
1
4
3
1
1
3
4
1
5
1
1
6
5
3
1
1
1
1
1
1
13
2
1
8
1
1
2
1
1
1
1
2
3
1
1
1
1
2
4
1
1
7
1
1
1
2
2
3
2
3
1
1
1
1
2
3
1
2
1
1
5
2
1
2
1
1
11
2
1
2
1
1
1
1
1
3
1
1
1
1
1
3
3
1
1
1
1
2
1
2
1
1
1
2
3
1
2
26
1
1
1
1
1
1
1
1
1
2
2
1
1
3
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
6
1
9
1
1
3
2
1
2
1
1
2
1
1
1
1
2
1
1
1
21
2
1
2
1
3
1
2
3
5
4
1
1
1
1
13
5
3
1
1
2
2
2
1
1
1
1
2
3
1
4
1
2
1
4
2
1
2
1
2
1
1
8
1
1
2
1
2
1
1
1
1
1
1
9
3
1
3
8
1
1
2
3
2
1
1
1
3
1
2
1
5
1
1
3
4
1
1
1
9
1
8
1
2
3
1
4
5
23
1
17
1
2
2
3
1
1
2
1
1
2
1
2
58
3
1
1
1
2
1
3
1
1
1
1
3
3
1
1
3
3
1
1
4
1
1
1
1
5
1
1
35
1
1
2
3
2
2
2
3
1
1
1
1
3
1
2
1
1
2
4
3
1
4
2
1
3
4
4
2
1
1
1
1
1
2
1
1
1
4
1
1
2
2
3
2
1
5
1
4
2
3
2
2
2
1
12
5
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
3
1
6
1
1
2
3
1
6
3
1
2
6
1
4
1
7
1
1
2
10
1
1
1
14
1
5
2
2
9
1
2
2
1
1
1
1
2
1
1
1
1
1
4
14
1
1
1
1
1
1
3
1
4
3
1
2
1
1
2
2
1
2
2
2
1
1
4
2
1
3
5
1
1
1
4
1
6
2
1
1
1
1
1
1
5
6
1
3
8
2
1
2
2
3
13
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
4
2
1
1
1
1
3
4
1
1
1
1
2
1
3
1
1
1
2
7
3
5
7
2
6
2
1
9
1
1
1
1
1
3
1
8
4
9
3
1
3
2
1
13
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
4
1
1
1
40
2
1
2
1
1
1
3
1
2
2
1
3
1
1
2
1
77
5
4
8
1
2
2
1
1
3
1
1
1
1
1
1
2
1
1
1
6
1
1
1
1
1
4
1
1
1
2
1
1
1
4
4
6
2
2
8
4
2
1
1
2
1
1
1
2
1
6
1
2
2
1
1
5
3
4
3
1
1
1
1
1
1
5
2
1
1
2
22
3
3
3
1
1
1
1
2
3
6
2
6
1
2
6
3
1
1
1
1
5
36
1
1
1
11
3
1
1
1
1
2
2
3
1
1
1
1
1
2
1
1
2
1
3
9
3
1
2
1
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
5
1
1
4
1
1
1
2
3
3
1
2
1
1
1
3
1
5
2
3
1
1
1
24
3
1
1
2
3
46
6
1
1
1
3
1
1
1
1
2
4
1
1
1
5
3
1
2
2
7
1
1
2
1
1
1
2
1
1
1
1
1
1
4
1
1
1
3
8
1
1
1
1
1
2
3
2
8
1
1
1
1
2
9
2
1
1
3
12
2
7
2
1
3
1
1
1
1
1
1
2
3
3
3
2
11
1
3
1
1
1
1
1
3
1
3
1
4
1
3
4
1
1
5
3
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
9
1
3
2
1
1
1
3
1
1
1
1
1
4
6
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
3
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
3
33
1
3
1
1
1
1
1
1
3
1
4
1
1
1
1
1
3
1
1
1
1
2
1
4
1
1
3
2
19
1
1
7
2
9
8
2
23
3
1
1
1
2
4
1
1
1
2
1
1
2
1
1
5
1
1
2
1
1
20
1
3
2
1
1
17
1
2
83
7
2
1
1
2
1
1
1
1
1
1
7
1
2
1
1
2
3
1
1
6
1
1
1
1
2
2
2
1
3
3
1
2
38
2
5
3
2
6
5
1
4
3
1
1
4
2
2
1
1
3
4
1
1
2
1
2
1
1
1
1
6
1
1
2
4
1
1
1
1
1
3
3
6
1
2
2
1
1
6
1
1
1
1
1
1
1
1
1
3
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
3
8
8
1
2
1
1
1
1
1
1
1
1
1
3
3
1
28
3
2
2
1
1
1
1
2
1
2
10
2
1
4
1
2
1
1
1
1
1
1
5
3
1
1
2
1
1
1
1
1
3
2
4
1
4
1
3
3
1
1
1
1
2
1
2
12
4
7
4
1
1
1
1
1
6
1
2
1
1
1
1
1
3
2
1
1
2
1
1
1
1
8
4
5
1
2
2
1
4
1
4
3
4
2
1
1
3
1
1
2
1
1
1
1
2
1
1
68
1
1
1
1
1
1
2
2
1
1
1
8
2
1
1
9
8
1
2
1
1
1
1
1
6
1
1
17
1
1
1
3
1
1
1
1
10
2
3
1
1
3
1
1
1
1
4
3
1
1
1
3
1
1
3
1
6
3
1
9
1
1
2
1
1
1
1
10
1
2
1
6
1
1
1
1
1
1
2
1
1
3
4
1
2
1
2
2
1
1
3
1
1
1
1
2
2
1
1
1
5
5
3
1
4
5
4
2
2
1
1
1
3
7
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
9
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14
4
2
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
2
3
1
1
5
2
1
3
1
2
1
1
1
1
1
10
1
1
1
1
1
1
5
1
1
1
2
2
1
1
1
1
1
1
1
2
4
1
3
3
2
2
6
1
10
1
1
1
1
2
1
2
2
1
1
1
18
1
2
1
2
1
2
1
2
7
1
1
1
1
3
1
1
9
2
1
1
1
28
1
4
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
5
1
1
3
1
2
1
1
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
4
6
1
4
1
4
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
5
1
1
1
1
1
3
1
2
2
1
2
4
11
2
3
2
5
1
7
4
1
2
1
1
1
1
4
2
1
1
1
3
4
1
1
1
4
6
1
2
2
1
1
1
1
42
2
4
2
1
1
3
1
5
1
2
2
11
1
1
1
2
2
2
2
1
1
3
1
1
1
1
2
2
1
1
1
10
6
1
1
1
3
1
1
2
1
1
1
1
2
1
3
1
1
1
2
7
7
5
1
4
1
1
1
3
5
11
18
2
1
4
1
3
1
1
1
1
1
1
1
3
1
3
13
1
1
2
1
2
1
4
1
3
1
1
1
1
2
18
1
1
1
3
1
4
6
4
21
1
2
1
1
1
1
1
1
1
1
1
18
5
1
10
3
1
2
1
4
2
1
36
7
1
1
1
1
7
2
1
3
1
4
2
1
1
1
1
8
6
8
4
3
1
4
3
1
2
1
2
1
1
1
7
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
3
1
1
1
1
1
1
1
1
2
4
1
2
2
1
5
1
1
1
3
2
1
1
1
1
1
2
1
1
1
6
1
1
1
2
1
1
3
2
1
1
5
1
1
2
1
2
1
2
1
2
2
1
5
3
1
1
1
9
1
1
1
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
6
2
1
1
2
4
1
1
1
1
1
1
1
1
1
2
1
4
3
1
1
1
5
1
1
2
1
1
5
3
1
4
11
15
3
1
2
1
5
1
1
1
1
1
2
2
2
1
1
1
1
1
1
5
2
1
6
2
3
1
5
1
1
1
1
7
3
5
1
1
2
1
1
1
3
1
2
1
3
1
4
2
2
1
1
6
3
1
7
3
1
4
1
1
1
2
1
1
45
1
2
2
1
1
4
1
1
1
1
1
1
2
1
1
1
2
1
2
2
3
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
2
2
1
5
9
7
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
5
2
1
1
3
7
1
1
1
1
1
1
15
3
3
2
1
1
3
15
13
2
1
2
1
1
1
1
1
2
1
3
2
1
4
7
1
1
1
1
1
1
2
1
1
2
1
11
7
2
1
1
3
1
1
2
1
3
1
3
2
1
1
1
1
1
19
1
3
15277
1
1
1
3
4
1
4
1
1
2
1
1
1
1
1
4
2
1
2
1
2
2
4
10
1
2
1
1
8
3
1
1
1
5
1
2
1
1
1
1
1
1
3
2
1
1
2
1
2
1
4
1
5
2
3
1
1
9
1
1
1
1
1
5
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
3
2
1
3
2
1
5
2
1
1
1
1
50
1
2
1
1
1
1
1
1
1
2
6
2
1
2
1
1
1
1
1
3
1
6
1
2
36
4
2
1
1
5
10
3
4
1
3
1
2
2
2
1
2
1
1
7
2
6
2
2
1
1
2
2
4
1
1
1
2
2
1
3
3
10
1
1
10
2
1
2
1
63
1
2
2
1
1
1
3
3
5
1
2
2
1
1
1
3
1
1
1
5
2
1
1
3
2
1
1
1
1
5
5
1
1
1
5
1
3
3
1
1
1
1
33
1
1
1
1
1
6
1
3
5
1
3
1
1
3
3
1
1
1
1
3
2
1
3
2
1
1
3
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
4
1
8
1
1
1
1
1
1
2
3
1
1
3
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
3
1
1
2
1
1
2
1
4
2
2
1
7
3
2
2
1
58
1
1
1
1
1
1
1
1
2
2
1
7
1
1
2
4
1
2
3
1
1
1
8
1
1
10
1
1
1
1
1
1
1
2
4
1
1
1
1
6
1
1
1
1
1
1
1
2
1
1
1
2
1
1
3
1
1
3
1
1
2
1
5
2
1
1
25
4
5
2
1
2
1
1
1
1
1
1
1
20
4
1
1
2
9
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
7
1
2
2
4
1
1
5
2
1
2
1
1
2
1
1
1
1
3
1
1
1
6
1
1
1
2
1
1
1
2
2
1
7
1
2
2
2
2
1
1
2
1
4
2
3
1
1
2
3
1
2
2
1
1
1
2
1
1
1
1
5
1
1
1
2
2
1
2
1
1
2
3
1
1
1
1
1
1
2
2
2
1
1
1
100
1
1
1
2
1
2
5
1
1
1
1
2
1
1
1
6
1
1
1
2
1
6
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
6
1
1
9
2
1
1
1
2
1
1
1
1
2
1
1
4
2
15
1
1
4
2
1
1
1
7
2
3
2
2
1
7
2
5
1
1
1
1
6
1
1
1
1
9
4
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
4
1
1
2
1
11
1
1
3
1
2
1
2
2
1
1
1
1
4
3
1
1
1
4
4
10
1
1
2
1
1
10
3
4
1
1
1
1
1
2
1
3
2
3
2
1
1
6
1
1
1
1
2
2
1
3
1
1
1
3
1
3
1
1
1
1
2
3
1
2
1
3
3
1
1
1
2
2
1
1
1
2
1
1
3
1
1
2
1
2
1
2
1
3
1
3
22
4
9
3
1
4
1
1
1
1
2
1
13
4
2
2
1
2
7
2
1
1
8
3
2
1
2
2
1
2
3
1
2
1
1
1
3
1
1
1
2
1
2
3
2
3
5
2
10
13
6
1
7
1
2
8
1
4
1
3
1
5
1
1
1
2
7
1
1
2
5
1
1
1
2
2
1
1
1
8
1
3
2
1
2
10
2
1
1
1
1
3
67
1
1
11
1
2
2
1
1
2
1
1
1
1
1
3
2
1
2
1
3
2
2
2
3
5
1
1
1
2
1
1
7
1
1
1
1
3
1
1
2
2
2
9
4
1
1
2
1
2
1
3
1
2
20
30
1
1
1
1
1
1
1
1
1
2
1
1
4
1
4
1
3
1
1
1
9
4
15
1
3
4
4
2
1
1
1
1
2
4
1
8
2
5
1
4
3
1
1
2
1
55
2
2
1
1
3
1
1
4
1
2
1
3
4
1
2
2
10
1
4
5
2
1
3
4
2
1
1
3
3
1
1
3
1
1
2
1
1
1
1
5
1
1
1
7
5
1
2
1
1
1
1
8
1
2
6
1
1
2
3
2
1
14
1
1
1
2
1
1
1
14
5
2
1
1
4
1
1
2
3
1
1
2
3
2
1
4
1
5
1
1
2
2
1
1
5
5
1
6
1
1
1
2
1
4
3
1
1
4
1
1
5
3
2
1
2
10
1
1
1
1
2
1
1
2
5
2
1
1
1
1
4
1
2
2
8
1
2
1
1
1
1
1
1
1
2
3
2
1
1
1
2
1
1
2
1
1
1
2
1
4
1
7
1
1
1
1
2
1
1
2
1
6
1
1
1
5
2
2
1
3
1
1
2
4
2
1
4
1
1
1
1
2
1
2
1
1
1
1
1
2
3
2
7
2
1
2
31
2
2
2
2
1
5
2
41
7
1
3
1
1
1
2
1
1
1
2
1
1
2
6
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
2
1
6
16
3
4
2
4
2
2
3
1
1
1
2
1
1
1
1
2
1
1
1
2
1
3
2
1
1
1
1
6
5
3
1
1
1
1
1
2
2
1
5
1
1
2
1
1
1
2
3
2
1
3
1
1
1
1
1
1
1
2
4
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
3
1
3
1
1
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
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
1
1
11
1
4
1
2
1
2
1
2
3
4
1
1
2
1
1
3
1
1
2
1
2
1
1
3
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
3
1
2
1
1
1
3
1
2
2
1
1
4
1
1
2
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
3
1
1
2
1
2
1
1
1
4
1
1
2
1
1
3
1
1
1
2
2
1
1
1
1
1
1
1
3
1
1
4
1
3
1
1
6
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
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
1
1
1
3
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
4
1
1
2
4
4
5
2
2
2
1
1
6
2
1
3
1
1
2
3
1
4
1
7
1
1
1
1
2
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
3
2
3
1
2
9
1
1
2
1
2
1
1
1
1
1
1
1
7
2
2
1
3
1
2
1
1
1
1
1
1
2
1
3
1
1
1
3
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
3
1
1
2
1
1
1
1
2
4
1
1
1
2
2
1
1
3
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
3
1
2
1
2
1
1
1
1
1
1
1
1
1
3
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
3
1
1
1
1
1
2
1
1
1
3
2
1
1
2
1
5
1
1
2
1
3
1
1
1
1
1
1
1
1
1
2
1
5
1
1
2
1
1
2
1
1
3
1
1
2
1
1
1
2
2
1
5
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
1
1
1
2
1
3
1
2
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
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
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
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
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
5
1
1
3
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
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
81
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
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
1
1
2
2
1
1
1
2
4
1
1
1
1
1
1
1
6
1
1
1
1
1
1
2
1
1
2
1
2
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
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
13
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
5
1
4
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
5
1
1
2
1
1
3
1
1
1
3
1
1
5
1
1
1
2
3
2
2
1
1
1
1
1
1
6
1
2
1
1
11
2
1
1
1
2
6
12
1
2
1
14
1
1
1
6
1
2
1
1
1
1
1
1
1
2
3
1
1
1
1
1
3
1
1
6
22
12
3
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
927
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
8
7
4
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
5
1
2
5
7
1
1
1
1
2
1
1
4
3
3
1
1
1
1
1
1
2
2
1
5
1
1
4
1
1
2
1
3
1
1
4
1
2
1
1
1
2
1
1
1
1
9
4
4
3
1
3
1
1
1
2
4
2
2
1
2
1
1
7
2
2
2
2
11
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
7
2
1
2
2
1
1
4
1
1
1
1
1
1
1
1
2
2
3
1
1
3
2
1
1
1
3
1
1
1
3
1
1
1
1
2
1
1
2
7
1
1
2
2
2
2
1
1
1
1
1
1
2
3
1
2
3
1
1
1
7
3
1
2
6
7
1
4
2
3
2
1
5
2
1
1
6
5
9
2
4
1
2
1
1
3
1
3
2
1
1
3
5
1
1
1
1
1
1
2
2
1
1
1
1
1
3
3
1
4
2
5
1
3
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
31
7
3
1
1
2
2
1
1
2
1
2
2
1
1
1
1
4
2
1
1
1
1
1
4
1
1
2
1
1
4
2
1
1
1
5
3
1
1
1
1
2
2
1
1
1
2
1
1
1
2
3
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
7
1
1
2
1
13
1
3
1
1
1
1
1
1
1
1
1
1
2
1
4
3
1
1
1
1
1
1
1
1
5
1
1
2
1
1
1
1
1
2
1
3
3
1
1
1
1
1
1
1
1
1
3
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
6
1
10
5
1
2
3
1
2
1
1
1
1
1
1
1
1
1
9
8
5
1
1
1
1
6
2
6
1
1
1
3
2
3
1
2
10
13
1
1
1
1
1
3
1
1
1
1
3
4
1
1
2
1
3
1
1
3
1
1
1
4
1
1
1
1
2
2
1
1
4
3
11
4
1
1
14
1
1
9
1
1
1
1
1
1
3
2
1
1
2
1
1
1
1
2
5
1
1
2
1
5
1
2
3
1
2
1
3
6
4
2
1
1
4
1
3
6
1
1
1
1
12
1
1
1
1
3
2
1
1
12
1
1
1
1
8
5
1
1
1
1
9
3
1
1
1
9
2
1
3
1
1
2
1
1
2
1
1
1
6
1
3
1
2
1
1
1
1
4
1
3
1
19
2
1
8
5
1
7
1
1
1
1
2
1
1
1
3
1
2
1
3
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
4
1
1
1
4
1
1
1
1
2
1
5
2
1
2
2
3
15
2
2
2
2
2
3
1
1
1
1
1
1
2
4
16
6
1
3
1
1
1
1
1
4
3
1
1
3
2
1
1
6
2
2
2
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
2
5
1
2
1
5
1
1
1
1
4
2
1
2
2
2
4
3
1
2
3
1
26
4
5
1
1
1
59
5
4
1
1
1
1
1
1
1
1
2
1
3
1
2
1
1
11
3
3
1
1
1
1
1
2
4
2
1
1
3
1
8
1
2
1
2
1
1
1
1
1
1
8
2
1
1
1
1
1
1
2
1
1
1
1
5
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
4
1
1
2
1
1
1
1
1
1
1
1
1
1
3
3
1
1
1
1
1
1
2
1
2
2
4
7
4
1
1
2
1
1
1
4
1
1
1
5
3
1
1
3
7
1
1
1
1
32
9
2
1
1
2
3
1
3
1
2
2
1
1
11
1
3
2
8
1
1
3
1
6
8
1
1
3
1
1
1
3
1
3
1
1
1
2
1
2
1
1
1
3
1
2
1
1
1
5
1
1
3
1
1
1
2
1
1
1
2
1
4
1
1
2
1
4
3
1
1
1
1
1
1
4
1
1
5
1
3
3
1
2
1
2
1
1
1
2
1
1
8
1
2
1
1
1
5
3
1
1
1
1
1
3
47
1
1
3
1
1
12
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
5
3
3
1
1
1
1
4
1
2
12
3
1
1
2
4
1
2
1
1
1
1
2
2
2
3
6
2
1
1
2
2
8
3
2
1
1
1
4
3
1
1
8
2
1
2
4
1
1
1
2
2
1
1
1
4
1
1
2
2
1
2
3
2
8
1
1
31
2
1
10
1
1
1
1
1
11
4
1
1
1
2
1
2
1
1
1
1
1
6
1
1
2
10
1
1
1
1
2
1
17
1
1
5
1
1
1
1
1
6
1
2
1
2
1
5
1
2
1
1
17
2
2
5
1
1
1
1
2
9
1
2
2
1
1
3
1
1
1
2
2
2
1
2
1
31
17
4
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
4
1
1
1
1
2
2
2
1
1
11
7
1
19
1
2
4
1
1
75
3
3
1
1
2
20
3
1
6
6
1
1
1
1
2
2
3
2
2
1
15
1
3
3
1
1
1
1
1
1
1
2
1
2
4
1
2
1
5
1
1
3
4
3
3
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
8
4
1
54
2
1
2
1
1
1
1
2
1
1
7
8
22
1
9
3
1
1
2
4
1
1
1
1
1
1
2
1
1
1
1
6
4
3
1
5
2
1
1
3
3
1
3
3
2
1
1
5
1
2
3
4
3
9
1
2
2
1
1
2
1
1
8
1
3
9
1
1
1
6
2
1
1
1
2
4
1
4
1
2
1
4
1
1
8
1
1
3
1
3
1
1
2
8
11
1
3
1
7
3
14
1
2
1
1
1
5
1
2
1
1
1
5
1
1
3
1
1
3
2
2
1
5
1
1
3
12
1
1
1
2
1
1
1
1
2
1
2
1
5
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
5
6
2
2
1
1
1
1
1
1
1
2
22
1
1
1
1
2
1
1
1
1
1
4
1
1
1
1
1
2
1
1
5
1
1
1
1
1
6
8
2
4
1
1
1
1
1
1
2
35
14
1
5
1
6
1
4
3
17
1
5
1
1
3
1
1
1
3
1
1
1
9
1
1
1
1
2
1
6
1
3
2
1
1
1
1
1
1
1
3
3
1
2
1
1
1
1
2
1
2
1
1
5
2
3
6
2
5
1
2
5
1
1
1
2
2
1
3
2
2
4
9
1
1
1
1
2
11
3
2
1
1
2
1
1
7
2
1
7
4
1
17
2
1
3
3
1
1
2
1
1
1
1
1
3
1
5
1
1
2
1
2
6
15
1
2
29
4
3
1
1
4
1
2
4
6
1
1
1
1
1
6
3
2
6
1
1
1
1
2
2
1
2
1
1
6
1
1
2
3
1
14
1
1
1
2
2
3
3
1
1
3
12
8
37
1
8
1
4
1
1
1
4
1
1
1
1
2
1
128
1
4
1
1
14
1
3
7
2
1
6
2
1
2
2
1
1
1
1
15
2
7
2
2
1
1
13
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
8
1
1
11
1
10
1
2
3
2
5
1
3
50
1
3
2
2
21
7
2
7
1
1
1
1
1
8
1
1
1
2
1
7
1
5
1
1
1
1
7
4
4
2
4
1
1
2
1
6
1
1
1
2
2
3
1
4
4
2
15
6
7
1
4
1
3
1
1
1
8
2
1
3
1
1
2
1
2
1
1
16
1
1
1
1
3
1
1
13
1
1
1
1
3
1
1
1
3
2
1
3
1
3
1
4
1
1
3
2
7
13
2
1
5
3
4
1
1
1
2
2
1
3
2
1
2
1
7
3
1
1
13
7
1
1
2
1
9
2
2
7
1
2
3
3
1
1
1
3
2
5
3
4
2
1
1
1
2
1
1
2
18
1
1
2
1
1
1
2
1
1
6
1
10
3
2
3
3
1
2
5
8
1
1
1
1
7
2
2
2
2
2
2
2
1
1
1
3
1
3
8
1
2
226
1
2
1
2
32
3
3
1
5
7
2
2
1
1
1
13
1
1
6
1
1
1
2
1
1
1
3
6
1
1
1
3
1
2
1
4
2
3
13
1
1
1
3
1
2
1
4
1
2
2
1
1
1
8
1
1
1
4
2
4
1
3
1
2
1
6
2
2
3
1
4
3
3
3
2
1
1
1
4
1
1
1
1
8
2
17
1
3
1
7
1
2
1
1
4
1
1
2
5
3
3
3
11
1
1
2
6
3
2
8
1
2
1
6
5
1
2
4
1
4
1
3
3
1
2
1
22
2
1
101
6
6
2
1
1
1
1
4
1
1
2
14
1
1
1
6
1
1
502
1
1
1
1
3
8
5
1
1
2
4
2
1
5
8
1
1
2
3
1
1
1
2
4
1
1
1
1
11
4
9
6
4
1
2
2
2
1
1
1
3
1
14
1
1
3
1
1
1
1
19
1
5
2
1
1
1
1
7
1
1
1
4
2
1
1
4
2
3
1
1
1
4
1
1
1
2
2
1
1
7
9
8
5
1
4
1
1
1
1
2
2
1
1
2
4
1
1
1
1
1
1
1
2
1
5
15
1
2
2
2
1
2
2
1
2
1
1
1
