1
1
1
1
1
2
1
1
1
1
1
1
1
1
6
1
1
2
1
3
1
1
1
1
2
4
2
2
1
2
1
1
1
2
1
3
1
1
9
1
1
9
2
7
1
1
3
1
3
1
1
1
1
1
3
1
1
1
4
1
1
4
4
1
3
1
1
2
1
2
1
5
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
1
1
1
2
1
1
1
1
1
2
3
4
2
1
2
1
1
1
6
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
4
1
1
1
1
1
1
2
3
2
2
1
2
8
2
2
1
2
2
1
1
5
1
2
3
2
1
7
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
3
27
1
1
1
1
2
1
1
2
10
29
1
2
2
11
1
3
1
1
1
4
1
1
1
1
1
1
1
1
6
1
1
2
3
1
1
1
1
1
2
1
3
3
2
2
1
1
1
8
1
1
2
1
1
4
1
2
3
1
30
1
3
1
2
1
1
1
1
1
1
1
1
8
3
1
1
1
1
1
1
2
1
3
1
3
1
2
2
1
1
2
1
1
1
1
1
1
1
6
1
2
9
2
1
2
2
7
1
1
1
3
3
2
1
3
1
7
1
1
1
1
2
14
3
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
5
5
10
1
1
1
1
1
2
5
2
3
2
1
2
2
1
2
1
3
1
2
4
3
1
3
1
1
1
1
1
1
1
1
2
1
1
1
5
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
4
1
2
1
1
1
1
2
1
1
2
1
17
1
4
4
2
1
2
1
1
1
1
1
1
1
3
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
8
1
1
1
1
1
2
1
1
2
2
1
1
1
1
3
2
2
1
1
4
1
2
1
1
1
3
1
5
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
3
1
1
2
2
3
2
1
2
4
18
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
5
1
1
1
1
1
1
2
1
8
1
1
1
93
1
1
1
194
1
1
1
1
5
2
3
1
1
2
1
3
4
2
7
3
2
4
1
1
1
2
1
2
1
4
1
1
13
1
11
6
1
4
2
1
2
1
1
7
1
1
181
1
2
2
3
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
3
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
2
1
9
1
2
1
2
1
2
7
3
1
1
2
12
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
4
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
100
2
1
1
1
2
3
1
2
2
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
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
5
1
5
3
1
2
1
1
5
9
1
2
1
1
1
1
1
4
4
1
2
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
2
1
1
3
2
2
2
1
1
4
1
1
1
1
1
1
3
1
2
1
1
1
9
1
1
3
2
44
3
1
2
1
1
1
1
1
1
1
1
13
5
2
2
1
1
1
1
2
1
1
2
29
1
1
1
1
1
11
1
1
1
2
1
11
1
1
3
1
5
1
98
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
2
1
1
1
1
3
1
8
1
2
1
8
2
1
2
1
1
1
2
3
1
1
2
2
1
3
1
1
1
1
3
3
1
1
5
1
6
1
24
1
1
1
2
1
6
3
1
1
1
1
4
1
1
1
195
1
1
1
1
1
1
1
4
2
3
1
1
3
1
3
11
2
1
2
1
1
1
1
11
1
1
1
1
4
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
19
2
3
6
5
1
3
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
9
1
1
2
3
4
2
1
2
1
1
1
2
1
1
1
1
1
1
2
19
3
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
8
1
1
1
2
1
1
1
1
3
1
55
1
1
1
1
1
6
1
1
1
6
1
1
1
1
3
1
1
4
1
1
2
1
3
3
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
14
1
1
1
34
1
1
1
1
3
6
3
1
8
1
2
1
4
1
1
5
1
1
1
1
1
1
1
3
1
1
4
1
2
1
2
1
1
1
1
4
1
1
1
3
1
2
1
1
1
1
2
1
1
1
8
4
1
2
3
1
1
24
3
2
1
2
1
3
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
1
1
1
6
1
1
2
1
1
1
1
2
1
1
1
1
8
1
1
3
2
1
1
5
1
1
1
1
1
52
3
1
1
1
6
1
1
2
4
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
4
1
1
2
3
1
1
4
1
1
4
1
1
1
1
5
1
1
1
1
2
1
1
2
1
1
1
4
1
1
1
1
1
1
1
2
1
2
1
1
7
5
1
1
1
1
1
1
2
1
1
4
2
1
6
1
3
1
2
1
2
1
1
1
4
1
1
3
1
1
3
5
1
2
8
4
1
1
1
1
2
1
1
15
1
1
3
1
1
1
1
3
1
1
1
2
6
2
1
1
1
1
1
1
2
1
1
1
4
1
2
2
1
1
2
1
1
1
2
2
2
46
1
1
18
1
1
1
1
1
4
1
2
5
1
1
14
1
1
2
1
1
1
2
1
1
1
1
18
3
1
1
1
1
1
1
1
3
1
1
2
1
1
1
5
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
20
1
1
3
1
1
1
1
3
1
2
1
1
1
1
1
1
1
3
2
2
1
1
2
1
1
1
131
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
509
3
12
1
4
1
3
8
1
1
1
2
1
1
1
1
1
2
1
1
7
1
1
1
1
3
2
1
1
1
1
1
1
6
1
1
1
2
1
1
2
1
1
4
2
5
1
1
1
1
4
2
1
3
1
1
4
1
2
1
4
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
5
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
2
10
1
8
1
4
2
1
1
1
1
1
4
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
3
5
6
3
1
1
2
1
1
2
2
3
2
1
2
1
3
1
1
1
2
2
1
1
2
1
2
3
3
92
2
3
1
1
1
5
1
1
1
3
1
1
2
1
1
3
1
1
1
1
2
1
1
1
1
4
1
1
1
1
10
1
1
2
1
2
1
2
1
2
3
1
4
1
1
1
1
5
1
1
1
1
1
1
5
1
1
1
2
1
10
5
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
4
4
1
1
1
1
1
8
3
1
1
1
1
1
2
3
1
1
2
1
2
1
1
1
1
1
3
1
4
2
2
1
1
1
1
1
1
4
1
1
1
1
3
1
1
1
2
1
12
1
5
1
22
13
2
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
15
1
3
1
1
1
1
3
1
1
1
64
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
2
1
5
1
6
2
1
1
1
2
1
4
2
2
1
2
1
1
1
6
1
1
1
1
4
1
1
1
1
1
6
3
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
2
1
1
1
1
2
2
1
2
1
2
1
2
1
9
1
1
1
1
2
2
1
1
3
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
3
4
2
2
1
1
1
1
1
2
1
1
1
1
3
7
1
1
1
1
1
1
2
1
11
4
1
2
2
1
1
1
1
1
1
4
1
1
3
25
3
2
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
2
1
1
1
2
4
1
4
15
3
13
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
19
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
3
1
1
1
1
1
1
1
1
2
1
2
6
1
4
1
1
1
2
8
3
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
3
7
4
496
12
1
12
1
2
2
1
48
1
5
1
1
1
1
1
2
1
49
1
2
2
1
1
13
1
1
3
1
1
3
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
1
1
2
1
2
1
1
1
1
1
1
1
3
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
3
2
1
1
2
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
2
477
1
1
1
1
1
1
1
1
1
1
1
2
1
1
6
6
3
1
1
1
1
2
1
5
1
1
1
1
1
1
1
1
1
3
1
1
1
2
5
1
2
1
1
1
1
1
127
1
1
1
1
1
9
1
4
1
1
2
2
1
2
2
1
1
2
1
1
4
3
2
1
7
1
1
1
4
1
1
65
1
1
1
1
1
1
1
2
88
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
4
4
3
2
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
3
1
4
1
3
1
1
1
1
1
1
1
7
1
1
1
4
1
92
1
1
1
1
1
1
1
1
1
6
2
2
1
1
1
1
1
3
1
1
1
1
1
2
1
3
1
1
2
40
1
2
1
1
2
2
1
1
168
5
1
1
2
1
1
2
1
1
2
2
2
1
2
3
1
1
2
1
2
8
4
3
1
1
3
1
1
2
2
1
1
1
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
6
1
1
1
1
3
5
1
1
3
1
2
1
5
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
5
2
1
1
1
1
5
4
1
1
1
1
1107
3
2
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
6
1
1
1
3
3
1
1
1
1
4
3
1
1
1
2
1
3
1
1
1
1
3
1
3
1
1
1
7
1
20
1
1
2
2
1
1
1
1
1
1
3
133
2
1
1
1
1
1
1
1
4
2
2
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
5
2
1
1
1
3
1
1
1
1
1
1
4
2
3
2
1
1
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
3
1
1
1
1
1
9
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
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
17
1
1
1
1
2
6
2
2
1
1
2
1
1
1
1
1
1
1
1
3
1
2
1
4
4
1
2
1
1
4
1
1
1
168
1
1
13
2
2
1
2
1
2
2
2
1
1
1
1
3
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
3
1
2
2
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
3
1
8
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
342
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
9
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
5
1
1
1
1
3
1
1
3
1
2
3
1
3
2
25
1
2
1
1
1
8
1
1
1
1
1
1
1
2
4
1
1
1
1
2
6
35
1
4
1
1
1
5
2
1
1
2
1
1
2
1
1
2
3
3
1
12
1
1
1
4
1
2
1
1
1
3
1
2
2
3
6
3
6
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
3
1
3
2
1
1
2
2
2
1
1
1
3
15
1
3
2
1
1
1
1
1
1
1
1
2
1
3
1
1
14
1
1
1
1
3
1
1
1
1
14
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
4
1
1
2
1
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
2
1
2
3
2
2
1
1
2
1
1
1
2
1
7
75
1
3
1
2
4
1
3
2
1
1
1
1
1
1
2
1
1
1
6
1
3
1
1
1
1
1
1
1
3
1
1
1
1
1
3
2
1
4
1
2
1
4
1
4
1
2
1
776
6
1
1
1
1
1
1
1
1
1
1
39
1
1
1
1
1
1
3
4
2
1
4
1
1
2
1
2
2
1
1
3
2
1
2
1
14
2
8
2
2
3
2
1
314
5
1
3
1
1
3
1
1
1
3
1
1
1
1
1
3
1
1
1
1
1
1
4
1
1
1
2
3
2
1
2
1
2
1
1
1
4
1
1
1
2
1
1
1
2
3
1
7
4
1
1
1
18
1
1
2
3
3
3
1
5
4
95
1
1
1
1
1
1
1
3
7
3
1
1
1
20
2
3
1
1
5
2
1
1
1
1
2
1
4
1
4
1
1
1
3
1
1
1
4
5
1
1
1
1
1
1
1
3
4
2
3
1
1
1
2
1
1
2
84
1
8
1
3
2
1
2
1
1
1
1
2
1
4
2
1
1
2
1
4
1
1
1
2
1
1
1
1
1
105
6
2
1
2
1
1
2
84
1
4
7
5
3
1
424
1
1
1
1
1
1
1
1
1
1
1
2
1
2
11
3
3
1
1
1
1
1
1
2
1
1
24
2
1
1
2
1
1
330
3
1
2
1
8
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
3
2
1
4
1
1
1
19
2
2
1
2
1
3
1
1
1
1
1
1
1
1
3
2
1
2
1
2
1
26
1
1
1
1
5
1
1
2
1
1
2
2
1
1
3
2
2
5
1
5
1
1
1
8
1
1
1
1
1
1
1
1
2
3
1
1
2
1
2
1
2
1
1
12
11
1
1
1
1
2
1
1
2
8
5
1
3
1
3
4
1
3
1
3
1
1
7
1
1
2
1
2
3
1
2
8
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
3
1
5
1
4
1
1
1
1
11
1
1
3
1
3
1
2
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
3
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
6
1
4
7
1
2
1
1
1
1
2
5
3
4
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
6
5
1
1
1
2
1
2
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
4
1
1
1
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
3
1
3
1
1
1
1
2
1
1
3
1
2
1
1
4
2
3
1
1
3
1
1
1
1
1
3
1
1
3
1
1
2
1
6
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
8
1
1
2
1
1
2
1
1
1
1
8
2
1
1
2
1
1
1
2
10
3
2
1
1
1
1
1
2
7
1
1
1
1
1
1
2
1
1
1
2
3
2
3
1
6
1
1
2
5
1
1
2
1
3
5
1
1
4
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
7
1
1
3
13
2
1
1
3
1
1
1
1
4
1
2
1
1
3
2
1
1
2
2
1
1
1
4
3
1
1
17
6
1
4
2
1
2
1
1
1
6
1
1
3
2
1
1
2
1
1
1
1
1
1
1
6
1
2
2
2
2
1
2
2
1
1
1
6
3
1
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
1
1
2
9
1
1
1
1
7
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
5
1
1
1
1
3
1
1
2
1
1
1
2
1
1
1
48
1
1
1
1
1
2
1
2
3
4
2
1
1
1
1
6
1
1
1
38
1
1
1
1
1
1
3
3
1
2
4
2
1
1
1
1
21
1
2
1
1
1
1
2
2
1
261
1
1
1
1
1
2
3
6
2
2
2
2
1
21
1
2
1
6
2
1
3
2
1
4
3
1
2
1
1
2
1
1
1
1
1
2
2
1
2
4
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
3
1
1
3
1
2
1
4
2
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
9
2
3
2
1
1
1
3
1
1
4
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
1
1
3
1
1
1
4
1
1
1
3
3
5
3
1
1
6
1
1
1
2
1
1
1
1
2
1
1
3
1
1
1
1
2
1
3
3
1
1
2
1
1
1
1
74
1
2
6
1
6
1
2
2
7
1
1
4
3
5
1
1
1
23
1
2
2
24
10
2
3
8
1
1
2
1
1
1
5
1
18392
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
2
2
2
1
1
6
2
2
9
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
7
1
2
1
1
2
1
1
1
1
8
2
1
1
1
1
1
2
3
1
1
1
9
11
3
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
9
8
1
2
1
2
1
1
5
1
1
1
1
1
1
1
4
1
2
1
1
1
8
3
1
1
3
2
2
1
3
54
2
1
1
1
1
2
1
1
6
3
2
1
1
2
13
3
2
1
11
2
1
1
1
3
142
1
1
1
1
1
1
6
1
7
4
11
1
3
1
1
1
3
3
2
1
3
1
1
1
2
1
4
7
1
4
1
9
1
1
2
6
1
1
9
5
2
2
1
1
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
2
1
1
20
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
3
4
1
3
1
1
1
1
1
6
15
3
2
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
4
1
1
2
1
2
1
1
1
1
1
1
5
4
1
2
2
1
1
3
2
1
2
3
3
11
1
1
1
1
2
1
122
4
1
2
6
1
3
1
5
2
1
1
1
2
4
1
1
1
2
1
2
1
1
1
1
8
2
23
1
1
1
2
1
1
1
1
1
2
1
2
1
4
2
1
1
1
2
1
1
1
1
2
1
2
2
1
3
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
2
2
1
11
1
1
1
190
3
1
1
1
7
1
1
2
1
1
1
2
1
1
1
1
1
1
8
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
269
1
1
1
1
1
1
5
4
19
1
1
1
1
3
1
20
1
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
66
9
1
1
1
2
1
2
1
1
23
5
2
3
1
4
1
1
2
1
1
1
1
8
2
1
1
3
1
2
2
1
1
1
1
1
2
12
3
2
2
1
1
1
1
1
1
1
2
3
1
1
5
1
1
2
1
1
1
1
2
4
3
1
1
1
2
1
6
1
3
1
2
1
2
1
1
1
1
1
1
1
1
1
1
9
1
2
1
4
4
2
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
4
1
2
2
1
1
1
5
1
1
1
2
1
2
2
1
1
2
1
1
1
1
3
1
3
1
1
2
2
1
1
1
1
2
7
1
1
1
1
1
1
1
1
2
2
1
2
1
1
3
2
1
1
2
103
1
1
3
1
1
1
1
1
7
1
3
1
1
1
1
1
1
1
1
2
6
5
4
1
1
1
1
1
1
3
1
2
2
14
1
1
2
2
1
3
1
1
1
1
1
6
1
2
1
1
2
2
2
14
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
3
1
1
20
2
5
1
1
1
2
1
1
6
2
1
1
1
1
1
1
2
1
2
13
2
2
1
1
1
1
6
2
1
4
1
1
1
30
2
6
7
3
2
1
1
1
4
1
1
1
1
1
1
2
1
2
10
1
2
1
1
8
2
1
1
1
3
1
3
1
4
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
4
8
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
3
1
5
1
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
16
1
1
1
1
5
1
1
3
1
1
1
8
1
5
2
1
1
1
3
1
2
1
1
1
21
2
3
4
3
1
2
1
3
2
1
1
4
1
1
1
1
1
2
1
1
1
1
5
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
4
1
1
1
1
1
10
2
3
1
1
1
2
1
4
8
1
2
1
1
1
2
1
1
6
11
7
6
4
3
1
1
1
1
6
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
2
1
3
11
1
1
1
1
1
1
3
1
1
3
1
2
1
1
3
4
1
1
3
1
3
3
1
1
1
2
1
4
1
26
2
2
1
1
1
1
1
6
3
1
1
1
1
1
6
1
1
1
1
1
1
2
2
1
3
1
1
1
2
2
4
1
1
1
2
1
1
1
1
1
1
1
2
2
1
3
1
3
1
1
1
1
1
238
4
2
18
1
1
2
1
1
1
1
1
1
2
1
4
5
19
35
19
2
38
8
2
1
3
2
3
1
2
1
1
1
1
1
1
1
1
1
4
1
1
2
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
2
2
3
2
1
7
5
1
1
1
1
1
1
2
1
5
1
1
1
1
1
1
1
3
1
1
1
1
5
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
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
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
5
1
1
4
1
2
1
4
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
4
1
1
4
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
3
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
6
2
1
1
1
1
1
1
1
1
1
1
3
2
3
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
6
1
2
1
1
1
1
6
1
1
1
3
1
3
1
1
1
6
2
1
1
1
2
1
4
1
1
3
1
5
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
4
1
1
2
1
1
2
2
4
1
2
1
1
3
3
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
3
2
1
2
2
1
1
3
4
1
1
1
2
1
1
1
3
2
4
1
1
1
2
1
4
1
2
1
1
1
1
1
2
2
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
3
1
1
1
2
5
1
1
1
1
1
2
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
6
2
1
3
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
6
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
3
1
1
2
1
1
1
2
1
1
2
1
2
2
9
1
2
1
1
1
3
2
2
1
2
1
1
1
2
2
1
3
1
1
1
1
1
1
1
1
1
1
5
3
1
1
2
1
2
1
1
1
1
1
1
5
1
2
1
1
1
1
2
1
1
1
1
1
1
6
1
1
2
1
1
3
1
1
1
1
2
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
1
3
1
2
1
1
1
1
1
2
2
3
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
3
1
2
1
1
1
3
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
3
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
3
3
1
1
1
1
1
188
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
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
4
1
3
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
4
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
3
1
9
1
1
1
4
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
2
1
1
8
1
6
2
1
1
5
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
5
1
1
1
2
5
1
2
1
1
1
1
15
1
1
2
1
1
2
1
1
3
2
1
1
1
5
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
7
1
3
3
1
1
2
5
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
6
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
253
264
1
1
2
1
1169
2
4
1
1
1
1
1
1
142
1
1
1
1
1
2
3
2
7
2
1
1
1
4
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
2
1
2
1
1
3
1
4
1
2
1
1
1
8
8
1
3
1
1
1
2
3
1
1
1
1
1
1
12
1
1
4
1
11
1
2
1
1
1
1
2
1
1
1
2
3
3
1
1
1
1
1
54
2
3
1
1
1
2
1
2
1
1
8
2
1
4
1
6
1
1
1
1
1
1
1
1
1
1
1
4
3
3
2
1
1
1
1
3
1
1
1
1
1
2
2
1
1
1
9
5
2
5
1
24
2
6
6
3
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
4
1
1
3
1
1
12
4
2
2
2
1
5
1
1
1
1
1
4
1
1
1
8
7
3
1
1
1
1
2
4
2
3
1
1
1
1
14
1
3
3
1
1
1
4
1
1
1
1
1
1
2
3
1
1
1
1
1
3
27
2
1
1
2
6
7
1
1
2
1
2
4
1
2
1
3
3
1
1
3
1
1
1
1
6
1
2
2
1
1
2
1
1
3
5
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
1
4
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
4
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
2
4
4
1
1
1
5
1
1
1
2
1
1
5
1
1
1
3
3
1
2
1
1
2
5
1
1
1
8
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
3
1
1
1
25
2
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
5
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
3
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
4
1
1
4
1
1
4
1
1
2
1
1
1
1
26
7
4
2
3
2
4
6
2
4
3
1
6
1
1
1
1
1
1
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
6
3
1
3
1
1
1
1
12
1
1
1
1
1
1
2
9
1
3
1
1
4
1
1
1
1
2
18
1
1
2
1
1
1
1
2
1
1
3
1
3
1
1
3
2
1
1
1
1
1
5
1
1
1
5
1
4
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
6
4
3
1
2
1
2
2
1
2
1
113
1
2
2
1
1
44
17
2
2
1
1
1
1
1
2
2
2
1
1
2
1
1
4
1
2
1
2
1
4
2
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
2
3
1
16
1
1
1
1
1
1
1
1
1
3
2
2
2
7
7
1
52
4
3
1
2
1284
2
1
1
2
1
1
51
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
3
1
3
1
1
3
3
1
1
1
1
2
1
3
4
4
1
3
2
1
1
1
1
1
1
5
4
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
3
1
9
3
1
1
1
1
1
1
3
1
1
2
1
10
3
2
6
1
1
3
1
2
1
1
1
1
1
1
3
2
3
1
8
1
2
1
1
6
2
1
2
3
1
3
1
1
1
1
5
4
1
5
5
2
1
1
1
7
5
2
1
2
12
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
2
2
1
1
1
1
21
1
1
1
1
1
2
2
1
2
4
1
4
3
3
1
1
1
1
1
1
9
6
1
2
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
2
1
1
6
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
3
1
3
7
2
2
2
1
1
1
2
7
1
1
7
2
1
1
4
1
1
1
1
1
1
1
2
1
1
8
1
1
1
1
2
1
2
1
37
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
7
1
4
3
2
1
3
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
3
3
1
1
1
1
4
4
1
1
1
1
1
1
3
5
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
3
1
1
2
1
7
1
2
1
1
1
1
1
2
1
15
1
1
2
1
4
2
2
1
1
1
1
7
2
1
2
4
1
1
2
1
1
1
1
1
1
2
3
1
2
1
1
3
2
3
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
5
1
1
1
1
2
2
3
2
1
5
2
1
3
1
5
1
2
2
1
3
1
12
2
4
1
1
1
1
1
1
1
1
1
2
3
2
1
2
2
1
1
1
1
1
6
2
1
1
7
1
2
8
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
5
1
1
5
4
1
1
5
1
1
1
4
1
4
1
1
5
1
4
2
2
1
1
4
1
1
1
1
2
4
4
1
1
2
2
1
7
2
1
1
1
1
1
1
1
2
1
6
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
3
1
5
2
4
3
1
1
1
3
2
1
3
1
1
2
1
1
1
1
1
1
1
4
1
3
1
1
1
5
1
1
1
2
1
1
1
1
3
1
1
1
4
16
3
2
1
1
1
2
1
2
1
1
1
4
1
5
1
1
1
3
2
1
1
1
3
6
1
1
1
1
1
2
1
1
1
1
1
2
1
3
2
1
1
1
1
6
1
3
1
1
1
1
1
2
1
2
1
1
1
2
1
3
1
1
1
2
1
6
3
2
3
1
1
1
1
3
4
2
1
1
1
2
1
1
3
2
1
1
1
2
2
2
1
1
1
1
1
2
1
2
3
1
1
1
1
1
2
2
6
1
2
19
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
7
4
2
1
2
4
3
1
1
1
1
3
1
1
2
1
1
2
17
1
1
9
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
19
2
2
1
2
2
1
1
1
5
5
2
2
1
1
1
1
2
1
5
1
1
1
1
1
4
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
3
2
2
1
1
7
3
1
1
1
2
3
1
13
3
8
2
1
1
3
1
1
1
28
1
1
3
4
1
1
22
4
1
1
1
3
1
2
5
3
1
32
4
1
2
84
2
1
1
1
1
1
1
1
698
2
1
1
2
1
1
1
1
1
1
2
3
1
1
1
4
1
1
1
3
1
2
1
3
3
1
1
1
1
1
1
1
14
4
1
1
1
2
1
30
4
1
1
19
11
1
1
6
2
2
1
7
2
1
1
1
8
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
2
1
1
1
2
13
1
1
1
137
1
3
1
5
20
4
3
1
1
1
1
1
1
1
1
1
2
3
1
1
3
8
1
4
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
2
1
1
2
2
1
3
1
3
1
1
1
1
3
1
1
2
5
1
1
1
2
1
1
5
1
2
1
2
5
1
26
2
2
1
1
1
1
2
7
2
1
1
1
1
1
1
12
1
3
1
1
1
6
18
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
3
6
1
1
1
7
27
1
3
1
3
3
5
3
1
1
1
2
1
1
1
7
3
2
1
1
6
2
1
4
2
2
1
6
3
1
20
1
1
4
1
2
1
12
4
2
4
7
2
1
6
1
1
1
1
2
1
2
2
4
5
1
2
1
1
2
2
3
9
3
2
3
5
19
1
5
10
1
2
2
3
4
2
3
1
1
2
3
1
1
1
1
1
1
1
2
9
3
1
1
3
2
1
18
4
3
4
2
1
1
1
1
2
3
2
1
1
1
1
7
2
3
4
1
1
1
1
9
1
1
3
2
1
2
3
1
2
3
109
1
6
1
1
6
1
1
1
2
4
1
69
1
1
6
3
1
1
11
2
4
2
54
1
3
4
1
1
1
1
1
3
1
1
9
4
1
1
1
2
1
17
1
1
1
3
1
1
1
1
1
4
1
2
1
4
2
1
1
2
1
6
1
2
1
3
1
1
1
2
1
2
1
1
1
38
7
1
1
4
4
2
1
4
2
2
9
1
1
1
1
2
3
1
2
1
1
1
4
5
6
1
2
3
1
2
1
1
2
17
8
1
1
3
3
1
1
1
2
477
1
2
1
1
1
1
1
3
2
3
1
1
2
1
8
1
2
1
1
1
4
3
2
5
1
1
1
4
3
2
2
1
1
1
2
1
1
1
1
2
18
1
1
2
1
1
1
3
1
1
1
1
2
1
1
22
3
1
3
2
1
4
1
3
2
1
1
2
1
1
4
1
1
3
1
1
4
4
5
1
3
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
4
1
1
2
5
1
1
2