1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
10
2
1
1
1
2
1
1
1
1
4
1
1
1
1
7
1
1
2
2
1
1
1
1
1
1
8
1
1
2
1
1
6
1
8
2
4
1
1
2
1
1
1
1
1
1
2
1
1
3
2
1
2
1
2
1
1
2
4
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
3
2
3
1
2
1
2
1
2
1
1
1
1
1
1
2
2
4
1
1
1
1
1
2
2
1
1
2
3
1
1
5
2
2
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
11
1
1
1
1
1
1
2
1
1
1
4
1
1
1
3
1
2
1
1
1
2
1
2
1
1
1
1
2
4
1
3
1
1
3
1
2
3
4
1
1
1
3
1
2
3
2
1
1
1
1
5
1
1
29
2
1
3
1
1
1
2
3
1
1
4
5
2
1
1
1
3
2
9
1
1
1
5
1
4
1
2
1
1
3
1
1
1
6
1
1
1
3
3
2
28
1
1
1
1
2
1
1
1
1
1
1
1
2
6
1
6
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
3
4
3
3
1
2
1
1
4
2
3
9
1
2
2
5
1
4
1
3
13
1
2
11
1
10
1
1
3
2
1
1
1
3
1
1
6
1
1
1
2
2
3
12
1
1
1
9
1
1
1
1
1
6
1
1
3
1
1
5
2
1
1
2
1
1
7
3
2
1
1
1
1
1
2
2
1
2
4
1
1
4
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
1
8
4
2
3
1
1
1
1
1
1
3
3
3
1
3
3
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
1
2
4
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
4
1
1
12
2
1
1
1
4
1
3
1
1
14
2
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
4
1
1
12
1
2
7
1
2
6
1
1
1
4
1
1
1
1
12
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
8
94
1
3
1
24
1
1
1
3
1
2
6
1
3
1
1
1
2
1
1
2
1
1
2
1
1
7
4
1
4
1
1
1
2
1
1
3
5
2
2
1
12
1
8
1
1
1
1
7
1
2
2
1
2
1
3
1
1
1
1
1
2
2
1
1
1
1
1
1
180
1
1
1
2
6
2
1
1
1
1
1
1
3
3
1
2
1
1
1
2
2
6
1
1
1
3
1
2
1
1
1
2
1
1
3
7
1
1
2
1
1
1
8
3
1
2
1
2
2
1
1
12
3
2
1
3
7
1
4
1
5
2
2
1
1
1
2
4
1
1
1
2
1
1
1
1
1
4
1
1
1
1
1
5
1
1
2
1
2
4
1
1
1
120
1
1
1
1
2
1
1
3
2
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
1
1
1
2
1
1
1
1
1
1
1
1
2
1
3
1
2
1
1
2
2
1
2
1
2
5
6
1
2
1
8
1
2
1
1
1
1
4
2
1
1
1
1
3
3
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
3
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
7
1
1
1
1
1
3
42
3
1
2
4
1
2
1
2
1
1
1
1
1
1
3
1
1
6
5
1
1
2
2
2
1
1
1
1
24
1
2
1
2
1
6
2
1
2
1
1
2
11
1
1
7
1
1
4
1
1
1
104
1
1
1
1
1
2
1
1
1
1
3
1
1
2
4
1
1
1
2
1
1
1
12
2
2
2
7
7
4
1
1
1
1
1
1
1
2
2
1
4
1
1
6
2
5
1
4
1
1
1
1
1
4
19
1
1
2
2
10
1
1
1
1
1
1
1
1
1
1
1
1
202
3
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
6
1
1
2
4
2
1
4
2
1
1
1
1
4
3
1
2
1
1
1
1
5
1
1
1
1
24
6
6
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
8
4
1
1
1
1
1
2
14
1
1
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
17
3
1
1
1
2
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
6
1
1
1
1
1
2
1
1
3
1
53
1
2
1
1
5
2
1
4
1
1
1
2
2
8
1
1
2
1
4
2
1
4
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
11
1
1
1
2
1
1
1
1
2
35
1
2
4
1
1
2
3
1
1
1
1
2
3
1
1
1
3
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
4
1
1
1
2
4
1
4
1
2
1
9
4
1
23
3
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
4
1
1
1
2
1
1
1
1
1
1
2
9
1
1
1
1
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
2
1
1
3
3
1
3
1
2
1
1
2
3
1
1
1
1
1
2
1
60
3
1
1
1
1
1
1
5
2
1
2
6
1
2
1
1
1
3
1
1
4
1
11
1
2
1
2
1
1
3
3
1
2
9
4
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
9
1
1
1
3
3
1
1
2
1
1
3
1
1
2
3
2
2
1
1
1
1
3
1
2
1
2
1
1
1
1
3
1
1
4
2
1
2
1
2
1
1
2
1
1
4
2
1
5
1
1
1
2
4
4
1
3
5
3
2
1
6
1
1
2
1
1
1
6
1
6
1
1
1
1
1
1
1
1
1
22
1
1
1
3
1
4
1
3
3
1
3
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
47
1
1
1
1
1
1
19
1
1
2
1
1
3
2
1
2
1
5
3
1
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14
1
2
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
16
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
131
1
1
7
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
514
1
12
1
6
1
5
2
6
1
1
1
1
1
2
1
1
8
1
2
2
5
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
2
2
1
4
2
1
1
2
3
2
1
1
2
3
1
1
1
1
1
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
3
1
1
4
1
9
12
1
4
1
1
5
1
2
1
1
2
4
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
5
1
8
7
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
3
2
2
1
1
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
7
1
2
1
1
1
1
1
1
3
1
1
1
5
2
1
1
2
1
1
3
1
1
1
2
1
1
1
5
1
1
6
1
1
2
2
1
7
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
3
1
1
1
8
1
2
1
8
1
1
1
4
1
2
2
1
1
2
1
1
3
1
1
2
1
2
2
1
1
4
1
2
1
1
5
1
1
1
1
15
1
1
1
1
22
14
1
1
1
2
1
1
1
1
1
1
1
3
1
2
1
2
1
1
3
2
1
1
1
4
3
1
1
1
1
2
2
1
1
3
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
14
1
3
1
1
3
2
1
67
1
1
3
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
4
2
1
1
2
1
2
2
1
1
3
1
3
1
1
1
1
1
3
1
6
1
1
1
1
1
1
1
1
1
1
2
2
1
9
5
1
2
1
1
1
3
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
3
1
3
1
2
3
1
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
7
2
1
1
1
1
5
1
1
3
2
1
1
2
1
10
1
1
1
1
3
1
2
1
9
1
1
1
1
6
1
2
1
3
1
1
1
1
1
1
1
2
1
2
1
1
19
1
18
1
1
1
1
4
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
3
1
1
1
4
2
2
17
2
10
1
1
1
1
1
1
2
4
1
1
3
1
1
2
1
1
1
1
1
3
1
1
2
2
1
1
1
1
1
1
1
1
2
1
27
1
3
2
1
1
1
1
1
1
3
3
1
3
1
1
2
1
1
1
3
1
2
1
3
1
1
1
1
2
1
2
1
1
2
1
3
3
5
1
1
1
1
1
1
1
1
1
5
2
1
2
2
3
2
4
1
7
1
4
502
1
1
15
11
2
1
1
1
1
1
46
5
1
1
2
1
3
1
1
49
1
2
13
1
7
4
1
1
2
2
1
1
1
1
2
1
2
4
1
3
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
5
470
1
1
1
1
4
2
2
2
3
1
1
1
2
1
1
5
1
1
1
2
8
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
128
1
1
1
1
1
1
8
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
5
4
1
1
1
3
7
1
1
2
2
2
1
1
2
2
1
1
92
1
2
1
2
1
1
1
3
2
1
1
1
1
1
91
1
1
1
1
1
1
1
2
2
2
3
1
1
1
2
1
4
3
2
1
1
1
1
1
3
1
3
1
1
1
1
1
1
2
1
1
5
2
1
1
1
2
2
1
1
8
1
1
1
1
1
1
90
1
2
1
1
1
2
1
1
1
4
1
4
2
1
1
1
1
1
3
1
1
1
1
1
3
1
1
1
1
2
1
2
1
1
1
3
41
2
1
1
1
2
167
4
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
6
6
1
1
1
1
1
3
1
1
1
2
13
1
1
1
2
2
1
1
1
2
1
2
1
4
3
2
1
1
5
10
1
1
1
1
4
2
1
4
4
4
3
2
1
1
1
1
1
1
1
1
2
2
3
1
4
4
1
2
1
1
2
1
1100
1
4
2
1
1
1
1
1
1
5
1
1
1
3
1
1
2
1
1
1
4
1
3
1
2
2
3
5
3
1
9
2
1
1
1
1
1
1
1
1
2
6
1
1
18
1
1
1
1
1
1
4
2
130
1
1
1
1
1
1
5
2
1
5
1
15
3
1
1
1
1
1
1
1
1
1
3
1
2
2
2
1
1
10
1
3
1
1
1
2
1
1
12
2
1
1
3
1
1
1
2
1
2
2
2
1
2
1
1
1
2
4
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
5
10
2
2
2
1
1
1
1
3
1
1
2
1
1
1
2
1
2
1
1
1
1
8
1
1
1
1
1
1
1
1
1
16
1
1
1
1
3
1
2
1
2
3
1
1
1
1
1
2
2
2
1
1
1
2
1
1
3
2
1
1
2
3
2
1
2
5
1
1
6
1
1
5
1
1
2
1
136
1
3
1
1
1
1
19
2
1
1
1
1
2
1
1
1
2
2
4
1
3
1
1
1
1
1
1
4
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
8
1
3
1
1
1
5
3
1
1
1
1
1
1
3
344
1
1
2
1
4
1
1
1
2
1
1
1
1
1
1
2
1
1
3
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
2
2
1
1
1
25
1
8
1
1
1
4
1
3
2
1
2
1
1
2
1
33
1
3
2
2
15
1
1
3
1
2
1
1
1
11
5
1
1
2
3
2
1
1
2
4
3
1
2
1
1
7
7
1
1
3
3
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
5
14
2
1
1
1
1
1
1
10
8
2
1
1
1
2
11
1
2
1
2
3
4
2
1
1
3
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
3
1
1
2
1
1
2
1
1
1
1
2
1
2
3
1
1
1
2
1
1
1
1
1
1
4
4
1
1
2
1
5
2
1
1
1
1
1
1
4
1
1
1
2
1
1
2
1
1
1
3
1
1
1
2
1
2
2
1
1
1
1
10
1
1
1
1
2
1
1
1
8
1
4
1
4
770
4
1
2
1
4
1
1
1
1
1
1
1
3
1
3
4
1
5
1
1
1
2
3
1
1
1
2
1
1
1
1
2
16
5
5
2
2
4
1
310
3
3
1
1
1
3
1
6
1
1
1
2
8
2
1
3
1
7
1
1
3
1
1
1
1
2
1
1
4
1
4
1
2
5
1
1
1
14
1
1
4
2
1
2
1
1
5
1
1
5
1
2
1
99
1
1
1
1
2
6
1
1
1
1
1
18
1
1
4
2
1
1
2
1
1
5
2
2
1
1
1
5
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
2
1
1
1
80
1
8
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
3
1
1
1
1
1
1
1
104
8
1
1
1
1
1
1
1
2
1
1
1
83
2
1
5
1
4
2
422
1
1
6
1
1
2
3
1
1
1
1
1
1
2
8
2
1
1
4
1
9
2
1
1
2
2
30
1
1
2
1
1
1
1
334
2
3
2
1
1
1
12
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
7
2
1
1
1
1
1
1
1
27
1
1
1
2
1
3
1
2
2
1
1
1
1
1
1
4
1
1
3
3
1
4
2
6
30
1
1
2
2
3
2
1
4
4
2
2
1
4
1
1
1
2
3
4
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
6
1
12
1
1
2
2
1
1
1
1
1
1
1
3
3
1
3
1
1
1
1
2
1
1
2
1
1
3
3
2
1
1
2
2
2
2
10
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
4
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
7
2
2
1
3
2
1
1
1
1
1
2
1
1
1
4
2
1
3
1
1
1
2
2
1
1
2
1
1
1
2
1
8
3
4
7
3
1
1
1
1
1
1
1
3
6
2
1
1
1
3
2
1
1
1
3
1
1
1
2
1
5
1
1
1
4
4
1
2
1
1
1
1
1
4
3
1
1
2
2
1
1
1
2
1
3
1
1
1
1
6
1
1
1
3
1
1
1
2
1
1
1
2
2
2
1
2
1
5
1
1
2
1
1
1
2
1
1
3
5
1
1
1
1
2
1
1
1
7
1
2
1
1
1
2
1
1
1
1
3
2
3
2
1
3
1
3
5
1
1
1
2
3
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
3
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
4
1
1
1
4
1
1
1
1
2
1
3
3
1
2
13
3
1
1
1
1
1
1
1
1
1
1
7
1
1
1
2
1
1
1
1
1
1
1
1
1
6
4
1
1
1
2
1
2
3
1
1
10
1
1
1
1
2
2
2
1
3
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
6
8
1
1
2
1
1
2
1
1
1
14
2
17
1
1
3
1
3
1
3
3
1
7
3
1
1
2
1
1
2
2
1
1
16
1
2
1
1
1
1
1
3
1
2
5
2
1
1
1
2
1
5
2
1
1
1
1
1
1
1
2
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
66
1
2
1
1
1
3
1
4
3
1
2
1
1
7
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
50
1
1
1
3
1
1
1
1
1
1
2
1
3
1
1
2
2
1
2
1
1
2
1
1
1
1
38
2
1
5
1
1
3
1
1
3
1
2
1
2
1
1
19
1
1
1
1
1
1
2
1
1
1
3
1
1
1
261
2
9
2
2
1
2
1
2
2
2
1
1
2
1
1
21
1
8
1
1
2
1
4
3
1
1
1
1
1
1
2
1
2
2
2
1
4
1
2
3
1
1
1
1
1
1
4
1
3
1
1
1
1
2
2
1
2
2
2
1
4
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
2
1
1
1
1
1
8
1
2
1
1
2
1
1
1
1
1
8
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
8
1
2
1
1
1
7
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
2
1
1
1
2
1
3
1
2
1
1
4
2
2
1
1
1
2
1
2
2
4
1
3
5
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
4
1
2
1
1
1
2
1
1
72
1
1
1
7
1
8
1
1
1
10
1
7
5
4
1
1
1
1
29
2
1
1
2
1
1
19
4
4
3
2
1
3
1
1
1
1
18487
459
3
1
2
2
3
1
1
1
2
1
1
3
1
2
1
7
1
1
8
1
1
1
1
1
1
1
1
1
1
1
1
12
1
2
1
4
1
1
1
1
1
3
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
10
1
1
1
1
1
1
2
1
2
1
1
2
1
5
1
2
1
1
1
14
2
1
1
4
1
1
1
1
1
1
1
1
4
2
1
2
1
1
1
1
2
2
11
1
2
2
1
1
1
1
1
46
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
9
1
1
3
1
10
1
3
1
1
1
1
3
1
1
2
2
143
1
1
1
1
2
6
8
2
1
13
3
3
2
2
2
1
1
2
1
1
1
1
5
1
1
2
1
1
2
5
1
1
5
1
7
1
2
1
1
4
1
3
8
1
2
3
1
1
1
1
1
4
1
1
1
1
1
2
1
1
2
1
3
2
2
1
1
24
1
4
1
3
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
3
1
1
2
5
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
3
1
2
2
1
2
1
1
7
2
4
1
1
1
2
2
1
14
3
1
2
2
124
4
2
1
4
4
1
3
1
1
5
1
1
1
2
1
2
1
3
3
3
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
4
4
1
2
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
4
1
1
187
1
2
2
1
1
7
1
1
2
1
1
1
1
3
1
3
2
1
1
2
1
1
1
4
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
241
1
1
1
1
1
1
1
4
2
3
25
1
2
1
19
1
2
5
1
2
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
70
1
6
1
1
1
2
2
1
2
1
2
1
1
1
1
1
20
1
1
1
6
1
2
3
1
2
1
2
2
1
6
10
1
1
3
1
1
1
2
1
1
2
1
1
1
18
1
2
3
1
1
2
1
3
2
4
1
1
1
1
1
1
3
8
1
1
5
1
1
5
3
1
1
1
1
3
1
3
1
1
1
1
1
1
3
1
1
16
1
2
1
2
4
1
4
1
1
1
2
3
2
1
1
1
1
1
1
1
4
1
1
7
1
2
2
2
1
3
1
2
1
1
1
1
3
1
1
4
1
1
1
1
3
1
1
1
1
1
4
1
8
1
1
1
2
1
2
1
1
1
2
3
1
5
2
3
4
1
101
1
1
2
1
1
6
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
1
2
1
7
3
1
1
1
1
1
3
1
1
1
4
1
1
2
1
1
1
1
1
11
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
5
1
1
1
20
1
1
1
4
2
1
1
2
2
6
1
2
1
1
1
1
1
1
1
1
1
1
1
14
3
1
1
1
1
1
2
1
3
3
1
1
1
36
1
1
5
2
4
1
1
1
1
3
1
3
1
1
1
1
1
9
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
5
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
3
5
1
1
1
1
1
1
1
1
4
1
1
1
8
1
1
5
1
1
1
11
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
4
3
5
2
1
1
5
1
1
1
4
2
1
4
1
1
21
6
5
2
2
1
5
1
1
3
1
1
7
1
1
4
4
1
1
1
1
1
1
2
2
1
1
14
2
6
2
3
1
1
1
3
5
1
1
1
8
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
5
2
4
1
1
1
1
1
4
1
1
1
1
1
8
1
1
1
1
1
1
11
13
2
1
9
1
2
3
1
1
1
1
1
2
2
1
1
5
1
1
1
1
1
4
1
2
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
14
2
1
1
1
5
1
1
1
1
1
3
1
1
1
4
1
2
3
1
1
1
1
1
1
27
1
2
3
2
4
1
1
1
1
1
1
1
2
1
1
6
1
1
1
1
1
1
1
4
1
1
3
3
1
2
1
2
2
1
1
1
2
235
4
1
1
18
3
3
6
2
5
20
36
1
19
4
50
7
1
5
1
1
2
1
2
1
1
4
1
1
1
1
2
1
3
1
2
1
1
3
1
1
1
1
1
1
4
1
1
3
1
4
20
1
1
2
3
1
1
1
1
2
1
1
3
1
1
2
2
1
1
1
2
2
3
2
1
3
4
1
1
1
1
1
1
1
1
2
3
4
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
3
1
1
1
1
1
3
1
2
1
1
2
1
3
1
1
2
1
1
1
2
1
3
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
2
1
3
1
2
1
4
1
1
4
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
3
2
1
2
1
2
1
2
1
1
1
1
1
2
3
1
3
1
2
1
1
5
1
1
4
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
5
2
1
3
1
1
3
1
2
1
1
1
3
1
1
2
1
2
3
1
3
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
5
1
1
1
3
2
1
6
1
4
1
1
1
1
1
1
1
1
2
3
1
2
1
1
1
5
3
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
8
1
6
1
4
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
3
1
1
2
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
2
1
1
1
2
1
1
1
4
3
2
1
1
1
1
5
1
1
2
2
1
1
2
1
1
1
4
5
2
5
1
3
1
3
1
1
1
1
1
1
1
2
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
9
1
8
4
1
1
2
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
3
3
1
1
1
1
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
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
3
1
3
1
1
1
1
4
1
5
2
1
6
1
1
1
3
1
2
3
1
1
1
1
2
1
1
5
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
4
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
3
2
1
1
1
1
3
2
2
2
7
2
2
1
1
1
1
1
1
1
1
1
3
3
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
1
3
1
4
2
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
2
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
5
1
1
1
1
3
1
1
5
1
1
1
3
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
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
2
1
2
1
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
1
1
1
2
1
1
1
1
1
3
1
1
3
4
1
1
1
1
1
1
1
1
2
1
2
2
1
2
236
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
4
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
3
3
1
1
1
5
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
4
1
1
1
1
1
3
4
6
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
16
1
9
1
2
1
2
1
4
1
2
1
1
1
3
1
1
1
1
1
1
3
1
1
1
4
1
2
1
1
2
2
1
11
1
1
2
1
1
2
1
1
1
2
2
1
1
2
3
1
1
1
1
1
1
1
1
7
1
1
2
2
2
1
6
9
2
3
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
2
1
1
1
7
1
4
1
1
1
1
1
2
1
6
3
3
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
8
252
266
1
1
1
1
1
2
1
1
1245
1
1
2
1
3
1
141
1
1
1
1
1
2
1
2
8
8
1
1
1
3
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
1
3
2
1
2
1
1
4
1
1
1
1
1
1
3
1
2
1
2
1
6
1
1
8
1
14
3
2
2
1
8
1
1
2
1
1
1
2
10
1
1
8
1
1
1
1
2
1
3
2
2
4
5
1
1
1
1
1
3
52
2
1
2
2
1
1
1
1
1
5
6
1
1
1
2
4
2
1
1
1
2
5
2
6
1
1
1
1
1
1
1
3
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
4
3
3
1
23
1
1
1
8
1
1
6
2
1
2
1
1
1
1
2
2
2
1
1
1
5
4
1
1
9
1
1
1
1
1
10
5
4
1
1
1
1
1
1
3
1
1
2
1
2
1
1
13
3
3
1
1
1
2
6
1
2
1
1
2
1
3
1
1
1
7
1
9
3
5
2
2
1
2
3
1
1
2
1
2
6
16
3
2
1
2
2
1
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
4
1
2
3
1
3
1
1
2
1
1
3
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
9
1
1
2
2
2
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
6
1
1
2
2
1
1
1
1
1
1
2
2
2
3
1
1
1
3
1
1
1
1
2
2
1
1
3
1
2
1
2
1
1
11
4
1
1
1
1
2
4
1
1
1
1
1
2
1
2
2
2
1
2
1
26
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
4
1
5
1
1
4
3
1
6
2
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
2
1
5
1
1
2
2
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
1
4
1
1
5
1
4
1
1
24
1
1
1
3
1
1
7
1
3
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
3
1
2
1
1
8
2
3
1
4
1
1
2
2
1
2
1
1
1
3
2
1
19
1
2
5
2
1
2
2
8
1
1
1
1
1
1
3
1
5
1
1
1
1
1
4
1
1
1
1
2
19
1
1
1
3
1
2
1
1
1
1
4
1
3
1
1
1
1
1
2
1
1
1
3
4
1
1
2
4
2
2
1
3
2
1
2
7
1
1
1
1
1
3
1
1
2
1
1
3
1
1
1
1
1
1
2
1
9
6
2
1
2
1
1
2
3
2
1
159
3
1
1
2
45
18
1
2
2
1
1
7
1
1
1
4
1
1
2
3
3
1
1
1
3
1
1
1
1
5
5
3
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
2
2
1
2
2
15
1
1
2
1
1
1
1
1
1
1
1
4
7
6
53
2
1
1
1
1
1
1
1
1
1297
1
1
1
2
1
2
1
1
49
1
1
1
1
1
1
2
1
3
1
1
4
2
1
1
1
1
1
1
1
8
5
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
2
1
1
2
3
3
2
2
4
1
1
1
1
1
6
1
2
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
7
6
1
1
1
1
1
1
1
1
12
4
1
7
1
1
1
1
1
1
1
1
1
1
1
1
2
4
1
1
1
1
1
1
2
1
1
6
1
2
1
1
1
2
1
1
4
1
1
1
2
1
2
2
5
4
1
1
1
4
2
1
1
1
8
1
2
2
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
3
2
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
5
3
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
4
3
1
1
2
1
1
2
3
2
7
4
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
3
3
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
2
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
5
3
1
10
3
1
4
1
1
1
8
1
1
1
1
2
1
1
1
1
1
4
1
2
7
2
1
2
2
2
1
1
37
2
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
12
2
2
2
6
4
1
3
1
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
2
4
4
2
5
1
1
2
1
1
1
3
1
3
1
1
3
7
1
3
1
1
1
1
1
1
1
27
1
1
1
1
1
1
7
1
1
2
2
2
1
1
1
1
4
2
1
1
4
1
1
1
1
1
3
1
2
1
1
2
1
3
1
6
1
1
2
1
3
1
2
2
4
5
1
1
1
1
1
3
3
3
2
1
1
1
1
1
1
1
1
8
1
1
1
2
3
5
1
7
1
1
7
1
1
3
1
1
1
2
1
1
2
2
5
1
2
1
7
4
1
1
3
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
5
1
2
1
2
7
1
1
7
1
1
1
1
1
1
1
1
1
1
2
6
1
1
1
1
1
1
1
4
2
1
1
1
1
3
1
1
1
3
1
1
2
1
1
2
1
4
1
2
1
1
1
1
1
2
4
1
1
1
2
1
5
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
3
1
1
1
1
4
1
1
1
1
2
1
2
1
2
2
3
1
3
2
2
1
5
1
1
4
1
1
3
1
1
1
4
1
7
1
3
2
1
20
1
1
1
1
1
1
2
1
3
1
1
1
1
2
3
1
1
2
3
1
1
2
1
4
1
1
2
2
2
3
1
1
1
1
1
1
1
1
7
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
3
1
1
1
1
1
1
4
1
1
1
1
1
1
4
3
2
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
1
1
3
1
2
1
1
1
2
1
1
3
9
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
10
2
3
3
2
1
1
1
1
3
22
1
9
2
1
1
1
1
2
1
1
2
1
1
1
7
3
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
2
2
2
1
18
3
3
1
1
1
5
2
1
1
1
1
2
4
1
2
1
1
4
2
1
2
1
2
1
2
1
1
2
1
2
6
1
4
3
2
1
1
3
1
1
2
1
4
1
1
1
1
1
4
1
1
1
4
6
19
6
2
1
3
1
1
1
1
1
1
1
2
3
1
1
33
1
1
2
1
5
23
4
1
1
1
1
3
1
5
2
1
1
1
1
36
1
2
2
80
2
1
1
1
2
703
1
1
2
1
2
1
1
1
1
1
1
1
4
3
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
5
1
1
1
7
3
5
1
6
2
1
1
26
1
1
1
24
18
2
1
1
4
4
1
2
1
1
2
1
1
1
12
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
8
2
1
3
137
1
1
1
9
2
20
3
2
1
1
1
2
1
1
1
3
2
3
2
12
1
1
4
1
1
1
1
2
1
1
1
4
5
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
5
4
1
1
1
2
1
4
1
3
2
1
1
1
8
1
2
1
1
5
15
1
1
1
1
1
1
2
1
8
1
1
1
1
1
1
1
2
6
1
3
1
1
1
5
1
28
1
1
1
3
3
2
1
2
2
1
1
1
2
1
2
1
4
1
3
1
9
1
38
1
3
4
35
1
1
3
9
3
1
1
2
1
2
7
7
2
1
3
1
2
1
2
1
1
3
1
4
1
1
24
1
4
1
1
5
2
2
1
7
7
1
2
1
1
2
2
3
1
1
1
1
1
1
2
1
1
1
4
2
9
1
1
2
4
1
2
26
10
1
11
1
1
2
2
2
1
1
4
1
1
8
5
2
2
1
2
1
5
1
4
1
1
2
2
1
14
1
1
1
2
6
3
2
1
1
2
1
2
1
2
7
2
3
1
18
1
1
2
4
1
1
1
178
3
4
11
1
1
1
2
1
1
4
1
1
1
68
1
10
2
8
3
2
1
1
3
1
1
4
1
55
3
6
2
3
1
1
1
18
8
1
1
1
1
1
10
1
1
1
1
2
1
1
1
4
1
2
1
4
1
1
1
1
1
1
2
3
2
1
1
5
1
1
1
1
1
1
2
3
2
1
27
1
5
2
1
1
2
3
1
1
10
1
1
1
1
3
1
2
2
1
1
5
1
1
1
1
1
1
2
1
2
1
1
2
4
3
14
1
2
1
3
2
9
1
3
6
1
1
1
1
508
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
2
1
1
2
1
1
1
5
1
4
6
2
1
10
1
1
1
2
16
1
1
1
2
1
1
1
1
1
2
6
3
30
5
1
1
2
1
1
1
5
1
1
2
2
1
1
1
2
2
4
1
2
1
1
8
2
4
1
1
3
2
3
1
1
1
1
1
2
1
1
1
2
4
1
1
1
2
1
1
5