77
40
39
66
48
52
33
27
39
36
46
39
46
53
43
33
61
46
59
45
47
37
52
22
31
31
34
16
30
39
27
28
51
30
38
42
28
27
25
36
39
20
19
35
24
33
14
25
25
22
35
18
28
18
24
23
38
43
28
25
28
19
65
28
34
46
41
23
25
22
40
28
24
33
30
19
42
39
37
45
48
31
12
24
24
34
24
22
11
13
28
17
18
19
45
24
15
15
19
28
18
29
22
37
27
25
20
20
17
30
14
34
17
21
23
35
18
24
15
18
17
20
15
21
31
16
31
28
22
9
30
15
21
20
29
23
22
18
23
30
20
19
18
19
32
13
22
13
18
20
47
13
13
11
21
33
13
17
13
15
20
12
21
29
15
12
22
21
19
15
24
18
30
12
23
21
16
18
44
27
14
13
26
23
16
10
17
10
14
15
17
20
15
17
14
35
34
41
28
26
21
27
35
25
21
21
19
8
11
18
15
34
15
41
22
12
12
24
28
17
17
19
29
20
28
17
26
17
13
35
18
21
13
8
28
30
10
14
27
24
22
20
16
22
22
15
19
12
13
18
11
17
17
23
22
20
23
16
8
13
8
15
19
22
12
19
22
17
14
17
14
8
22
16
17
22
19
20
26
11
14
13
17
10
15
18
20
13
19
25
23
12
14
11
15
13
17
30
10
17
15
11
24
14
11
11
16
5
12
13
24
18
19
26
8
18
12
9
21
15
13
12
16
14
22
15
12
29
22
11
26
12
10
7
8
13
15
26
8
8
12
5
9
12
13
18
11
9
7
14
14
17
18
10
18
15
21
19
9
17
25
14
10
10
16
18
6
13
16
22
10
9
16
10
14
18
9
28
13
18
12
13
10
10
15
16
21
26
16
19
10
5
14
13
42
28
12
10
13
12
16
10
20
12
17
14
8
11
20
11
8
28
7
17
16
18
14
10
11
8
10
6
12
14
16
16
15
8
9
16
18
19
11
12
6
9
8
17
19
15
14
9
8
16
26
31
8
14
20
20
6
29
9
20
10
21
21
25
16
10
20
23
32
13
16
12
14
15
23
16
10
14
16
13
16
12
12
8
16
21
22
9
18
12
7
13
30
7
17
19
5
13
30
7
28
8
17
25
16
15
11
5
11
19
13
12
16
10
8
9
18
12
9
13
23
14
17
9
12
17
22
7
12
17
11
9
14
17
13
13
17
19
6
8
15
15
14
9
12
14
13
13
14
12
17
15
12
18
13
9
12
15
25
5
8
13
9
9
3
18
9
3
24
13
17
17
13
29
16
16
19
19
10
7
10
10
5
11
11
12
10
7
13
7
10
14
12
32
10
19
11
8
17
18
17
26
13
8
11
10
8
20
15
21
19
16
14
18
6
9
9
13
9
12
13
13
7
20
10
10
14
10
10
4
16
20
5
13
7
7
14
19
4
10
13
9
9
10
11
10
12
7
16
8
7
14
33
12
5
29
16
11
15
10
6
11
21
12
8
12
11
3
17
16
31
19
9
8
9
19
12
7
18
16
9
23
12
10
16
8
14
5
8
13
9
16
27
15
13
11
8
8
17
10
13
12
22
9
11
14
11
8
14
13
6
8
11
29
22
8
16
23
7
13
9
9
35
13
20
16
14
34
11
16
10
7
9
17
14
12
6
6
13
27
8
11
13
8
8
9
5
9
13
13
9
12
15
14
20
4
17
5
12
36
25
10
19
10
5
10
13
16
11
9
18
7
12
5
13
11
15
3
19
9
7
26
10
12
15
5
6
8
10
4
11
13
20
10
23
14
18
3
24
15
14
10
7
12
9
13
8
13
13
13
11
5
11
9
4
11
12
7
17
8
10
5
9
12
12
7
8
16
15
24
11
9
10
12
11
14
6
14
22
11
8
5
10
10
13
12
10
5
4
13
16
10
10
13
28
7
9
16
8
10
18
6
19
10
13
9
18
16
19
15
4
17
20
9
17
12
19
12
6
15
12
23
4
15
27
19
11
11
8
11
8
10
5
7
17
7
10
10
12
5
18
4
9
7
22
13
20
8
6
16
6
3
13
10
14
9
14
7
15
6
10
20
12
8
7
9
14
13
7
9
11
9
11
8
17
14
6
5
12
5
18
13
8
7
3
13
9
9
10
8
17
7
10
10
10
6
8
7
15
9
7
7
11
4
9
8
18
16
7
7
12
20
15
7
8
10
6
18
5
4
20
14
6
8
10
8
8
19
4
14
17
7
6
10
12
5
6
13
12
4
16
9
18
13
20
10
12
9
11
4
15
5
13
14
6
13
12
13
7
11
8
15
10
7
10
16
7
11
12
9
13
9
8
7
6
10
13
5
9
4
5
17
14
18
12
9
5
9
7
11
11
10
12
8
9
19
12
9
14
10
10
19
12
9
15
9
15
11
8
17
5
15
7
18
6
15
6
11
9
14
6
12
2
13
5
5
12
14
9
4
5
6
5
14
12
8
3
15
6
9
4
11
19
9
6
8
7
15
10
20
18
9
14
12
6
16
22
6
28
15
8
12
8
10
6
16
8
3
10
5
11
9
15
11
6
4
13
12
16
12
8
7
9
7
9
6
7
12
6
8
10
9
9
13
10
10
14
15
2
6
2
9
25
6
10
9
18
6
8
11
12
7
15
6
15
11
15
5
8
10
11
8
4
11
5
12
7
10
4
7
10
7
16
22
9
15
6
7
9
7
11
14
16
23
13
6
30
7
6
6
12
9
6
4
5
9
8
9
12
12
7
9
6
12
19
3
11
10
11
18
6
12
15
20
7
8
9
7
12
16
10
10
5
16
8
10
6
8
11
6
7
8
9
12
19
6
12
7
9
4
3
12
10
5
6
9
19
6
19
9
6
9
18
29
11
9
6
12
8
10
7
15
7
9
9
11
11
7
3
17
9
9
8
5
15
24
24
16
10
19
8
8
7
11
8
8
6
5
17
12
9
14
10
7
2
5
5
5
7
3
8
15
7
7
11
5
6
18
11
5
20
8
9
9
8
5
9
9
6
11
7
8
8
18
9
5
11
2
6
7
8
12
8
6
8
8
8
12
12
6
9
8
11
7
12
4
5
8
17
6
16
6
11
4
6
13
15
3
6
4
5
15
5
7
17
17
21
2
12
2
8
4
7
20
9
6
4
6
6
8
7
7
14
8
6
8
6
5
4
28
7
14
15
5
8
10
6
10
3
12
10
4
11
13
5
5
7
5
8
8
5
5
8
10
5
6
14
17
14
6
2
11
24
5
6
9
17
5
11
5
11
8
7
15
13
9
4
8
11
7
8
9
8
11
6
7
7
9
9
12
7
17
10
9
21
9
6
11
8
4
20
15
8
7
4
13
10
6
6
2
5
6
9
8
9
5
5
9
9
12
3
6
8
7
12
9
13
13
12
5
15
13
6
10
15
14
11
9
4
11
7
7
20
8
9
9
11
8
7
9
4
7
11
8
8
10
1
9
9
9
10
8
4
10
9
9
5
9
12
34
4
5
7
14
12
14
7
6
11
7
6
4
10
9
18
12
10
14
8
8
4
12
9
3
10
6
8
3
5
10
12
7
9
2
4
11
9
9
10
7
13
6
6
13
5
5
8
2
2
6
3
10
9
8
9
8
2
5
4
8
3
11
11
14
13
15
14
15
12
5
5
7
6
4
3
15
7
9
18
5
5
4
8
10
8
12
10
4
6
12
12
9
2
8
9
11
24
10
7
7
7
8
9
8
18
8
8
4
7
17
2
5
10
8
7
6
4
8
6
5
5
12
1
6
10
5
10
14
5
15
5
5
8
3
5
12
1
5
11
9
6
6
7
5
5
7
8
4
6
3
6
6
6
6
7
10
10
7
7
4
7
10
5
13
9
9
8
7
4
7
10
10
14
10
8
10
4
7
10
1
7
10
8
5
7
6
9
6
8
7
7
5
10
13
5
3
16
9
6
2
5
7
4
13
5
6
20
6
11
10
12
3
12
8
1
5
8
9
16
1
5
8
10
9
10
5
5
7
10
5
6
8
10
4
9
10
13
12
2
10
10
12
11
7
5
1
13
9
4
2
10
7
11
11
5
4
4
6
8
5
9
3
1
5
4
6
11
12
7
10
6
7
8
13
2
7
4
4
5
3
7
7
4
13
6
4
13
14
6
8
6
3
6
6
16
6
6
8
8
7
10
7
10
9
4
10
14
7
13
5
9
2
5
12
10
12
14
1
19
9
9
5
1
4
7
7
8
4
9
6
6
12
8
11
2
5
7
6
17
10
27
12
5
8
16
12
10
5
8
2
8
9
7
11
7
8
8
10
4
7
26
2
2
5
6
8
7
9
14
5
7
5
12
15
5
11
6
12
6
8
16
12
6
8
10
5
21
11
10
6
5
5
3
9
16
6
4
3
15
5
2
5
13
14
2
3
2
15
10
8
4
10
8
8
15
6
8
8
2
5
3
13
10
7
5
5
8
3
8
6
4
8
8
4
11
8
7
5
6
8
12
9
5
3
3
4
8
3
3
12
13
2
7
5
6
7
4
8
6
6
7
6
7
8
4
10
5
5
12
10
4
8
3
10
6
12
5
7
4
9
7
3
11
3
9
9
5
8
3
5
4
11
2
14
6
6
4
5
10
12
7
6
7
14
15
8
6
16
7
3
7
5
12
14
6
8
7
6
2
8
14
14
11
7
5
5
2
10
3
9
5
2
4
6
8
17
9
10
4
15
6
10
4
5
5
2
6
10
10
5
7
7
12
5
4
8
21
5
11
8
7
0
11
9
10
0
5
7
7
3
3
8
13
6
5
4
9
5
6
17
6
18
8
16
13
5
14
9
14
16
4
5
4
8
11
8
6
5
22
8
4
4
6
5
17
2
2
6
5
3
2
5
5
13
14
12
10
5
2
10
18
2
8
5
13
14
4
22
10
15
12
7
8
6
4
8
5
15
12
12
5
4
4
8
8
7
10
2
8
8
11
5
3
9
7
12
9
10
6
5
13
7
2
8
2
8
10
4
9
4
6
10
3
6
3
5
10
6
1
6
8
8
10
4
5
6
2
11
4
10
4
3
5
11
7
5
6
4
5
5
7
5
3
7
12
6
4
4
5
3
2
14
11
9
12
8
1
4
6
17
3
7
11
6
8
4
8
6
5
10
7
4
7
7
6
9
7
9
6
11
5
11
12
14
7
7
7
6
5
11
3
15
6
6
8
9
6
4
8
31
11
3
6
7
12
12
18
10
7
6
11
9
15
0
6
6
2
6
6
15
5
7
4
6
34
10
7
4
3
1
2
8
3
2
2
5
6
10
4
7
5
4
13
4
6
2
9
13
4
3
3
6
4
4
6
8
6
4
5
3
11
10
6
6
2
6
6
23
5
4
7
5
4
8
12
0
5
7
4
12
8
6
6
14
7
4
22
7
10
2
5
1
7
6
7
4
10
5
3
6
10
7
17
7
8
23
5
3
7
5
8
9
8
6
7
4
6
3
11
4
9
9
5
6
2
6
4
7
19
6
7
4
4
12
9
24
11
8
9
5
1
5
13
6
3
11
4
13
2
5
3
11
4
10
5
6
6
4
6
8
9
9
13
4
9
2
10
15
4
4
8
8
3
7
4
5
8
5
5
7
4
4
8
6
27
6
9
1
6
6
7
10
5
13
5
5
10
6
8
5
9
6
8
8
6
6
3
7
4
2
1
5
4
6
4
4
8
18
7
4
12
3
2
3
6
8
8
4
3
12
5
5
5
10
3
12
5
8
6
11
11
5
5
1
8
8
5
15
10
5
9
2
6
9
5
7
4
8
7
2
8
3
8
16
5
8
4
7
9
21
16
3
6
7
4
7
6
24
9
3
5
11
6
7
3
7
9
4
8
8
10
12
15
8
4
6
6
7
3
3
8
11
4
6
10
6
4
9
7
14
20
12
16
4
3
6
14
4
7
4
3
8
6
4
7
24
8
10
4
6
6
6
6
7
9
8
8
6
4
4
5
9
6
7
25
12
5
6
9
3
4
6
4
7
11
5
3
6
5
8
7
6
4
11
3
2
7
6
10
9
10
10
4
7
10
14
7
6
2
1
7
6
3
6
3
4
8
8
2
11
4
2
2
5
5
2
3
6
5
5
11
4
7
7
7
2
8
2
5
6
4
4
5
1
7
3
3
9
7
10
3
10
6
5
3
7
11
9
6
3
4
6
7
13
11
5
10
22
5
7
4
12
3
5
4
5
3
11
6
1
2
5
2
7
15
6
9
1
15
9
11
4
3
7
7
8
10
4
0
6
3
6
1
6
10
5
4
10
1
5
8
9
5
5
25
4
3
8
20
4
6
2
5
6
5
24
7
1
9
12
3
8
13
2
7
3
11
7
5
8
4
4
14
9
5
6
4
12
9
8
2
2
13
13
12
7
7
3
13
9
3
3
3
5
7
5
3
2
7
9
8
3
5
3
12
4
8
9
4
4
4
4
7
13
7
6
4
6
10
4
1
7
8
7
7
8
2
3
4
6
11
7
8
3
2
4
7
5
29
4
4
6
13
8
7
6
3
5
5
1
5
6
9
4
9
8
7
1
5
2
6
4
10
5
6
6
4
3
6
1
2
7
5
6
2
3
4
4
8
9
10
5
5
14
7
7
3
8
8
6
3
5
5
5
6
5
7
7
5
1
3
5
6
6
10
8
2
2
8
6
12
10
9
9
4
2
6
4
4
8
4
4
12
10
11
7
3
8
3
2
10
12
14
3
5
7
18
8
10
4
2
2
14
19
5
3
10
6
8
3
5
5
4
5
5
3
6
7
7
1
9
6
6
7
6
4
6
5
7
5
2
6
4
7
8
8
7
4
3
5
4
11
3
2
12
1
2
6
3
4
3
11
5
3
6
18
3
1
11
10
3
8
1
8
6
5
3
9
9
2
8
4
8
4
7
1
5
4
4
2
10
4
5
5
4
5
6
5
12
12
1
4
2
7
7
5
2
5
2
8
5
7
8
2
2
4
1
4
5
2
6
4
15
12
7
2
5
3
3
6
1
7
4
23
5
8
4
4
5
7
3
7
5
8
3
3
12
2
6
6
13
3
7
7
5
2
2
22
6
2
6
8
3
1
13
5
6
6
11
5
19
3
3
13
8
4
4
6
7
14
7
9
6
7
4
9
4
8
4
3
3
5
12
5
5
7
3
6
3
7
4
3
3
10
8
6
3
4
6
6
6
3
3
6
3
5
5
10
18
5
7
7
6
4
14
4
6
3
8
4
5
4
4
6
5
3
6
7
1
3
3
8
6
12
1
5
7
5
4
2
2
9
14
6
5
11
5
1
6
2
13
7
7
11
3
3
2
12
3
5
3
2
7
6
3
3
5
8
9
21
11
5
5
4
9
2
7
5
18
4
7
11
3
2
7
5
7
6
9
7
5
2
6
4
7
10
11
9
5
5
7
5
5
6
5
12
6
2
4
6
4
7
2
6
7
8
10
5
3
11
9
4
4
4
3
6
10
6
3
1
5
3
6
5
9
7
6
4
8
3
9
12
6
2
8
2
9
6
2
6
3
8
3
5
5
6
4
2
5
8
2
2
2
3
7
1
6
2
11
7
6
2
6
9
12
2
3
2
7
5
0
13
7
20
11
11
6
4
6
3
4
4
6
5
1
5
4
6
4
8
12
11
4
12
4
8
3
8
4
3
3
6
9
3
7
2
15
5
3
4
4
1
4
4
10
7
5
5
5
3
4
8
3
14
8
6
3
7
12
8
4
4
2
5
4
7
10
6
10
5
4
3
3
1
5
5
7
4
8
5
5
1
9
4
6
4
11
9
4
32
11
6
5
3
15
9
6
1
4
3
4
3
5
5
4
11
11
1
8
8
0
14
6
8
4
6
7
4
8
9
5
0
2
7
4
9
5
2
4
4
3
2
2
6
6
3
3
5
5
4
3
2
9
3
7
5
4
15
3
6
4
4
5
4
1
9
6
5
2
11
6
16
6
7
8
4
4
2
2
2
4
21
6
4
17
5
10
1
8
4
6
6
4
12
1
13
2
8
6
12
1
2
2
8
5
3
15
4
4
3
7
8
9
2
6
3
4
5
9
3
4
0
19
3
4
2
6
8
10
13
4
9
19
7
10
2
9
4
4
4
5
3
3
3
2
2
15
4
3
6
7
10
6
2
4
5
6
2
3
4
5
7
6
8
10
2
4
1
1
1
1
2
3
4
9
3
13
1
3
10
7
10
8
6
12
5
3
6
3
6
9
2
5
5
10
3
4
5
1
6
3
6
4
9
9
7
5
2
7
3
9
5
6
6
3
3
8
2
3
3
4
5
3
10
17
8
3
1
2
10
1
2
6
17
4
3
5
15
7
3
15
2
4
4
7
2
5
7
3
4
12
9
3
5
6
2
1
1
9
5
7
6
7
6
5
4
15
5
5
13
0
5
7
3
6
4
2
2
9
9
2
2
1
7
3
6
15
4
0
7
4
9
5
6
4
5
7
13
3
2
2
3
6
7
3
9
4
9
5
3
4
6
7
3
4
2
4
3
6
8
2
5
2
4
8
10
13
4
7
4
3
3
6
4
5
7
7
6
5
8
8
4
7
1
2
3
3
10
3
3
4
5
2
6
4
2
8
3
0
3
4
2
6
4
6
4
10
3
3
4
4
4
2
7
3
4
9
12
5
3
4
7
4
7
5
3
7
6
4
2
1
2
3
5
2
2
3
4
12
6
4
9
13
5
3
6
4
14
0
9
5
3
10
5
2
4
1
4
9
3
3
6
0
4
6
5
3
5
5
9
15
2
5
5
1
2
2
2
1
8
4
9
8
9
3
3
1
3
4
3
5
1
11
3
8
4
3
3
5
7
2
7
2
5
1
10
8
2
3
11
6
2
4
4
6
7
6
3
2
14
2
17
13
4
4
4
4
8
4
4
2
2
11
3
6
0
17
2
4
7
2
9
3
7
3
7
7
4
3
0
5
5
5
4
2
4
4
5
5
14
12
4
10
7
1
3
3
2
9
7
3
5
6
1
6
3
4
3
12
5
6
11
5
5
4
4
5
9
2
5
2
8
5
10
8
5
3
3
5
8
5
2
4
4
2
3
5
8
6
7
11
4
4
8
3
3
5
3
2
5
8
6
11
3
3
5
5
6
8
4
24
7
3
4
7
6
9
3
7
3
5
4
4
8
6
2
1
4
3
9
5
5
4
3
4
3
7
1
2
15
3
6
2
3
10
4
4
4
8
5
1
5
2
3
3
3
5
5
4
4
2
2
8
5
4
3
6
11
2
2
4
6
3
3
7
5
5
3
1
8
2
7
2
0
6
3
1
1
3
3
4
4
5
5
0
11
7
3
2
5
5
11
8
6
7
5
5
7
5
4
4
3
4
4
2
2
3
4
6
13
6
5
7
2
6
8
17
2
4
4
4
1
3
2
1
5
4
5
7
5
5
10
3
4
4
12
1
4
8
6
7
1
4
2
6
0
4
4
5
7
17
1
6
5
6
2
4
3
15
5
3
2
9
3
3
8
5
5
10
4
1
6
3
9
9
8
3
7
4
4
0
5
3
4
2
4
9
4
5
7
7
3
11
4
4
5
6
3
2
8
5
4
5
5
8
2
3
4
7
24
3
5
7
7
5
4
7
4
3
3
6
17
4
4
16
4
5
2
3
10
4
8
3
1
4
7
6
5
2
2
8
0
2
8
3
10
1
8
5
3
4
2
17
1
5
13
4
8
5
5
16
5
1
6
2
2
0
4
4
3
5
6
28
2
7
4
5
4
9
4
5
2
4
4
7
2
5
2
6
1
5
5
2
6
2
8
5
5
5
5
7
6
6
1
3
2
4
3
1
4
7
4
5
5
3
3
5
3
2
5
6
2
5
8
4
6
8
5
4
4
17
6
2
6
1
2
3
3
3
6
2
2
11
4
14
7
3
4
4
4
4
3
9
3
5
5
3
7
2
3
8
8
3
10
0
5
4
3
2
2
5
1
9
1
7
5
6
6
3
2
4
6
5
1
6
5
3
10
4
7
4
6
4
1
9
2
5
5
7
10
7
3
7
18
3
4
7
2
1
2
6
11
2
9
4
6
5
2
11
2
2
14
1
3
8
6
8
3
7
1
3
6
5
3
0
8
5
2
3
2
8
8
1
1
8
1
3
8
2
1
8
6
7
0
9
9
8
2
5
2
3
2
2
3
4
3
6
3
5
1
2
2
4
5
6
4
4
1
9
7
12
23
9
3
5
4
3
5
7
10
1
4
1
1
3
4
6
4
7
8
2
5
12
3
6
5
7
5
11
7
4
4
5
4
4
2
1
1
2
8
5
4
7
11
4
12
2
2
3
4
4
9
5
0
3
1
7
7
3
8
4
2
2
2
4
7
7
8
5
2
7
5
3
1
8
0
12
4
4
4
5
5
3
5
4
5
0
3
3
2
4
6
2
3
2
4
7
8
6
5
2
6
2
3
7
7
7
2
4
5
0
3
3
4
0
2
3
6
6
9
10
9
6
8
7
15
2
3
10
2
5
5
19
3
12
4
4
4
1
3
5
3
9
2
4
8
5
4
2
2
4
0
5
5
0
6
7
5
8
6
4
7
9
3
7
6
2
4
2
6
3
2
1
5
0
5
3
2
12
0
2
3
3
4
8
14
2
4
5
12
3
11
6
5
1
2
6
2
8
5
3
2
5
5
2
3
2
5
2
3
3
3
3
2
2
2
7
2
7
0
2
1
3
1
3
8
7
4
3
5
4
3
2
3
11
9
1
6
11
1
2
6
10
3
8
4
3
3
5
3
5
5
2
1
16
5
6
3
2
4
2
4
2
3
3
2
1
13
4
7
8
2
4
5
6
4
7
9
2
7
5
2
5
6
4
3
4
2
1
9
7
6
2
1
4
8
5
2
4
3
7
5
3
3
2
8
11
3
4
0
2
4
2
7
7
5
5
10
5
3
5
3
5
12
5
4
1
3
1
0
4
8
3
3
1
1
17
11
6
11
5
2
9
0
5
5
3
13
1
1
3
3
2
4
10
3
7
13
7
3
5
2
4
2
3
3
2
3
9
5
3
1
4
11
5
2
18
1
3
4
14
11
1
3
1
5
4
0
5
2
2
3
1
4
3
2
0
2
2
1
11
7
4
5
8
5
3
3
2
3
9
5
0
2
10
2
7
5
15
11
2
3
4
1
3
2
2
3
8
4
2
3
15
5
12
6
13
5
7
3
20
5
3
6
3
2
8
5
1
3
4
3
2
6
10
13
1
11
1
3
0
4
1
5
1
7
6
2
4
1
5
6
4
2
1
5
9
1
5
2
3
11
3
3
6
3
5
1
5
7
2
1
3
11
5
4
17
4
3
9
3
6
0
4
1
3
6
3
0
3
3
3
1
1
1
0
10
8
3
2
6
5
6
12
6
6
4
4
2
7
5
3
4
0
10
3
1
4
2
4
4
5
10
8
1
3
7
8
3
3
3
2
6
4
4
7
4
9
6
2
4
4
7
2
3
7
2
6
8
3
2
7
8
2
8
7
6
5
4
6
4
3
6
3
2
3
3
1
6
5
3
5
1
6
10
3
7
13
10
11
3
1
1
1
2
2
8
17
3
5
6
2
7
7
6
8
2
6
1
3
3
5
6
3
4
6
4
3
13
4
2
3
3
4
0
4
5
2
4
3
2
5
4
3
5
3
4
6
3
3
6
1
3
3
8
4
6
2
1
5
7
1
7
3
2
0
6
7
3
6
1
2
2
2
8
2
0
0
4
9
6
3
1
6
10
7
8
9
2
1
3
5
11
3
2
5
4
8
1
2
9
3
1
2
0
8
3
1
6
3
7
4
3
5
0
7
3
5
2
2
3
5
6
3
1
3
6
2
1
1
9
8
30
7
2
2
5
13
7
3
10
3
4
3
2
0
3
3
2
5
5
3
2
3
3
3
2
3
3
4
17
7
5
5
2
5
2
3
2
3
8
2
15
4
3
1
7
3
6
2
4
2
5
5
3
3
5
5
2
3
2
2
3
2
8
4
1
3
4
5
1
7
10
1
2
1
7
6
2
5
3
3
1
1
4
2
1
5
4
6
6
3
2
1
6
1
4
1
3
3
12
4
18
9
1
6
2
3
3
2
5
10
4
11
2
3
6
6
1
4
2
3
10
2
4
7
3
3
10
3
2
2
14
4
4
6
2
11
8
2
11
2
4
5
7
9
3
3
1
4
3
1
4
3
6
2
4
11
3
4
3
9
1
6
6
1
12
1
8
2
14
3
0
4
3
5
1
7
2
3
5
5
2
1
3
9
5
1
3
3
11
2
0
6
3
4
6
8
2
5
12
5
1
13
5
2
5
10
2
3
5
3
2
9
7
2
16
4
2
9
4
4
7
5
4
2
3
3
5
2
7
3
5
5
4
4
2
4
3
8
2
3
2
5
5
3
3
7
1
5
5
3
4
5
3
5
6
2
2
4
3
3
4
8
2
4
1
6
4
4
2
7
3
4
5
11
11
11
4
6
2
0
3
2
6
2
15
3
7
4
3
3
2
4
2
7
7
3
1
2
5
5
3
3
4
4
8
14
3
2
6
4
4
3
3
5
1
1
5
1
3
2
1
2
2
5
4
2
3
3
4
6
7
1
5
4
4
13
3
3
4
6
4
2
4
1
5
3
14
7
3
2
2
2
7
4
2
3
4
5
2
4
5
1
3
2
3
2
7
4
1
6
4
3
7
0
2
13
7
12
2
4
9
10
1
4
6
6
2
2
3
2
2
7
3
10
2
5
2
1
1
8
5
1
5
7
2
5
8
7
1
1
4
13
6
13
6
4
5
1
0
2
9
2
6
2
4
3
1
5
2
4
5
9
2
0
4
2
2
4
2
5
2
4
2
4
6
2
2
5
3
1
17
1
6
2
2
3
5
2
3
3
1
4
11
3
5
21
5
1
3
2
5
11
2
2
0
7
4
5
1
6
6
4
7
4
3
4
1
8
1
0
3
2
6
4
6
4
4
3
4
2
2
2
5
4
4
7
3
2
3
6
5
3
3
3
8
6
8
6
13
0
2
2
6
4
3
1
9
0
2
9
7
3
2
2
8
2
6
3
2
4
3
3
3
2
1
5
0
3
7
9
4
2
2
2
4
2
3
12
2
8
7
6
5
3
6
4
1
6
4
2
3
8
1
5
7
7
4
5
6
2
2
4
4
3
9
1
9
1
6
2
4
4
10
8
1
7
10
4
5
5
2
4
1
0
4
3
7
6
2
6
5
0
1
5
2
5
0
7
2
3
5
6
5
13
3
2
5
6
2
2
1
4
11
5
0
1
3
5
3
4
3
2
2
7
3
4
4
4
3
4
5
3
2
1
10
1
3
3
0
1
1
3
4
5
1
7
0
5
4
4
1
2
4
2
4
5
5
3
4
7
8
2
8
3
2
3
3
3
2
4
5
7
2
5
2
3
1
1
6
6
4
3
7
2
3
4
7
3
0
4
5
2
5
2
6
4
4
3
4
2
3
4
5
0
2
4
5
3
3
10
2
2
1
5
0
2
3
2
2
0
8
2
1
2
0
2
6
4
1
0
8
6
5
4
2
3
2
3
10
2
4
4
6
4
2
3
6
1
7
2
3
2
1
3
0
5
4
5
3
1
4
5
10
4
2
2
2
3
3
1
3
3
4
10
2
10
2
5
3
2
5
3
5
6
3
2
3
3
2
3
3
16
5
4
6
3
6
1
4
1
3
3
3
4
3
6
7
7
4
8
4
8
5
8
8
0
4
3
15
7
5
11
2
4
3
2
4
6
5
3
2
5
6
2
13
6
4
0
0
2
1
6
6
6
10
1
4
4
10
2
6
1
7
4
2
2
7
10
6
6
3
5
3
2
2
1
10
9
4
2
5
3
3
3
0
1
7
2
1
16
3
2
3
9
0
3
3
11
6
0
3
5
3
3
6
4
12
4
6
5
4
2
3
5
4
4
3
3
2
2
5
3
2
2
3
5
2
2
5
18
2
2
6
3
10
3
3
9
5
5
5
5
3
9
1
2
2
5
1
6
2
11
0
4
8
1
5
3
5
15
3
2
1
5
1
3
2
5
7
25
4
2
4
5
0
3
15
1
6
3
5
10
2
3
5
8
5
4
2
4
4
5
4
7
1
4
2
5
5
4
3
2
3
8
2
0
0
2
5
3
6
5
4
5
2
1
3
3
4
0
2
5
8
4
4
7
2
2
15
1
12
12
7
4
5
1
4
0
5
4
5
6
0
2
3
0
0
3
4
4
4
9
3
1
4
2
6
3
2
4
3
2
4
0
3
2
3
15
1
2
3
2
1
4
3
9
4
2
1
10
2
5
6
4
2
3
3
7
2
0
3
4
2
1
8
1
6
1
5
2
5
1
3
4
2
3
1
2
4
4
3
1
5
1
3
3
3
7
5
3
1
8
1
8
6
4
4
1
3
2
4
6
5
3
4
5
1
1
5
3
2
3
2
5
6
10
2
3
5
5
2
2
10
6
2
3
5
2
4
3
4
6
3
1
2
4
3
3
5
3
3
4
7
2
5
1
5
2
2
5
3
3
2
4
4
4
4
6
5
4
1
2
5
2
8
2
3
4
3
2
4
2
6
5
6
1
3
1
2
0
17
5
7
3
10
2
2
7
4
6
2
5
1
7
6
1
2
3
4
1
5
1
2
4
2
3
6
2
6
2
4
10
2
1
4
10
5
2
1
8
2
7
2
3
3
7
1
3
1
3
1
1
4
4
0
3
0
3
1
13
2
4
3
4
4
5
0
2
4
3
1
7
2
4
2
4
5
0
8
2
1
5
2
2
3
5
1
1
3
3
4
3
18
2
4
6
5
3
14
2
4
6
4
0
1
4
5
2
2
3
10
2
3
0
2
2
1
5
6
3
2
5
2
12
4
2
3
5
3
7
4
4
2
6
1
9
4
4
8
3
1
1
3
4
2
3
3
2
3
4
1
12
4
7
4
5
2
4
3
5
1
16
3
6
2
2
4
8
5
5
3
3
2
1
3
3
4
2
3
3
1
3
6
4
2
4
4
3
3
1
0
6
1
6
2
3
4
2
1
2
3
1
3
1
0
7
3
5
2
5
2
3
7
4
5
7
4
3
4
3
1
2
4
9
2
4
17
1
1
3
2
3
7
4
1
3
8
17
6
3
3
9
3
3
12
4
6
5
3
1
8
3
0
8
3
1
5
3
3
3
0
6
3
2
2
3
5
3
4
2
2
8
5
8
2
8
2
9
2
8
1
4
1
1
4
3
4
3
4
4
3
3
6
2
3
3
7
0
2
2
3
2
1
4
2
11
3
4
0
5
6
2
7
4
2
4
0
2
3
6
3
3
2
2
3
3
5
2
1
1
4
2
5
2
2
3
0
2
7
5
0
1
3
5
3
2
1
2
2
1
2
0
5
1
5
19
12
2
1
2
2
3
4
3
1
4
6
3
0
0
1
4
1
5
4
2
1
8
5
2
4
1
3
1
3
4
3
8
6
9
9
2
6
4
1
3
4
4
5
2
2
2
3
2
3
3
1
1
3
3
2
3
3
1
4
9
6
3
10
0
2
0
1
4
0
1
3
2
1
17
5
2
1
0
0
2
4
1
9
1
1
4
4
7
8
2
4
1
18
3
2
1
5
5
5
1
5
3
3
3
4
4
2
11
1
2
10
8
6
1
21
2
3
2
4
10
0
1
1
2
5
20
3
3
6
8
5
11
0
2
10
3
5
4
11
2
1
6
4
8
5
2
4
2
6
5
1
2
3
2
6
5
4
3
0
2
1
7
5
2
5
3
3
5
3
5
4
0
1
4
1
6
2
2
5
4
5
4
2
4
7
16
11
1
7
2
4
3
2
2
2
4
4
6
3
5
15
1
2
1
3
1
4
3
2
1
4
2
10
4
5
5
3
4
1
3
9
9
2
3
4
1
3
5
2
3
4
6
4
1
14
2
1
2
5
2
1
3
2
16
3
3
4
3
0
4
6
4
5
10
4
8
3
0
0
1
3
1
4
6
5
3
3
1
3
4
3
1
4
3
7
3
2
3
0
1
1
4
3
2
4
4
4
9
4
1
5
14
1
3
2
1
3
2
3
6
3
2
2
4
5
2
8
1
0
4
6
3
1
7
4
3
15
2
3
3
11
3
4
2
3
10
5
1
6
4
3
0
3
3
4
0
1
13
7
0
3
0
5
5
3
2
3
1
12
2
4
0
2
2
0
1
7
3
2
7
10
1
14
2
3
2
2
1
3
3
2
4
3
4
2
2
2
0
4
5
4
3
3
1
5
3
2
4
3
5
5
0
4
2
4
3
0
2
3
5
1
2
2
2
1
4
3
2
1
1
14
2
1
8
4
2
8
4
4
0
4
2
3
2
3
3
0
1
1
0
1
10
6
8
2
12
9
1
3
3
3
1
2
3
2
4
0
2
5
4
4
3
0
6
1
5
5
5
2
3
8
4
4
0
4
1
4
12
3
3
3
4
1
2
3
2
3
2
7
3
8
1
2
2
3
5
4
1
3
2
2
3
2
2
4
3
3
2
7
2
2
3
2
3
3
11
2
2
2
3
4
4
2
3
1
3
5
4
1
3
3
5
3
3
2
12
0
10
2
1
1
2
1
2
1
11
2
4
3
1
2
3
4
5
3
2
2
0
3
3
4
2
1
11
3
5
5
4
1
1
0
5
4
3
1
3
11
3
10
4
4
2
3
1
7
5
2
3
4
5
2
2
5
1
1
3
2
2
2
3
3
1
3
2
0
3
0
23
1
1
2
4
14
3
0
5
5
3
4
2
0
7
2
4
3
6
2
1
11
2
4
4
2
8
1
3
8
4
4
2
2
6
11
0
3
0
0
2
2
4
4
3
7
5
4
5
1
3
7
1
2
4
3
2
0
2
0
2
4
3
1
2
0
1
1
8
4
4
2
1
3
0
2
5
2
7
3
2
2
1
2
1
4
12
3
5
4
3
4
2
3
3
2
4
0
1
8
4
3
1
8
5
3
1
3
4
1
8
8
2
1
3
10
3
1
2
1
3
7
2
1
4
3
1
13
1
1
3
3
2
2
6
12
0
3
2
1
4
5
5
2
2
2
4
2
0
8
3
3
2
2
3
2
5
3
5
2
1
4
4
2
5
0
3
0
0
1
10
3
2
19
5
2
1
1
5
4
2
1
8
4
5
4
1
2
3
3
4
0
4
2
0
7
2
4
14
2
3
0
6
2
5
1
5
8
4
3
4
3
1
0
0
2
2
3
3
2
2
1
2
6
4
3
1
2
2
4
2
4
8
2
3
1
2
1
6
3
2
1
7
3
4
1
2
0
3
2
3
2
4
4
3
2
3
2
2
0
2
3
6
3
10
7
4
16
2
2
1
5
9
3
4
0
1
1
1
5
2
5
3
1
0
3
8
5
1
3
4
0
4
2
4
1
5
3
2
3
3
6
4
2
2
1
3
2
4
3
19
4
4
3
5
3
2
11
1
7
1
6
4
4
2
5
4
10
8
1
4
2
1
2
2
3
1
7
0
3
2
2
1
1
4
4
2
9
4
0
7
4
2
1
6
2
2
2
3
3
1
2
2
2
3
7
2
2
4
2
3
1
1
1
3
5
5
4
3
3
0
3
2
3
1
1
4
2
1
4
3
3
5
15
2
0
4
0
3
2
5
3
2
4
2
2
4
2
9
3
2
5
2
1
0
4
3
3
3
2
2
3
0
1
3
2
2
2
1
2
3
2
6
1
7
4
2
1
1
1
1
3
3
2
6
4
1
3
2
0
2
2
3
1
4
4
1
6
0
1
0
7
3
5
3
1
1
3
5
2
2
0
1
2
4
2
0
1
0
2
2
13
5
0
3
3
1
3
1
3
3
8
2
2
4
8
2
1
3
1
0
2
3
6
2
4
2
4
1
1
4
7
3
1
2
1
5
5
4
6
4
1
5
3
0
9
6
3
1
3
4
2
4
1
3
3
3
9
4
1
1
2
2
5
2
5
1
3
3
20
1
1
0
3
8
7
4
2
3
8
1
3
1
5
3
2
4
0
4
3
4
3
2
2
0
9
1
2
2
5
0
4
11
1
4
8
5
1
4
4
3
3
3
3
1
1
5
2
3
8
0
0
0
2
1
0
3
5
5
4
3
0
1
1
3
1
1
4
2
10
0
6
3
1
2
4
0
1
2
2
2
0
3
3
4
0
2
1
2
7
0
1
2
2
3
2
2
8
2
2
3
4
3
0
5
2
1
0
5
4
2
4
3
4
1
2
4
1
2
4
2
2
1
2
0
3
1
3
1
0
3
2
2
7
3
10
2
4
0
4
0
1
3
1
4
2
0
2
2
1
2
1
5
2
7
4
1
2
2
3
2
6
5
5
1
3
6
1
5
4
4
1
2
3
2
3
5
1
4
4
5
6
3
0
2
2
9
3
3
10
4
2
2
4
0
2
1
2
1
1
3
2
2
1
2
2
1
2
2
2
3
2
1
2
3
1
3
4
7
3
1
3
6
1
5
7
6
1
1
0
2
1
1
5
2
6
1
12
2
1
10
2
5
3
4
0
5
0
2
2
0
3
5
4
3
1
2
6
3
0
3
2
0
2
9
0
0
1
0
6
0
2
22
10
1
1
4
0
11
2
1
2
1
10
3
3
2
4
1
2
1
5
2
3
2
6
4
2
2
2
4
4
1
1
1
2
4
3
1
4
1
2
4
6
2
1
2
3
4
11
2
2
2
2
5
2
2
12
2
2
1
15
3
3
6
5
3
6
6
5
1
4
3
1
0
0
0
3
4
9
4
5
1
3
5
5
1
4
1
3
2
2
1
3
1
5
9
3
2
2
1
4
1
8
0
4
4
5
4
4
3
0
1
2
1
1
3
4
2
1
3
2
1
1
3
1
11
1
1
1
1
1
6
5
7
1
7
3
3
10
12
4
9
3
4
0
4
8
1
2
11
6
4
1
1
1
4
3
3
5
1
15
2
1
2
6
2
1
2
3
1
1
2
2
1
1
1
3
2
2
3
3
2
2
3
1
2
2
4
2
7
3
0
4
4
4
2
9
3
1
6
2
3
1
1
11
2
1
10
3
1
4
6
5
3
2
1
0
5
4
4
2
1
6
1
1
2
1
4
1
3
2
3
4
3
3
3
16
7
3
2
2
2
3
0
12
3
16
1
2
4
3
5
3
5
5
3
2
4
5
2
2
1
3
2
1
2
2
22
1
4
2
2
2
3
10
1
1
1
2
3
3
0
6
3
2
4
4
2
2
1
1
7
2
1
2
0
1
3
9
13
7
3
3
2
3
2
11
2
2
1
3
2
3
3
1
4
2
10
2
1
2
2
4
4
10
5
2
2
2
2
1
2
1
5
1
12
1
1
2
2
6
2
2
6
3
3
1
5
4
4
1
2
2
2
3
3
3
3
2
2
1
4
1
10
0
2
4
4
3
3
3
5
3
2
4
7
3
1
2
1
6
5
2
2
2
2
4
4
1
6
2
3
3
1
2
3
1
3
2
2
0
1
3
3
2
3
3
1
3
4
1
0
6
2
2
4
1
1
0
3
3
2
1
2
3
2
3
12
3
2
4
7
1
0
1
4
1
1
6
3
6
0
9
2
2
5
6
4
2
5
3
2
3
4
7
3
5
0
3
2
1
2
9
2
1
4
0
2
3
3
3
2
2
1
4
3
3
12
1
1
5
5
3
1
0
1
3
1
1
8
0
5
4
1
6
1
1
1
2
3
2
1
0
2
2
2
4
3
2
2
3
13
0
3
1
4
3
3
3
5
1
2
1
5
2
3
2
11
1
0
2
1
3
2
3
3
2
1
2
2
1
3
1
0
1
1
3
3
6
4
2
1
1
7
2
3
1
1
3
1
1
0
0
2
4
0
1
4
5
1
2
0
1
3
2
1
3
2
3
2
2
4
3
1
2
6
2
5
6
3
4
5
3
9
2
2
3
6
3
4
4
3
1
1
2
2
1
1
2
2
0
1
1
1
1
3
2
2
2
1
2
3
5
1
5
2
1
5
2
4
2
2
3
0
4
2
9
3
7
2
5
0
3
1
3
3
2
1
3
6
3
2
0
3
3
0
1
1
4
1
2
3
9
9
2
2
4
3
3
0
1
14
3
1
0
3
8
1
3
1
4
7
3
3
4
0
2
1
2
5
2
4
1
2
2
2
2
6
4
1
4
2
0
1
1
1
1
1
1
11
3
3
7
0
14
1
7
6
2
1
2
5
4
1
4
2
3
3
2
1
2
0
3
3
1
16
6
3
2
6
3
4
5
2
1
2
4
5
0
3
3
4
2
1
0
3
7
2
0
11
4
2
4
1
1
3
2
3
1
1
0
1
1
2
5
5
3
7
0
1
2
0
5
11
2
4
5
2
3
1
0
2
1
2
1
0
0
4
5
2
1
2
0
2
0
3
2
9
1
2
2
3
2
2
2
1
11
2
2
1
1
2
9
3
0
2
3
1
3
5
0
4
2
4
0
1
0
1
0
2
7
2
2
2
2
0
3
0
3
1
4
2
4
4
2
6
3
3
3
4
2
0
3
3
3
3
2
0
1
3
7
4
2
2
11
4
0
0
9
2
2
5
14
1
3
4
2
4
2
10
2
4
4
2
2
2
2
1
2
1
5
1
3
0
3
3
4
9
0
5
5
5
3
0
5
1
0
5
2
2
1
2
2
0
0
3
4
5
3
3
2
1
0
6
2
1
9
6
1
2
2
0
3
3
0
0
5
5
4
1
3
4
9
2
3
8
0
2
3
1
0
18
2
6
6
0
2
3
1
5
3
2
4
2
10
3
3
2
2
6
0
2
3
2
4
1
4
3
3
1
3
4
0
2
0
2
3
2
3
3
3
2
1
1
2
3
2
2
1
2
1
4
1
3
16
2
10
6
0
5
3
0
2
5
4
4
3
1
6
1
3
2
2
5
3
3
2
2
2
1
0
0
3
0
7
3
5
2
1
3
5
5
3
3
1
3
2
2
5
4
7
3
2
0
4
4
3
3
3
2
4
1
2
2
2
2
7
1
2
3
3
1
3
13
2
5
2
2
8
2
3
1
3
1
1
1
1
3
4
12
0
4
4
1
3
3
3
2
1
2
1
5
10
0
1
4
6
1
4
4
5
1
5
1
5
4
3
1
1
0
4
4
1
2
1
1
3
4
3
2
2
0
3
2
2
4
0
0
2
2
2
2
2
4
1
2
2
4
3
2
4
5
1
7
2
1
1
0
3
5
2
2
3
2
4
4
4
5
3
0
3
3
2
2
5
3
2
0
2
3
1
0
1
1
0
1
1
3
2
4
5
1
4
1
1
12
2
2
3
6
2
10
4
4
0
1
3
5
3
3
1
7
3
6
4
3
2
2
1
13
6
0
7
5
1
2
2
2
0
4
2
1
2
3
3
1
0
0
3
4
2
6
2
0
13
3
0
5
2
5
3
1
0
4
1
1
2
5
2
1
1
2
1
2
1
3
1
0
1
2
1
2
2
2
5
1
15
0
3
2
7
2
2
1
0
1
2
4
1
4
3
1
0
0
0
4
2
3
2
2
1
0
3
0
2
1
4
6
1
2
1
0
15
1
0
1
3
6
2
1
3
2
2
0
4
5
0
1
4
1
1
0
3
1
0
3
5
3
6
3
1
0
3
5
2
3
3
7
4
1
1
10
2
2
5
1
8
6
6
2
2
4
2
0
2
5
3
5
2
9
3
2
1
3
0
2
6
3
0
3
13
3
2
1
5
3
3
3
2
2
9
0
0
2
2
4
2
0
2
3
3
0
2
0
4
4
3
1
8
2
1
3
0
3
2
2
2
6
3
5
2
2
5
5
2
1
4
2
3
1
1
4
2
4
1
3
9
0
1
2
3
2
2
3
2
1
0
3
2
4
0
2
4
0
4
2
3
7
3
4
3
3
1
3
3
1
4
7
1
1
1
9
3
3
2
2
11
1
2
4
4
2
6
2
9
12
1
1
3
5
2
2
1
0
2
1
1
2
4
3
2
2
5
1
3
1
2
2
1
2
11
0
1
4
3
1
3
2
3
6
2
2
2
2
1
4
6
2
2
2
3
1
2
2
1
2
5
1
0
2
1
1
3
1
1
3
3
1
1
0
6
2
3
3
1
2
2
0
1
0
2
3
2
9
1
0
1
0
1
4
2
1
5
2
1
1
1
24
1
1
3
2
4
1
5
5
0
3
1
2
0
1
5
2
3
6
0
3
0
4
2
4
9
1
1
7
2
3
3
4
3
2
8
5
1
2
0
0
2
1
0
3
6
3
7
2
0
0
1
1
2
1
1
1
3
1
3
1
10
2
0
3
1
0
1
4
4
9
1
4
4
2
2
2
1
3
3
1
3
8
3
6
3
2
3
1
5
1
0
0
4
0
3
3
1
3
3
3
1
2
2
3
1
0
2
0
3
0
4
2
1
3
5
5
1
1
1
4
9
5
1
2
2
12
3
1
1
3
3
0
2
5
1
0
1
3
5
1
0
2
2
2
3
2
2
2
2
0
4
2
3
2
5
3
0
3
1
11
3
1
1
1
3
2
8
4
6
3
1
1
6
6
4
11
3
1
1
23
2
4
3
3
2
1
2
1
3
2
1
1
4
2
2
2
4
9
22
3
2
0
1
2
6
6
2
1
3
0
2
1
3
7
2
0
1
6
1
6
2
1
2
0
4
2
4
0
1
1
12
5
5
3
4
1
10
2
9
2
6
2
1
1
1
3
2
3
0
1
3
0
1
0
3
1
3
2
1
0
3
2
3
2
3
2
2
3
4
0
2
0
3
2
3
4
2
2
3
0
4
0
0
1
1
3
3
3
0
3
5
2
2
1
3
1
2
1
0
0
3
7
2
3
1
4
1
1
0
1
1
5
0
3
3
4
2
2
1
2
1
4
2
1
0
4
2
2
5
3
3
2
5
2
5
0
11
1
1
3
2
3
0
4
1
2
3
2
2
3
5
1
1
1
2
2
2
1
4
2
3
2
1
5
1
1
3
3
3
1
3
1
2
3
0
0
2
0
5
1
6
1
1
1
6
2
1
1
1
7
3
2
4
10
2
1
2
7
2
3
3
0
2
2
12
3
3
3
2
5
2
7
1
3
5
3
5
1
0
1
4
2
13
5
1
3
4
5
2
5
10
3
1
2
3
2
2
2
3
2
0
1
1
0
5
1
4
3
2
1
1
1
1
4
2
2
3
1
6
1
2
0
5
0
2
2
10
1
1
2
2
2
0
1
1
5
2
12
2
2
0
2
2
4
3
2
0
4
1
0
2
1
2
0
1
2
1
7
1
1
2
3
5
4
1
1
2
4
3
1
3
5
5
2
2
2
3
1
0
2
5
0
3
1
1
2
1
1
3
2
1
1
3
5
2
1
0
2
1
4
4
1
0
2
3
2
10
0
4
1
3
4
2
1
4
0
0
1
2
1
1
2
4
1
3
2
6
1
2
0
2
0
11
2
5
0
2
4
2
3
1
1
0
2
0
5
3
3
2
0
1
0
1
3
3
3
4
0
4
2
1
3
2
14
1
5
7
3
1
0
4
1
1
0
7
1
2
2
0
3
2
3
2
3
3
4
1
1
2
1
3
6
2
1
0
3
13
3
5
0
2
2
2
5
3
3
6
1
0
4
1
1
3
2
2
4
1
3
3
2
2
2
8
2
9
3
4
1
6
0
1
1
2
1
7
3
2
3
2
1
3
0
2
2
4
2
1
0
2
0
3
3
4
1
2
0
0
5
4
3
1
1
1
2
3
2
2
7
2
2
1
8
2
3
2
6
1
7
4
3
1
1
2
1
4
2
2
3
1
1
5
0
10
2
1
1
2
2
2
2
1
1
3
3
0
5
4
4
1
1
3
1
2
15
3
2
0
0
7
1
2
2
1
4
5
0
5
7
8
0
1
1
3
1
1
3
3
1
3
1
5
2
2
3
4
2
2
5
2
2
1
1
1
2
0
7
2
3
4
1
4
2
7
3
5
1
0
2
3
1
1
3
2
3
2
3
1
2
1
3
0
1
2
1
3
1
3
3
2
2
8
1
1
2
1
2
3
2
4
1
0
6
2
11
1
10
2
4
2
2
3
3
0
2
2
1
0
0
0
2
1
1
1
1
6
1
2
2
3
2
3
5
2
0
10
2
8
9
1
2
0
1
8
4
2
6
3
2
2
3
1
1
3
1
2
3
3
3
1
0
1
2
4
2
0
2
3
0
1
8
2
6
6
2
1
5
5
3
3
1
4
0
3
2
2
6
2
2
1
1
2
1
1
3
2
0
2
0
6
4
2
1
1
1
4
2
0
1
2
1
0
0
0
10
5
4
3
3
3
2
1
2
2
0
1
3
3
6
2
3
1
1
1
2
2
2
2
5
2
0
2
0
3
0
5
0
3
2
3
8
3
1
3
1
11
1
2
1
2
10
1
1
0
3
0
3
3
0
0
0
3
3
0
0
2
4
2
7
8
3
6
0
2
6
1
1
0
6
3
0
1
0
3
1
4
4
3
3
0
2
2
1
4
3
1
3
0
3
1
1
5
3
0
4
1
2
5
1
3
1
0
2
5
5
2
0
2
3
1
0
2
2
0
2
1
1
3
3
1
3
6
4
6
0
1
2
2
2
1
2
5
6
1
5
2
2
2
1
3
1
0
4
2
3
0
1
4
1
1
0
2
1
2
2
3
1
2
1
0
3
12
7
0
2
4
0
13
0
4
2
1
2
3
3
2
1
1
2
2
0
3
4
0
3
3
1
3
2
5
3
1
3
9
2
1
4
4
6
1
0
5
1
4
2
3
2
0
1
0
3
1
5
1
1
3
2
1
3
2
1
5
10
3
1
1
2
3
1
2
0
0
7
1
0
7
2
2
1
0
2
12
1
0
4
1
10
1
6
2
1
2
3
5
3
3
1
1
5
1
5
0
0
2
1
0
1
6
5
3
5
2
3
2
2
0
0
3
1
1
4
4
1
0
11
1
3
3
2
2
1
2
1
1
2
1
0
2
0
0
2
4
2
4
0
2
2
2
2
3
3
0
2
1
0
1
2
1
2
1
2
1
1
1
2
1
2
0
1
5
1
4
2
3
1
3
2
4
6
1
0
1
4
0
2
0
1
2
4
4
3
1
4
1
3
12
4
0
1
0
7
1
12
2
3
2
2
4
0
11
2
1
1
11
4
3
1
3
3
2
2
3
1
0
4
1
0
2
2
1
5
1
4
2
0
1
1
4
1
1
4
3
0
10
2
1
2
11
0
1
1
0
10
2
2
11
0
2
6
1
1
1
0
5
0
2
2
2
13
0
3
1
1
10
0
2
1
2
2
1
2
2
1
4
13
5
3
4
2
3
3
2
1
2
4
0
2
16
3
4
1
1
3
2
4
0
0
2
5
0
0
3
0
4
0
6
3
1
2
0
0
1
3
4
2
2
2
2
2
3
2
4
2
1
5
2
1
5
1
3
1
1
0
1
1
3
1
0
2
3
1
2
7
2
0
4
1
4
3
1
1
1
3
4
5
2
5
1
1
1
0
2
6
1
4
1
5
1
1
3
2
0
2
18
1
4
5
1
0
1
4
7
1
2
1
1
5
3
1
2
5
2
4
2
2
2
2
1
3
2
2
2
4
3
3
3
2
1
0
1
0
7
2
0
2
1
2
2
4
2
2
5
1
1
2
1
1
4
1
2
3
2
2
2
4
2
3
2
1
2
2
7
1
4
3
5
5
2
0
3
2
1
2
0
2
2
1
0
2
0
0
0
3
1
3
2
1
2
2
2
4
2
6
1
5
2
1
4
0
1
5
2
1
2
3
0
2
2
3
6
4
0
4
3
1
3
4
3
0
1
1
3
1
1
2
2
0
0
1
1
1
1
1
1
1
3
4
9
2
4
2
0
3
3
2
2
3
13
3
3
1
1
1
8
4
1
1
0
3
1
3
1
2
7
1
1
2
10
7
2
0
3
1
13
0
2
2
0
2
0
1
0
3
2
1
3
0
3
1
2
6
0
2
2
2
1
3
1
1
5
2
0
2
3
2
1
3
0
1
2
0
4
3
8
3
1
3
2
2
2
2
7
0
2
1
0
2
0
2
1
0
3
5
4
3
1
1
1
3
1
2
1
2
2
1
2
0
1
1
2
1
0
2
16
1
1
1
2
1
1
2
10
0
2
9
0
3
1
3
3
5
1
2
15
2
2
2
2
0
1
5
11
1
1
1
2
2
1
2
4
3
0
4
4
7
0
0
1
1
0
1
3
0
3
2
1
0
2
1
2
3
3
3
1
1
16
3
1
2
0
3
5
1
3
5
0
1
0
3
0
3
15
2
0
2
0
2
0
2
2
1
4
1
4
2
2
0
0
1
0
1
0
2
1
2
2
3
3
3
2
1
2
1
2
3
0
3
2
0
1
2
1
2
0
1
2
1
1
3
2
0
2
1
4
1
5
0
9
4
1
3
3
2
2
2
2
15
1
1
1
1
3
1
3
0
2
1
1
2
1
2
1
0
3
2
3
3
1
5
2
6
1
3
2
2
4
2
8
3
17
2
2
0
3
1
0
4
1
3
5
1
3
2
5
5
0
1
5
1
1
4
5
2
0
2
2
1
3
3
4
5
4
1
1
4
4
1
2
1
3
1
2
2
4
0
1
1
2
2
0
1
1
4
4
1
2
0
1
1
6
3
0
1
2
2
1
12
0
2
4
1
1
1
1
1
0
1
2
3
4
2
3
2
0
1
1
8
2
0
4
10
3
1
0
3
0
0
3
1
3
2
1
1
1
3
8
1
3
3
1
2
2
1
10
1
1
3
2
2
2
0
2
1
1
1
1
3
0
6
3
5
1
4
1
2
1
1
2
4
1
3
1
1
0
0
2
1
1
10
1
0
1
2
6
5
0
0
0
3
1
1
2
2
2
2
2
1
2
0
1
0
4
0
1
5
5
1
5
11
2
1
1
4
0
2
0
0
1
0
1
2
0
1
5
2
3
3
9
5
1
0
3
3
3
0
1
2
3
1
1
2
0
1
4
1
3
1
2
2
3
0
3
1
1
4
1
2
2
2
4
0
3
2
1
2
3
6
2
2
1
0
0
2
3
1
2
1
3
2
3
4
2
1
4
3
7
5
2
5
1
2
3
1
3
1
0
0
1
1
2
0
3
2
0
2
1
2
2
0
6
2
0
0
2
1
6
2
1
2
5
3
6
1
3
1
1
0
3
1
3
2
3
2
1
0
3
3
1
2
3
2
5
0
6
2
4
0
2
4
0
0
3
3
3
0
3
5
0
1
2
3
1
1
0
3
3
1
1
1
3
1
5
0
1
1
1
1
2
1
2
2
0
3
0
1
1
2
1
3
2
14
1
1
3
2
3
3
3
1
3
2
2
1
1
3
2
2
4
2
1
3
3
5
4
2
5
1
1
1
0
2
2
1
1
1
5
2
2
0
5
16
3
0
4
0
2
1
1
7
4
1
1
2
4
4
8
6
2
3
6
2
0
19
1
0
1
2
2
5
1
5
3
6
2
8
4
0
0
0
1
2
1
3
2
0
2
1
2
1
1
1
0
2
1
3
1
1
1
1
1
1
1
4
0
11
3
3
0
2
0
3
2
1
1
3
0
2
2
1
1
2
2
1
1
2
1
0
1
0
2
2
7
3
4
1
3
2
1
3
2
3
0
0
2
2
1
3
2
2
3
0
1
4
3
7
8
2
0
6
2
1
2
0
14
1
4
1
1
2
1
2
1
0
2
3
0
2
0
0
9
2
2
2
1
1
1
3
0
2
1
5
3
0
1
2
1
0
3
0
2
5
2
0
2
2
7
6
3
4
1
12
0
3
3
3
3
1
3
0
1
3
0
1
2
1
2
8
2
4
2
8
1
1
1
2
5
1
1
3
0
1
3
2
0
2
1
2
2
1
1
3
1
1
3
0
2
0
2
3
2
3
0
2
2
10
2
3
2
9
0
4
1
2
2
1
1
1
0
1
1
3
0
3
1
1
2
1
4
1
2
5
11
0
1
1
0
2
4
0
0
1
2
2
0
0
3
1
1
2
2
1
1
1
1
2
0
2
2
1
1
1
0
3
5
2
3
0
0
3
1
1
2
1
10
2
1
1
7
1
2
5
2
0
0
3
0
0
5
4
3
0
2
1
2
2
1
0
11
9
14
2
2
4
0
3
4
1
1
3
3
2
0
5
3
0
7
0
4
1
1
4
1
3
0
3
1
2
0
2
1
4
1
1
1
0
1
2
3
0
0
4
2
5
2
3
3
1
1
2
1
1
9
2
2
3
0
1
1
3
0
0
1
3
0
2
2
1
3
2
2
1
2
1
4
5
2
1
0
5
1
1
0
0
0
4
2
1
1
0
2
4
1
2
2
2
1
1
3
1
2
3
1
3
1
2
2
1
1
1
1
1
0
2
6
2
0
2
1
3
3
2
0
4
1
3
1
2
1
1
1
0
3
0
0
1
3
2
1
1
4
2
1
0
0
0
0
2
9
1
1
0
4
2
7
0
5
0
2
1
3
1
1
4
3
0
0
1
2
3
0
2
0
2
4
1
1
2
2
0
4
0
0
2
4
1
0
1
2
0
0
5
2
2
1
3
2
2
2
2
2
1
2
5
5
3
1
1
3
3
0
2
0
3
1
2
3
3
0
2
1
7
1
0
11
2
1
2
2
2
1
1
3
0
3
9
2
2
2
0
4
2
2
3
3
1
3
3
5
1
1
3
3
2
1
0
0
0
4
2
2
1
1
0
1
2
1
4
2
1
1
1
0
1
3
0
1
3
2
0
2
1
3
0
3
2
1
1
2
11
0
1
1
2
2
6
3
5
2
4
2
1
3
3
4
2
1
2
3
8
3
6
3
2
4
1
2
2
2
1
1
1
3
1
2
1
0
0
1
0
3
2
2
3
3
0
1
1
2
1
1
3
0
1
2
1
1
2
5
1
2
1
3
2
5
0
0
2
3
2
8
1
3
0
1
2
0
0
0
10
2
2
1
2
2
3
5
3
7
6
2
1
1
2
7
2
0
2
2
0
2
2
1
1
1
13
2
1
12
0
1
2
5
2
1
7
2
1
2
1
2
3
2
1
5
1
0
1
3
1
0
1
3
4
1
0
3
2
0
2
1
2
1
0
1
2
2
0
1
9
2
3
2
0
0
0
10
2
4
0
1
1
3
0
2
2
0
1
0
0
7
2
1
0
0
2
3
1
4
1
1
11
3
0
1
1
2
7
8
2
2
2
1
2
3
2
0
2
3
2
4
4
4
2
2
6
1
1
1
2
0
2
2
2
2
4
1
1
1
3
1
1
4
1
1
2
2
0
0
3
4
1
1
2
1
1
1
0
0
3
3
0
4
2
1
0
2
4
6
0
3
2
2
6
1
2
1
1
1
2
2
1
0
1
3
1
6
3
8
1
0
2
0
1
2
4
1
1
2
0
0
2
4
0
2
1
0
2
2
0
1
1
2
0
1
2
2
1
1
4
0
7
3
2
2
0
0
2
1
0
2
3
2
1
0
2
0
2
2
8
1
11
0
0
1
2
0
3
3
3
1
2
0
5
1
0
7
2
4
2
0
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
2
1
2
2
3
2
1
1
0
2
2
5
3
0
1
0
0
3
3
1
1
9
2
1
2
1
4
1
1
2
3
1
1
2
18
1
0
1
0
3
3
2
0
1
2
0
4
7
0
2
1
3
2
2
0
2
2
3
1
0
2
1
3
4
0
2
4
1
5
2
2
2
1
4
2
7
2
1
4
2
2
1
11
2
4
3
2
1
4
0
1
1
3
0
4
2
15
1
1
1
0
1
1
0
1
2
1
2
1
2
3
0
1
0
1
1
6
3
3
1
2
1
0
1
2
2
2
0
2
2
1
2
4
0
2
2
0
1
8
3
2
6
0
0
3
3
3
2
7
3
2
0
1
1
1
3
1
4
4
0
10
1
0
2
1
2
2
3
1
3
1
0
1
4
3
2
0
3
2
1
0
4
3
1
2
0
1
0
4
2
3
1
0
2
3
1
1
3
5
1
1
1
4
2
4
1
2
2
1
2
1
1
2
1
1
1
1
2
0
1
0
2
2
3
3
3
3
5
1
3
2
0
7
1
0
3
2
1
3
1
1
1
1
2
1
1
1
0
1
3
1
5
1
2
1
1
7
1
0
0
2
1
1
1
1
1
0
1
1
2
3
0
0
4
1
5
3
1
0
4
1
2
1
7
0
1
5
0
3
1
1
2
2
1
3
3
2
0
2
1
1
1
1
2
2
9
2
2
0
3
2
0
3
1
5
2
0
0
2
1
0
1
8
1
2
0
1
2
2
4
0
1
4
1
2
2
3
2
1
1
7
0
2
2
1
0
3
5
2
6
2
2
2
2
0
4
3
1
0
5
1
2
0
2
6
2
1
1
1
1
1
1
1
1
3
0
1
3
2
2
2
2
2
2
2
2
0
1
2
1
2
1
2
1
0
0
1
0
3
3
2
2
0
1
4
1
2
1
0
1
1
0
1
4
1
1
10
2
1
1
2
0
1
5
2
1
1
1
1
6
3
3
2
3
2
1
0
2
3
1
3
7
2
2
3
0
3
0
5
2
1
0
2
7
1
7
1
0
6
0
0
3
1
2
0
0
2
1
2
9
2
2
2
1
6
3
0
4
2
2
8
0
1
5
12
2
1
4
1
0
2
1
3
13
3
13
2
0
2
0
4
0
1
0
1
0
8
1
6
0
1
3
2
1
2
1
0
1
4
4
2
1
0
1
0
0
2
3
1
6
1
2
1
1
0
0
1
1
3
1
0
0
2
0
2
0
1
2
2
1
1
0
4
1
8
1
8
2
4
3
1
2
1
3
2
1
1
2
1
1
3
3
0
0
2
2
4
1
3
2
2
0
4
2
4
1
0
1
0
3
2
0
5
1
2
0
2
2
3
0
2
0
1
0
4
2
1
1
0
0
0
4
2
0
0
3
4
2
2
2
2
1
1
1
4
3
2
6
2
3
3
1
1
1
0
0
2
1
3
0
4
0
10
2
1
2
0
0
0
3
14
1
3
2
2
2
0
2
2
3
9
1
0
0
2
1
3
2
1
0
2
1
1
0
1
4
2
4
1
1
2
0
0
3
0
0
0
1
3
0
1
1
2
2
3
2
0
1
6
1
0
1
5
3
1
0
2
1
1
0
1
1
1
0
1
1
0
4
2
3
2
1
2
0
5
5
0
0
1
3
1
1
2
0
0
2
2
2
0
2
3
1
0
1
2
3
1
1
2
1
0
6
1
2
3
1
1
2
2
2
2
0
0
0
1
1
3
4
1
1
0
5
5
1
2
2
5
4
1
11
1
2
1
1
2
4
0
2
0
3
0
3
6
3
0
1
2
3
1
1
2
1
1
4
6
1
3
2
3
1
1
0
2
1
3
1
6
1
0
1
1
1
1
1
1
1
1
2
2
2
3
2
2
1
5
0
1
2
4
0
0
3
0
1
1
1
0
0
2
1
1
2
1
2
2
1
1
2
0
1
3
1
1
2
2
1
2
1
1
1
2
2
1
2
3
3
1
4
2
3
2
2
3
0
3
4
2
14
0
2
1
0
1
0
1
2
0
0
2
3
3
1
1
1
2
1
1
3
3
0
1
0
0
0
5
1
3
3
2
0
2
0
1
1
2
1
3
2
2
3
1
2
2
3
1
2
1
5
2
0
6
0
1
0
0
2
1
4
0
1
2
2
1
11
0
2
0
6
6
5
1
4
1
1
2
2
0
1
0
1
1
1
0
1
1
2
1
5
1
0
1
1
1
1
6
2
2
0
0
5
0
3
2
1
0
1
2
0
1
5
1
1
1
1
0
5
2
3
1
0
3
0
4
1
1
4
2
0
0
3
0
3
1
0
3
2
2
1
2
6
1
2
0
1
1
2
0
0
1
0
1
1
1
0
2
4
1
2
1
2
2
0
2
1
0
3
3
17
3
1
1
3
1
5
1
0
0
4
5
1
0
0
1
1
1
3
0
7
0
1
1
1
1
2
4
1
6
2
2
2
8
2
2
6
2
4
3
0
1
3
2
2
2
1
0
1
0
0
4
2
3
3
3
3
0
2
1
1
2
2
1
6
2
1
2
1
1
2
0
2
2
3
0
0
0
5
1
2
0
1
1
0
1
3
1
3
5
3
2
1
3
1
2
2
1
1
3
4
1
1
2
2
3
2
3
3
1
0
6
2
1
0
1
0
0
2
0
4
2
0
3
6
3
0
0
1
1
1
1
22
2
3
0
1
2
1
0
2
0
0
3
1
2
2
3
2
3
2
0
0
2
1
1
0
2
1
2
2
3
3
3
1
0
2
2
0
2
0
1
2
0
1
4
2
1
1
0
2
0
3
12
1
1
3
0
1
7
3
2
0
1
1
1
0
8
1
2
3
3
1
2
1
2
3
0
0
1
4
3
4
1
4
3
1
1
1
2
4
0
5
2
2
0
1
3
0
1
0
1
1
0
3
2
1
0
3
1
2
1
3
2
3
1
5
1
3
1
0
0
0
1
0
4
3
3
2
1
0
1
0
1
0
2
2
4
1
1
2
2
21
1
0
4
10
1
0
2
1
1
1
0
3
0
0
1
4
2
6
2
1
7
1
1
1
8
2
1
1
1
0
2
2
1
2
2
0
6
8
2
3
5
2
2
5
2
0
3
0
1
0
1
0
1
1
1
0
1
1
0
1
2
1
3
1
0
3
1
1
3
3
1
2
2
5
2
2
4
1
2
2
1
1
1
0
0
1
0
7
0
1
0
0
1
2
2
2
0
7
6
2
5
1
3
0
3
3
5
5
3
1
3
1
3
0
1
2
1
2
1
0
1
5
2
1
2
1
2
2
0
1
3
0
2
0
0
1
1
6
2
2
1
0
2
1
2
4
1
2
2
2
4
2
1
1
2
0
1
1
4
5
2
2
1
2
3
1
2
2
3
0
0
1
1
1
1
1
0
2
2
1
4
2
1
1
1
2
1
2
3
0
1
1
2
3
0
0
0
0
1
0
3
1
1
1
1
3
2
3
1
0
2
0
0
2
1
1
4
0
1
0
2
1
1
1
1
2
3
5
1
1
1
1
3
1
0
0
4
1
1
1
2
0
2
12
3
1
2
1
1
0
5
1
1
1
0
4
1
1
0
2
0
2
3
2
2
1
1
3
2
2
7
3
1
1
1
3
4
3
1
1
0
1
2
2
2
2
1
7
0
1
0
1
1
0
2
1
0
1
9
4
1
4
4
0
0
2
2
3
0
2
2
0
0
0
1
0
3
6
1
2
1
2
10
0
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
8
1
2
2
2
1
0
2
0
3
0
4
0
2
2
2
2
11
2
2
3
1
2
2
4
2
3
3
0
1
0
2
2
0
1
0
1
1
1
7
2
1
3
1
1
3
1
10
1
1
1
2
1
2
1
1
2
0
3
3
1
0
3
1
0
3
3
6
3
4
0
0
0
3
1
1
0
1
2
2
0
1
0
1
7
1
1
1
0
1
6
5
2
2
1
0
0
2
0
1
2
3
1
1
1
0
0
1
2
0
0
2
1
0
0
12
1
2
1
1
4
1
3
1
2
0
0
3
1
1
4
5
0
0
1
1
14
0
3
1
1
3
0
0
0
2
1
1
3
3
2
2
2
2
3
1
1
4
2
0
4
2
2
1
1
1
1
4
1
6
2
1
0
0
2
2
2
0
1
2
2
0
2
1
2
0
1
3
2
1
0
1
2
1
1
0
1
2
0
1
1
1
1
5
3
1
1
3
1
0
1
1
0
1
1
0
3
0
5
0
2
1
3
10
1
2
1
0
2
0
2
6
1
2
0
1
3
0
2
1
1
1
2
2
1
1
1
0
1
2
1
3
1
1
0
2
0
5
1
1
4
0
1
1
6
0
1
0
2
1
0
1
1
1
1
5
0
0
1
4
1
0
2
1
1
0
1
2
4
0
1
0
2
1
0
1
1
1
0
3
3
2
3
1
4
2
1
1
3
2
1
0
0
0
2
1
0
1
0
1
5
14
3
4
1
2
1
2
1
1
0
0
1
4
11
1
10
1
3
2
2
1
1
1
4
0
2
1
3
2
2
2
2
1
4
1
2
1
0
5
4
0
0
3
0
0
2
2
1
1
1
4
1
3
1
1
1
3
2
0
3
5
2
1
0
2
2
1
3
6
2
1
2
1
5
1
2
0
3
9
1
1
0
1
3
0
6
0
2
3
1
1
0
1
4
2
0
3
1
1
0
0
0
0
2
1
9
3
0
1
0
2
1
2
2
0
2
1
0
1
2
2
0
0
2
1
0
1
1
0
0
1
3
1
0
2
0
1
1
1
1
0
0
0
5
1
1
0
2
1
1
5
2
0
0
5
0
0
0
2
0
4
2
0
2
0
1
2
4
1
0
3
1
3
1
3
2
2
6
3
3
3
0
3
1
1
2
3
0
0
0
0
1
0
0
2
1
1
1
1
1
2
0
1
1
2
3
0
2
1
1
0
1
0
0
1
10
0
1
3
1
1
1
10
5
2
3
2
3
2
0
1
2
1
0
5
3
1
0
0
8
1
0
8
7
4
1
1
1
0
5
1
0
2
1
0
2
2
2
0
2
2
1
7
0
4
2
2
8
0
3
4
6
1
4
2
5
2
2
1
3
2
1
1
0
3
3
0
1
2
2
0
0
0
0
1
4
1
1
0
0
1
2
2
2
0
2
1
0
1
2
1
8
3
0
1
2
0
0
1
0
2
0
9
3
2
0
8
3
4
2
0
1
1
0
1
3
2
1
1
2
2
1
1
15
0
5
3
1
7
1
1
1
1
2
2
1
0
0
1
0
1
0
2
0
2
0
2
2
8
1
1
2
0
2
0
6
3
2
2
0
1
3
2
3
3
0
0
1
0
1
1
1
4
0
3
2
1
0
3
2
2
1
2
3
0
0
4
2
0
1
1
1
2
1
12
1
2
0
0
2
1
2
0
4
1
3
0
1
4
1
1
3
0
2
4
0
3
0
0
2
6
0
2
6
0
4
0
6
3
4
1
1
0
2
0
1
3
5
2
4
1
1
1
10
1
2
0
2
3
1
1
2
0
1
2
1
1
1
2
5
3
2
1
3
1
0
1
1
1
1
1
3
2
2
2
1
0
0
1
1
2
0
2
3
0
0
1
1
3
0
4
6
1
1
0
1
3
0
1
0
5
1
4
5
2
1
2
2
0
3
0
0
4
3
8
0
1
3
1
1
4
5
1
2
3
0
1
1
1
1
0
1
0
1
1
1
2
8
3
1
2
4
0
6
1
1
1
2
12
0
2
1
1
2
3
0
3
1
1
0
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
3
1
2
1
1
2
4
0
0
0
3
2
0
2
1
1
0
2
1
1
1
1
6
5
2
1
2
7
2
1
3
0
1
1
1
1
0
0
4
3
1
3
0
1
0
0
3
2
4
0
1
1
0
2
1
2
0
1
0
0
4
0
1
1
6
4
1
0
13
2
1
2
1
3
5
0
0
1
0
1
1
1
0
1
1
0
2
0
2
0
0
10
1
3
3
1
1
1
2
2
0
5
0
0
1
3
2
1
4
1
1
2
2
2
2
1
1
0
1
4
1
0
8
2
3
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
2
5
2
0
2
8
2
2
2
1
0
2
0
3
0
0
1
2
0
0
4
2
1
2
0
1
1
1
1
3
1
8
0
0
0
0
0
2
2
0
0
3
3
1
1
2
2
1
1
0
2
1
1
1
1
2
0
0
5
4
3
0
3
4
7
1
7
1
2
1
3
1
1
0
3
1
0
4
1
1
0
2
3
0
1
1
0
1
2
1
1
1
0
1
2
3
0
1
0
1
3
2
0
1
2
2
1
1
2
9
2
1
3
1
4
2
1
4
3
2
3
4
2
2
1
1
5
2
1
5
1
0
1
1
3
1
0
1
0
1
2
0
1
0
4
3
1
0
0
1
1
0
1
1
0
2
2
2
1
3
0
1
1
5
1
2
1
1
1
1
1
0
1
0
3
2
5
4
1
2
1
0
1
0
1
1
4
1
2
3
2
0
1
0
0
3
0
0
5
2
0
2
1
4
5
1
1
1
1
0
0
1
0
1
3
0
2
0
1
2
1
0
1
3
2
0
1
4
1
18
1
2
0
1
2
1
0
2
3
2
2
4
1
0
0
1
0
3
3
1
0
2
0
0
1
1
2
0
1
0
1
0
0
1
2
5
1
1
7
1
2
1
15
8
2
2
2
0
5
0
4
0
1
7
1
0
2
0
0
3
0
2
0
5
2
1
1
5
4
2
0
1
6
2
2
0
0
0
0
4
2
1
4
2
9
1
4
2
3
1
5
0
0
2
1
1
2
10
2
0
0
2
1
1
0
9
11
2
0
1
0
3
2
0
1
1
0
2
1
2
3
1
2
9
2
1
1
5
1
0
5
2
0
0
1
0
1
3
1
1
1
1
1
2
1
2
5
2
8
1
0
0
1
3
0
2
0
2
0
2
2
1
0
0
1
0
2
2
1
4
3
0
1
1
0
0
9
4
1
2
1
1
11
3
1
0
0
2
0
2
2
0
3
2
0
0
1
1
2
0
1
0
1
1
0
1
0
5
0
0
1
1
0
2
2
5
1
0
3
1
1
1
1
2
1
2
1
1
0
1
1
0
0
0
6
1
2
4
0
0
1
0
0
4
1
0
2
0
0
0
3
0
1
0
2
3
1
1
1
0
0
0
1
1
0
1
3
0
0
3
1
6
2
0
0
3
0
0
0
2
0
2
2
0
6
4
2
2
1
3
0
2
1
1
3
0
2
1
1
1
0
1
1
9
1
4
1
1
1
0
1
1
2
1
0
1
2
4
2
1
0
0
0
1
4
0
1
1
1
3
1
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
7
0
1
1
1
3
13
2
1
2
1
0
2
1
0
4
1
2
10
1
0
2
1
1
3
1
1
2
0
2
0
2
0
0
5
1
0
3
0
1
0
3
4
0
0
0
2
1
0
2
0
3
1
1
0
1
7
0
0
0
0
2
2
3
3
2
3
4
0
4
4
4
0
1
3
0
1
0
1
1
0
2
0
1
1
2
1
2
2
1
1
1
0
2
2
2
2
2
2
2
2
2
0
0
1
1
1
2
2
1
0
3
3
2
0
1
3
4
1
1
0
1
1
13
4
1
1
1
1
5
1
0
1
0
0
3
1
1
0
1
8
2
3
1
1
2
2
2
2
3
1
1
0
1
0
16
4
7
2
2
2
0
6
4
4
1
1
1
2
3
0
2
5
1
2
0
2
2
5
2
0
2
3
1
1
2
1
1
2
1
0
0
2
0
1
1
0
3
2
1
0
1
5
0
0
4
2
0
0
5
2
1
2
3
1
0
3
2
0
1
0
0
2
4
7
0
3
2
1
2
0
0
1
2
0
5
0
2
2
1
2
0
0
2
3
7
2
1
1
2
15
1
0
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
0
6
1
0
0
2
1
1
1
1
0
0
2
0
1
1
0
1
3
0
2
4
3
3
0
1
0
0
3
6
0
1
0
1
3
0
2
1
2
0
2
1
2
2
2
1
1
5
0
0
0
2
7
1
0
2
0
2
0
1
2
0
6
8
2
2
1
0
1
1
0
1
2
3
3
0
2
0
1
0
0
1
1
2
1
0
1
2
2
1
3
2
1
1
0
2
0
1
8
2
3
0
2
2
2
1
4
1
1
1
1
4
2
0
1
0
1
0
0
2
1
0
11
2
1
1
4
1
2
1
0
2
2
1
2
5
0
7
0
1
1
1
2
2
1
1
1
0
1
1
1
1
5
18
1
0
0
14
2
0
1
3
1
0
1
0
1
1
1
1
3
2
5
1
2
0
1
0
0
3
3
1
0
1
1
3
3
4
1
1
4
2
0
0
1
2
1
1
4
2
3
0
0
1
0
1
1
0
0
1
0
3
1
2
0
1
0
3
0
0
0
1
1
7
0
0
2
0
0
2
4
0
8
3
1
0
2
2
1
1
1
1
1
5
2
1
1
1
1
0
1
2
1
1
0
0
3
1
2
5
1
1
1
4
0
1
0
3
0
2
1
1
1
0
0
2
0
1
2
3
0
2
0
1
1
2
1
1
3
0
1
3
1
4
2
1
0
0
0
2
0
3
2
0
1
2
2
0
3
3
1
0
0
3
1
1
1
0
2
0
1
1
1
2
4
1
1
0
1
2
0
2
1
2
3
0
0
3
0
0
0
1
0
0
0
6
10
1
0
2
0
0
4
3
1
1
1
0
1
0
2
0
0
2
2
2
1
1
0
3
2
3
1
1
13
0
1
3
2
1
0
2
1
2
0
0
0
1
2
0
0
2
0
0
2
2
6
0
1
2
2
8
0
1
0
0
3
1
1
0
3
1
1
0
1
2
0
1
2
0
2
0
5
3
1
0
1
2
1
1
3
0
0
0
1
0
4
2
0
4
2
0
2
2
0
2
0
2
1
1
0
0
2
2
2
0
1
4
1
0
1
0
1
1
2
7
0
1
0
0
1
5
0
1
4
1
1
1
1
0
1
0
2
2
0
1
0
2
1
0
6
1
0
1
1
2
0
0
0
1
2
1
3
0
1
0
3
4
4
1
2
0
1
7
3
0
1
1
2
0
2
2
1
0
1
1
0
2
2
2
0
0
2
1
2
0
2
2
1
3
1
1
1
1
3
0
2
1
0
2
0
1
1
9
1
0
1
1
1
1
0
2
3
1
0
4
1
1
1
2
2
0
2
3
2
1
0
2
8
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
2
3
2
0
1
0
1
1
0
1
3
0
2
1
0
0
2
1
1
3
0
1
1
0
1
2
0
3
3
2
0
0
0
1
5
2
1
5
3
0
1
1
1
1
0
2
4
0
2
1
2
0
0
6
2
3
1
1
0
1
9
2
0
2
4
1
0
4
1
1
6
1
1
0
5
1
1
0
1
6
1
2
0
0
2
0
1
3
1
1
0
0
6
0
3
2
2
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
2
0
0
3
0
0
1
3
1
2
0
2
1
3
1
0
0
2
0
0
0
1
2
2
0
3
0
3
0
5
1
1
2
3
1
0
0
0
1
2
2
3
0
1
0
2
1
2
0
0
2
2
1
0
1
1
1
0
0
1
2
6
1
2
0
2
6
2
0
1
1
1
3
1
2
2
3
1
9
4
0
1
1
2
1
1
0
0
3
4
0
0
1
1
6
1
0
4
3
2
2
0
1
3
0
0
2
0
0
0
4
2
1
4
0
0
3
2
0
0
2
1
1
3
1
0
1
1
3
0
3
2
0
1
1
1
3
0
0
2
3
1
0
2
0
1
2
2
2
1
0
0
0
2
11
4
1
3
2
0
1
6
3
3
0
0
0
2
0
2
3
2
1
1
2
1
0
0
2
3
1
1
0
0
0
0
4
0
1
3
1
2
0
2
1
1
1
2
2
2
0
2
2
0
9
3
1
3
3
1
3
1
0
0
3
0
0
0
4
3
0
2
0
0
1
3
1
1
0
1
1
1
1
1
1
0
1
0
2
0
3
0
4
1
3
2
0
0
4
1
1
3
0
1
1
0
2
0
3
1
1
3
0
3
2
1
0
2
2
0
2
2
2
0
0
2
0
0
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
4
2
4
1
2
1
4
2
2
4
1
0
1
1
2
1
1
1
1
2
1
2
1
4
1
2
12
2
1
0
7
2
4
0
2
2
3
3
1
0
2
3
1
1
0
0
1
2
2
1
3
6
2
0
9
1
0
5
2
0
1
2
1
1
0
2
0
2
2
0
0
1
0
3
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
3
0
0
1
0
1
1
1
2
5
0
0
3
3
3
1
1
1
3
1
4
2
2
1
2
1
1
1
1
0
3
0
1
0
1
0
1
1
1
0
0
1
0
2
2
3
1
2
1
0
0
0
1
0
1
2
1
1
1
0
1
0
1
1
0
0
2
2
1
1
1
2
0
0
1
3
1
1
2
2
1
3
2
1
0
2
1
0
0
0
1
3
0
1
0
3
0
0
2
0
3
0
1
0
2
0
2
3
10
0
1
3
0
1
0
1
1
1
0
1
0
2
0
0
1
2
2
2
0
4
0
3
1
0
2
7
1
1
2
1
0
2
2
0
1
2
1
1
2
4
0
1
5
3
1
0
4
1
1
1
1
3
2
0
0
2
6
1
2
3
5
3
0
2
0
0
0
1
0
2
3
2
2
1
0
0
1
0
0
0
0
2
3
4
3
0
0
1
11
3
1
2
0
1
1
2
2
0
0
3
1
0
1
0
2
0
1
0
0
0
1
1
1
1
0
3
2
0
0
24
1
1
1
0
1
0
1
1
1
0
0
1
5
0
0
4
0
1
1
2
1
2
1
0
2
2
1
1
0
0
0
1
3
0
1
3
0
1
0
0
3
1
0
0
1
1
1
1
1
1
2
0
2
3
1
2
2
0
3
3
1
2
1
0
1
4
0
0
1
5
1
0
10
6
1
0
0
0
1
1
1
0
1
0
1
3
2
0
1
0
1
3
3
1
1
0
1
1
1
0
0
1
0
0
0
3
1
3
0
1
0
2
1
0
2
2
1
0
2
1
0
0
0
1
1
0
1
0
1
1
1
6
1
0
1
4
1
2
1
0
1
3
0
3
0
1
1
3
2
0
0
2
1
0
1
0
0
1
1
2
8
0
11
1
2
1
1
6
2
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
2
1
0
2
1
1
0
0
1
0
1
0
9
2
5
2
1
1
1
2
0
2
0
1
1
6
0
4
1
1
2
4
1
1
2
1
6
0
1
1
1
0
1
1
1
4
6
0
0
4
3
3
2
2
0
7
4
0
4
2
0
1
0
0
1
0
0
4
1
0
1
1
0
2
2
7
0
3
1
2
2
2
1
1
3
0
1
0
2
1
7
0
1
1
0
1
1
0
1
1
1
1
2
3
0
1
0
1
2
0
1
1
0
7
0
0
1
2
0
2
3
0
2
4
1
3
1
0
2
2
2
3
0
0
1
2
0
0
2
1
0
1
2
0
0
1
0
4
1
0
0
0
0
0
0
4
0
1
0
3
2
0
0
1
3
2
1
0
1
1
2
2
1
0
0
1
4
0
0
3
3
0
0
1
2
1
0
0
1
1
1
1
1
0
2
0
0
1
1
0
2
1
1
3
1
0
3
1
2
4
3
11
0
1
2
0
0
2
0
2
1
1
8
1
1
1
1
4
0
1
2
0
2
0
2
2
0
1
0
2
1
0
1
1
0
3
2
2
2
1
1
7
1
1
1
0
9
0
3
0
2
1
0
1
1
0
0
0
0
3
2
1
0
2
0
2
0
2
0
2
2
3
0
0
0
1
4
1
3
0
7
1
9
6
2
0
3
0
1
1
0
1
1
2
6
2
0
3
2
2
2
0
1
1
1
1
0
0
0
0
1
1
5
1
3
1
0
0
0
2
0
1
1
0
3
0
0
1
3
2
2
0
0
1
3
2
1
0
1
1
5
0
1
1
0
1
1
2
0
1
0
0
1
0
1
2
1
1
0
1
1
1
0
2
2
1
0
8
5
0
0
1
0
4
1
1
2
0
0
0
1
0
9
2
0
1
2
0
1
1
1
2
2
4
1
0
1
0
0
5
1
1
2
1
4
1
10
3
1
2
1
0
0
2
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
3
2
1
1
0
1
0
0
9
0
0
2
2
0
0
0
1
1
0
3
1
3
3
0
1
0
1
2
0
2
2
3
6
4
0
1
3
1
0
0
0
0
0
2
2
2
2
0
0
1
2
0
9
0
1
0
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
3
3
1
1
0
1
3
2
0
2
0
0
4
0
1
2
2
0
1
1
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
1
2
1
1
2
3
5
1
1
0
0
3
0
0
1
0
1
0
0
1
2
1
2
0
2
2
0
1
7
5
0
2
15
2
0
0
0
3
2
3
2
2
0
2
1
0
2
1
2
2
2
6
5
3
1
1
1
2
1
2
3
0
2
0
1
1
1
2
3
1
0
4
0
12
1
2
0
0
1
0
0
1
0
0
2
1
1
1
2
1
7
7
2
1
0
2
0
8
0
1
1
0
0
1
3
1
0
2
1
0
1
1
0
1
1
2
1
2
1
0
1
1
0
0
3
3
3
0
0
0
1
2
2
0
0
0
2
0
2
1
1
2
1
2
0
0
0
1
0
1
0
3
1
0
0
2
0
1
0
1
0
1
3
2
1
2
2
0
0
2
1
0
1
1
0
0
0
1
0
2
0
3
1
8
1
1
0
3
0
0
0
2
0
6
0
2
0
1
1
1
1
1
0
0
2
2
3
1
4
0
0
1
4
0
3
2
1
0
16
0
2
2
2
0
0
1
0
5
1
0
0
1
0
1
3
1
0
1
0
1
5
2
3
1
1
1
3
2
2
3
3
0
0
0
0
2
8
7
0
0
1
2
1
0
1
4
3
2
1
1
1
5
1
0
1
0
0
0
1
0
1
2
2
0
0
1
3
0
4
0
0
2
1
2
0
1
1
0
0
3
2
2
1
3
1
1
0
1
2
2
3
1
0
1
2
1
2
1
0
1
1
1
0
1
1
3
2
1
2
1
0
0
0
0
0
1
7
2
1
2
2
0
0
2
3
0
1
1
0
3
3
0
1
9
0
1
1
2
3
4
1
1
1
1
2
1
0
0
0
0
4
1
12
2
1
2
3
2
0
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
2
2
0
1
0
0
1
0
0
2
3
0
0
1
5
1
2
1
3
0
2
4
0
0
0
1
0
7
0
4
1
0
3
1
3
2
1
2
1
2
1
1
0
1
0
1
2
0
0
0
10
0
1
1
1
0
1
1
0
1
1
2
3
2
1
2
1
0
0
0
0
0
0
2
1
0
1
1
0
1
3
3
0
1
1
0
1
1
0
0
0
0
1
2
4
0
3
1
2
1
2
3
0
4
0
1
0
0
2
1
0
0
1
5
1
1
2
0
2
2
2
0
0
3
2
0
1
0
0
1
2
1
1
3
0
0
0
5
0
0
0
1
1
2
1
0
4
1
1
2
2
16
0
0
0
1
1
2
1
0
3
2
4
0
1
7
0
3
1
0
3
1
1
0
2
0
2
1
2
0
0
0
0
5
2
2
2
0
1
1
3
1
2
0
0
2
4
1
1
0
1
2
0
5
0
0
1
1
0
2
2
2
2
0
2
1
1
0
0
0
1
0
4
0
0
0
2
2
0
1
0
2
3
1
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
1
2
1
0
1
1
10
3
0
0
1
2
2
1
3
1
0
1
0
1
2
0
0
0
1
1
2
3
1
2
1
1
2
2
0
0
8
1
7
2
2
3
0
2
0
0
1
0
2
0
3
2
2
2
0
1
0
3
1
1
3
0
2
13
1
6
1
0
0
0
2
1
0
0
0
2
0
0
0
2
16
1
1
1
2
1
2
1
3
0
2
1
0
5
1
2
0
3
1
4
2
4
0
0
3
0
1
0
1
2
0
1
0
12
0
2
0
0
3
1
0
5
0
0
2
4
1
1
0
1
0
2
3
1
1
2
1
0
0
1
0
1
0
4
1
5
4
1
0
3
1
1
1
2
0
0
2
4
0
1
7
1
1
0
2
2
1
0
1
1
5
0
0
1
3
1
2
0
0
1
0
0
2
0
4
1
0
0
1
0
1
2
1
3
0
0
0
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
0
3
0
0
2
2
0
1
3
1
0
1
1
0
0
4
2
2
2
0
4
1
2
1
2
0
1
1
1
1
0
1
2
1
0
2
0
1
4
1
2
0
0
0
2
1
1
2
3
1
0
2
0
0
0
2
1
5
0
2
1
2
3
1
0
1
0
3
4
2
0
4
1
3
0
2
0
2
1
1
0
1
1
2
2
2
0
1
1
0
1
0
1
0
0
0
1
0
1
1
2
1
1
0
1
0
1
2
1
0
0
1
0
2
4
2
1
1
1
5
2
1
0
1
2
2
1
1
0
0
1
2
17
1
2
0
1
5
1
1
0
1
0
1
2
0
1
2
6
1
2
0
2
1
0
0
3
0
4
1
0
0
0
3
2
0
1
1
0
1
1
2
0
1
0
1
3
1
1
3
0
3
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
0
1
2
2
1
0
2
2
2
1
3
0
0
1
1
0
0
3
0
0
1
0
1
3
0
1
3
3
0
0
32
0
3
0
1
3
2
1
1
0
1
1
1
2
3
1
1
1
0
0
0
2
8
4
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
1
2
0
0
1
2
1
1
1
0
1
1
2
3
4
2
0
9
4
4
0
0
0
3
0
0
0
1
2
1
0
5
1
0
1
3
1
4
1
2
2
1
3
2
8
1
0
1
3
0
2
1
0
2
3
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
3
1
1
1
3
2
1
3
1
0
1
1
0
5
3
2
1
0
1
0
0
1
1
2
0
2
1
1
5
3
0
0
1
2
1
2
1
1
1
2
1
0
1
5
3
1
0
1
1
1
1
0
0
1
0
0
7
3
1
0
1
0
5
0
0
5
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
2
3
0
0
0
0
1
1
3
0
2
1
1
1
2
2
3
2
0
1
1
1
2
1
1
0
0
0
2
0
3
1
0
0
1
1
2
1
0
2
2
6
0
2
0
2
2
1
1
1
0
1
1
2
0
1
1
0
2
1
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
5
1
0
0
2
2
8
1
0
1
2
0
1
0
1
1
4
0
0
1
0
1
1
0
1
4
0
0
0
1
0
0
0
0
1
1
1
0
0
3
1
2
1
1
1
2
0
0
1
1
2
0
1
3
0
3
2
2
0
1
1
0
1
0
1
0
0
0
0
0
3
0
2
0
2
3
3
3
0
1
6
0
1
0
1
1
0
0
8
0
2
1
1
3
1
3
2
4
0
1
1
3
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
2
3
0
2
1
1
0
3
0
1
1
0
4
3
2
0
0
0
2
15
1
0
1
1
2
2
0
0
2
1
0
0
1
1
2
0
4
1
0
5
0
1
1
1
0
2
0
2
4
2
2
2
1
2
0
1
0
3
0
1
4
1
0
1
2
0
1
21
2
0
0
0
1
1
1
0
1
1
1
0
2
1
1
0
10
1
2
2
0
0
1
1
4
1
2
0
2
2
1
0
1
1
0
1
1
1
0
1
0
2
0
2
1
0
2
2
0
3
0
1
1
1
1
6
2
1
2
1
3
0
2
3
7
1
1
1
10
0
0
1
1
1
0
1
1
2
1
10
1
4
0
0
1
1
3
0
1
3
0
1
1
0
0
1
2
2
1
0
0
1
1
1
0
1
2
2
2
1
2
0
0
2
0
1
1
3
1
2
0
2
0
1
0
1
0
1
0
2
3
1
0
0
7
0
0
2
0
1
0
1
2
0
2
1
1
0
0
4
7
0
0
2
1
2
0
2
0
0
0
0
0
1
1
1
0
0
1
8
3
1
3
1
0
1
1
0
3
1
1
1
1
0
2
1
0
0
2
3
0
1
1
3
0
2
0
0
0
1
0
0
2
1
3
8
2
2
0
0
3
1
1
1
1
1
1
1
0
2
3
2
0
1
1
3
3
0
0
0
1
3
0
3
1
0
0
1
7
1
1
0
0
1
1
0
1
1
0
3
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
2
0
0
3
0
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
0
3
1
2
0
1
2
1
1
1
7
0
2
1
0
0
0
1
1
2
1
1
3
0
0
1
4
0
1
1
1
0
0
0
2
0
1
0
0
0
1
3
1
0
0
1
8
2
1
1
0
2
1
0
3
1
1
2
1
1
0
0
2
1
0
0
1
0
2
1
2
1
1
0
1
0
0
0
1
3
1
0
1
1
1
2
1
1
3
0
0
1
2
0
4
1
0
0
0
0
0
1
1
2
0
1
5
2
0
0
0
1
1
3
1
2
0
0
1
3
0
1
0
3
1
0
1
1
0
0
0
1
2
2
2
1
2
2
1
2
0
0
2
1
1
1
0
0
2
2
0
1
0
1
2
2
1
3
2
0
0
2
0
0
0
0
0
2
1
0
0
1
16
3
2
1
0
2
2
0
2
2
0
1
0
0
0
0
1
0
0
2
0
2
2
1
1
2
1
1
1
0
1
0
2
1
0
0
0
0
1
1
14
0
1
12
1
4
0
0
1
1
3
0
0
0
10
1
0
0
1
2
1
1
1
1
0
1
2
0
1
1
0
4
5
0
0
2
0
1
0
0
0
1
2
1
2
1
0
0
0
1
2
0
3
0
6
0
0
1
0
1
1
0
2
1
2
1
0
3
3
0
1
0
0
0
0
1
0
1
0
5
2
1
0
0
1
3
1
0
0
1
0
0
0
2
1
2
1
4
2
1
0
2
1
4
2
0
1
2
2
2
0
3
3
0
0
0
3
0
3
2
1
1
0
1
2
11
0
0
1
0
1
4
2
2
0
1
2
5
0
1
2
0
2
11
2
2
0
1
1
2
1
4
0
0
2
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
1
3
0
0
0
2
1
1
1
2
1
1
2
0
1
1
0
2
1
0
0
6
0
0
0
3
0
0
0
1
1
0
1
1
1
0
0
2
2
0
1
2
3
0
0
1
1
2
0
1
2
0
1
0
2
1
2
0
2
0
3
2
1
2
10
9
2
1
1
3
2
1
1
1
3
3
0
2
2
0
1
5
1
0
0
2
1
1
0
0
1
1
0
1
0
0
1
1
8
1
0
0
0
1
4
1
2
1
0
6
0
1
0
0
1
1
0
3
1
3
2
0
1
0
1
1
0
1
0
1
4
1
1
0
0
2
2
1
1
1
0
9
1
0
3
1
0
2
2
1
0
1
1
1
3
2
1
1
1
1
0
1
1
2
0
2
0
0
1
0
0
1
0
3
1
1
3
0
0
1
0
1
0
0
0
0
0
0
1
1
1
5
1
0
0
2
0
3
1
2
1
0
0
0
0
2
2
1
2
1
1
0
1
2
2
1
3
1
1
1
2
2
2
1
1
0
1
2
1
0
0
1
1
1
2
0
4
0
2
2
1
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
1
0
0
1
0
1
1
3
2
1
7
3
2
0
0
3
1
0
1
2
1
5
0
1
2
5
1
0
0
0
1
0
0
0
1
2
0
0
3
0
1
0
3
1
1
2
1
2
1
1
1
1
1
4
2
1
4
1
1
0
3
0
0
0
3
0
3
0
0
2
1
1
0
1
1
1
0
1
3
0
6
0
1
0
0
0
0
3
0
1
0
1
1
1
0
2
1
1
2
2
0
4
1
1
0
0
3
1
1
0
2
1
0
1
1
1
1
2
0
0
1
0
1
1
0
3
0
0
0
1
0
0
0
1
0
1
2
1
1
0
1
2
3
1
6
1
0
0
0
10
0
2
0
2
1
1
1
1
1
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
7
2
1
0
1
1
1
0
1
1
1
0
0
0
2
0
10
1
1
0
1
0
0
1
0
0
0
1
0
1
4
0
3
1
1
4
0
2
1
1
1
0
0
0
1
3
1
1
0
9
3
1
1
1
0
2
0
1
0
2
0
1
0
1
1
0
1
1
4
2
0
1
1
0
2
0
0
5
2
3
0
1
1
0
0
0
2
4
4
1
0
0
0
0
1
1
2
1
0
0
3
6
0
1
3
1
2
2
0
5
1
1
2
1
1
1
1
0
18
0
1
0
0
2
1
0
0
1
0
0
2
1
6
2
2
8
7
1
0
0
1
1
1
7
1
0
2
3
1
1
3
1
0
1
1
0
0
1
0
1
2
1
0
0
2
0
1
0
1
2
0
2
1
0
15
0
0
0
1
1
0
1
2
0
0
2
1
5
5
1
2
0
1
2
0
0
0
0
4
0
2
1
1
7
2
0
0
3
3
0
2
1
3
3
2
0
1
2
0
1
0
0
0
3
1
2
2
1
2
0
0
1
0
1
0
0
0
2
1
0
1
1
0
6
0
0
0
1
0
2
1
2
1
1
0
1
1
1
5
3
0
1
1
0
1
2
0
0
0
6
1
1
1
1
0
1
2
0
1
3
0
1
2
0
2
1
0
0
1
1
2
0
0
0
0
3
2
1
1
0
2
2
1
0
1
1
2
1
0
0
0
0
3
2
1
0
5
2
0
1
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
2
0
11
1
1
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
0
1
1
0
2
0
0
2
2
1
1
0
0
0
0
1
0
0
1
1
0
2
1
0
3
1
2
0
0
0
1
3
0
2
1
0
0
1
0
2
2
0
3
0
1
3
2
2
0
1
1
1
0
3
1
0
0
2
1
1
1
6
1
0
0
1
0
0
1
0
2
0
0
4
0
0
1
0
0
3
1
0
1
2
1
1
2
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
3
1
2
2
0
1
1
1
0
1
6
0
1
11
0
2
1
4
1
1
0
0
1
2
0
0
1
3
3
1
1
0
3
1
1
1
0
0
0
2
0
0
2
1
0
0
3
1
0
0
1
0
0
0
0
2
1
3
0
1
1
1
4
0
0
4
0
0
1
2
1
0
1
3
1
0
1
0
1
2
0
3
2
1
2
0
1
0
0
2
0
0
3
0
0
0
0
1
0
3
1
0
1
1
1
1
0
0
0
3
1
2
1
3
0
1
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
4
3
2
1
2
0
2
2
0
1
2
1
0
0
1
1
1
1
1
3
1
0
3
0
0
1
0
1
0
1
3
0
0
1
0
0
1
0
2
2
1
6
0
0
2
11
1
2
1
0
1
3
0
1
7
1
0
1
10
0
1
2
1
1
1
0
2
0
3
1
1
2
1
2
0
3
1
0
0
0
1
1
0
0
1
1
0
1
2
0
0
13
2
0
1
1
1
2
1
1
1
0
2
0
2
3
1
1
4
1
1
0
0
0
0
1
4
1
5
0
0
1
2
0
0
4
0
2
1
1
1
0
4
0
1
0
0
0
0
14
2
4
0
0
0
0
0
0
1
1
1
3
0
4
0
2
0
1
2
0
5
0
0
5
1
0
1
1
3
2
1
0
1
2
1
1
0
0
1
3
0
2
0
1
1
1
1
0
3
0
0
1
0
0
0
0
6
1
1
0
0
3
1
1
0
1
1
1
0
2
0
1
0
0
2
0
1
1
2
1
1
3
1
1
1
1
2
0
1
1
5
1
0
5
0
1
0
1
1
3
1
1
1
1
2
1
0
0
1
1
0
0
0
0
5
0
2
0
1
9
1
1
0
2
1
3
1
1
0
3
0
0
0
2
1
3
0
1
0
2
0
0
1
0
0
1
0
0
1
2
4
1
0
2
5
0
0
0
2
2
1
2
0
1
0
1
0
1
2
2
1
0
2
0
0
0
1
1
1
1
0
2
0
0
2
9
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
4
0
3
2
0
1
0
1
1
2
5
1
0
0
1
1
0
0
1
0
4
3
0
0
0
2
1
0
0
2
1
4
0
0
0
0
4
1
0
0
1
1
8
1
0
3
2
2
2
0
1
2
2
1
2
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
4
0
1
3
1
0
2
2
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
3
0
1
3
2
0
2
0
0
1
0
1
0
0
3
0
1
0
0
1
1
1
1
2
1
0
3
0
0
1
2
2
2
0
0
0
1
3
0
0
0
2
1
0
0
1
3
0
1
3
1
1
1
0
1
0
0
1
2
0
2
0
0
1
1
0
2
0
0
1
2
1
9
1
1
0
3
3
0
1
0
0
0
3
2
2
1
2
1
1
0
2
1
1
1
1
2
2
21
2
0
0
6
0
1
0
1
2
2
1
1
0
0
1
2
1
0
1
0
4
2
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
1
0
1
3
0
1
0
1
0
0
3
1
1
0
0
1
0
1
3
1
6
1
1
0
1
0
1
0
2
3
2
1
4
1
0
0
1
6
0
2
0
1
3
2
1
1
1
1
0
1
3
1
1
0
1
0
3
0
1
0
0
2
2
0
0
1
2
1
1
2
1
0
1
1
1
2
0
2
0
0
6
2
0
0
3
1
0
1
0
5
2
0
1
0
0
1
0
1
1
1
2
0
9
0
1
1
1
1
1
5
0
3
0
0
0
0
2
2
0
0
1
1
1
0
2
0
0
4
10
2
1
2
0
2
0
2
1
1
1
1
2
0
11
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
3
0
0
0
0
3
1
3
2
0
0
0
1
2
0
0
4
1
0
2
1
2
1
1
18
1
1
1
0
2
3
0
0
5
2
0
0
0
0
3
0
1
2
0
1
0
2
0
3
0
0
2
0
1
0
2
1
0
3
0
0
2
1
2
2
1
1
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
4
1
1
1
0
0
3
0
7
0
0
0
3
0
0
0
1
3
0
1
1
0
1
1
1
0
2
2
1
0
10
2
2
0
1
5
1
6
0
2
2
1
1
0
1
2
2
2
1
0
2
3
1
0
0
0
0
1
3
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
5
0
0
1
1
2
0
1
0
0
3
0
1
0
0
0
2
0
1
2
2
2
1
1
6
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
3
1
0
1
2
0
0
1
0
2
1
0
2
0
0
1
0
0
3
1
1
2
1
0
0
1
3
0
0
0
1
1
2
1
0
0
0
1
2
3
1
1
1
1
1
6
2
2
0
0
1
2
1
0
0
1
0
1
0
0
1
1
0
2
1
0
1
0
1
1
0
3
6
0
0
1
0
1
4
0
0
2
2
5
0
0
1
1
0
0
1
2
1
0
1
0
2
2
0
1
1
0
2
0
1
0
1
5
1
0
3
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
0
0
0
2
0
0
3
2
0
2
2
0
2
2
13
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
2
0
2
2
0
0
0
0
1
1
1
2
0
2
0
0
1
1
0
1
0
1
0
0
2
0
0
3
0
3
0
0
3
1
0
1
1
6
1
2
1
2
0
1
1
0
1
0
0
0
1
4
0
1
0
0
1
2
1
0
2
0
1
2
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
2
0
12
1
1
0
4
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
3
1
0
1
0
2
1
0
0
1
0
5
0
0
0
0
0
1
0
0
2
3
0
0
1
1
1
0
0
0
1
0
1
1
1
0
11
1
1
1
0
1
0
5
0
0
1
1
0
1
1
0
0
0
0
0
0
1
11
2
1
0
0
0
0
2
1
0
1
0
0
1
3
0
1
1
0
1
1
1
0
2
2
1
1
0
0
0
3
1
1
3
0
11
1
0
2
0
1
2
0
0
5
0
0
1
0
0
1
0
1
0
0
5
2
1
0
0
0
0
0
2
0
0
1
1
1
0
0
12
1
0
0
3
1
0
0
1
1
1
3
2
1
1
1
2
1
0
1
2
2
2
2
0
0
1
1
3
1
1
1
0
2
0
2
1
1
0
0
13
0
4
1
0
1
0
0
1
1
1
0
2
1
2
1
0
1
0
1
0
0
4
3
0
1
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
16
0
1
0
4
0
3
1
2
1
0
0
0
2
0
5
1
0
0
1
2
0
0
0
0
1
0
4
0
1
4
0
3
2
1
1
2
1
1
0
0
2
0
0
0
1
0
0
14
2
0
2
0
2
1
1
0
1
0
0
0
3
3
1
1
0
0
2
2
2
1
0
0
0
0
1
1
0
4
1
2
2
1
0
0
0
2
1
0
0
2
0
0
2
0
1
0
3
1
0
1
0
0
0
1
0
1
1
0
0
2
1
0
1
2
1
3
1
1
1
0
0
0
0
0
1
0
0
20
5
2
2
1
2
1
2
1
1
1
2
0
2
0
2
0
0
1
2
2
0
2
1
0
2
1
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
5
0
3
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
2
3
2
0
0
1
1
0
2
0
1
0
1
1
0
0
1
1
0
0
2
1
3
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
2
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
2
1
2
1
0
0
0
0
1
0
0
4
0
2
3
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
1
1
0
1
0
3
0
2
0
0
0
1
2
1
0
3
0
0
0
2
0
2
0
2
2
1
1
0
6
1
2
1
0
1
1
1
1
0
3
5
23
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
4
1
0
0
12
2
1
0
2
0
0
3
0
1
1
1
0
0
2
0
0
5
0
0
1
0
1
2
0
1
1
0
1
0
0
1
3
0
16
3
2
2
1
0
1
2
3
0
0
0
0
3
1
0
1
1
0
1
0
0
0
1
0
0
1
3
0
0
0
0
1
1
0
1
0
2
2
0
1
1
0
0
0
0
0
2
1
0
1
1
2
1
1
0
2
0
1
1
0
1
2
0
0
1
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
1
0
2
0
2
2
2
1
1
3
0
3
1
6
1
2
5
1
0
0
2
2
0
1
1
9
1
0
0
1
0
1
1
0
0
1
0
3
1
0
2
0
3
1
4
0
1
1
0
1
0
8
1
2
0
1
0
0
1
0
0
2
1
0
0
2
1
2
0
2
0
1
1
7
0
0
0
1
0
1
0
6
0
0
0
1
0
0
0
0
6
1
1
3
0
1
1
3
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
1
0
2
1
3
2
0
0
0
2
7
1
0
1
3
0
4
1
2
1
2
0
1
5
1
1
1
1
0
0
1
1
1
3
2
1
0
1
0
0
4
1
0
0
1
0
0
1
0
0
0
1
0
1
8
0
0
1
2
0
1
1
0
2
5
2
0
0
1
0
2
0
1
0
0
2
1
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
5
0
2
3
0
0
1
0
0
1
0
1
0
10
1
1
1
2
0
2
2
0
6
2
1
1
0
0
0
0
0
0
1
1
11
1
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
1
1
1
1
0
1
3
0
0
0
0
1
1
1
1
0
4
1
0
2
3
1
0
0
1
0
1
0
0
1
0
3
1
2
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
7
0
1
1
2
0
0
1
1
1
1
6
1
8
0
3
2
0
3
3
0
0
1
1
1
1
1
2
1
3
0
1
2
1
0
0
0
6
0
8
0
0
1
0
0
1
0
1
0
0
1
2
1
3
2
1
2
0
3
3
1
0
0
0
1
0
1
0
3
1
1
0
2
1
0
0
1
1
0
2
1
3
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
1
5
1
2
7
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
3
0
1
19
0
2
1
1
0
0
0
0
0
0
1
2
0
2
2
1
1
1
2
3
4
0
0
1
0
2
0
5
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
3
0
2
1
0
5
0
3
1
1
0
1
0
0
0
2
1
1
0
0
1
5
0
2
8
2
1
3
0
1
0
2
1
0
0
0
1
0
1
1
1
0
0
1
7
2
1
0
0
0
3
3
2
0
1
2
0
0
1
1
1
3
0
0
0
0
0
0
1
1
10
1
0
1
2
1
0
3
1
1
0
0
0
1
1
1
1
1
0
1
0
0
2
2
2
2
3
1
0
3
0
0
2
1
0
1
2
0
1
0
0
1
1
1
1
1
0
1
3
2
1
1
1
1
4
1
9
1
1
0
6
13
0
3
3
1
0
0
0
0
0
1
0
3
1
6
1
2
1
0
0
0
0
0
0
1
3
0
0
1
3
0
0
0
1
1
1
0
2
5
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
1
0
2
0
0
2
5
1
2
0
0
0
2
1
1
3
0
0
7
0
1
0
1
0
2
0
3
1
4
1
1
1
3
7
2
1
1
0
9
2
0
0
5
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
3
2
0
2
1
0
1
0
2
2
1
1
0
1
1
1
1
0
0
0
0
2
1
1
0
0
0
0
3
0
0
1
2
1
3
0
2
1
0
1
1
0
1
0
1
2
13
3
1
1
0
2
0
1
1
1
7
0
2
2
2
2
0
2
1
0
0
0
11
0
1
3
0
0
1
2
0
1
0
0
2
2
2
1
0
1
1
1
2
1
1
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
7
0
1
0
1
1
1
0
2
3
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
1
12
1
2
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
3
2
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
0
5
0
1
2
1
4
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
2
1
0
2
2
1
22
0
2
0
1
0
1
0
5
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
4
2
1
0
1
7
2
0
4
0
1
1
0
3
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
9
0
0
2
0
1
3
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
2
2
1
0
2
1
0
0
0
0
1
2
0
1
0
0
1
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
8
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
2
1
1
2
2
0
1
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
1
1
0
2
1
3
1
2
0
0
1
0
1
2
0
4
2
0
0
2
0
3
0
1
0
1
0
0
0
1
0
9
1
2
1
1
3
3
0
0
1
0
1
0
2
4
0
0
2
1
1
4
0
0
2
2
1
0
0
1
1
1
0
0
2
1
1
0
6
0
1
0
4
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
0
1
0
0
4
2
0
2
0
4
0
2
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
5
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
1
0
2
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
1
2
3
0
0
2
0
0
1
0
2
0
2
0
0
0
5
1
1
0
2
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
1
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
3
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
4
0
3
1
1
0
2
1
1
1
0
2
0
0
1
1
3
0
3
0
0
1
1
4
2
1
0
0
1
1
2
0
0
1
0
1
2
0
0
2
0
1
2
1
1
0
1
1
2
3
0
2
0
0
1
0
0
2
1
0
5
1
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
2
1
1
2
2
1
0
0
1
6
0
0
0
0
0
0
1
1
3
1
0
1
5
0
7
1
1
1
0
0
1
0
0
6
1
1
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
0
6
0
1
1
0
2
1
2
1
0
0
8
0
0
1
0
0
0
0
3
3
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
2
2
1
2
3
0
0
1
4
0
1
1
0
0
0
2
1
1
1
2
0
1
3
2
2
0
3
1
3
0
3
1
0
0
1
0
2
1
1
0
1
2
2
1
0
1
1
3
0
2
3
0
1
1
2
1
4
0
0
2
0
0
2
0
6
1
1
1
0
3
0
1
0
2
0
6
0
0
2
2
0
1
2
0
2
3
0
0
0
2
2
1
0
0
0
1
9
0
0
2
1
0
0
8
1
0
0
0
0
2
1
6
1
0
2
2
0
0
0
1
1
1
2
0
2
1
1
3
0
1
1
1
1
1
1
3
0
2
1
7
0
2
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
1
2
0
0
0
1
2
1
0
0
3
1
0
0
0
2
2
0
1
1
0
2
1
1
2
1
3
0
0
0
0
0
0
4
3
0
0
5
0
0
1
1
0
0
1
0
1
4
1
1
0
7
3
2
0
4
1
1
2
1
2
1
0
3
0
0
0
1
1
4
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
1
2
1
2
0
1
3
2
1
0
0
0
2
1
2
2
0
0
0
1
1
1
3
2
2
0
1
1
2
0
1
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
3
1
2
2
0
3
0
2
1
1
1
2
0
1
1
2
0
0
0
1
1
2
1
0
0
1
1
3
0
4
1
2
1
0
2
0
0
0
1
0
1
0
2
1
1
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
4
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
5
1
4
0
1
3
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
1
1
1
1
0
1
1
0
0
3
1
0
1
1
2
0
1
0
1
1
2
2
2
0
2
1
1
3
1
2
3
1
0
0
0
1
1
0
0
7
0
1
1
2
0
0
0
1
1
0
1
0
2
1
0
0
1
0
2
0
1
10
0
0
1
0
0
1
2
0
0
1
2
0
1
1
2
1
1
0
1
2
1
0
1
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
4
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
1
1
0
0
2
2
1
0
0
0
3
2
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
2
3
4
0
1
0
0
2
2
1
0
1
0
2
0
0
0
1
0
0
1
12
2
1
0
0
2
4
0
0
0
0
1
0
1
0
0
0
2
1
1
0
2
1
2
1
1
1
1
2
0
0
0
0
2
0
0
1
0
0
2
1
1
1
2
1
2
4
0
0
0
2
1
1
0
0
2
1
2
0
2
1
1
1
0
2
0
2
1
1
1
0
0
2
1
1
0
5
0
1
0
0
1
0
2
0
2
1
1
0
0
0
1
0
0
1
1
0
3
1
1
1
1
0
0
0
0
1
5
1
9
0
0
1
0
1
3
0
0
0
1
1
1
0
1
0
1
7
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
2
0
7
1
2
0
1
1
1
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
3
10
0
1
2
0
1
0
1
0
0
2
3
3
0
1
3
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
2
2
1
1
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
2
0
1
0
0
2
1
0
0
1
0
1
5
1
2
1
0
0
0
2
0
3
1
0
0
0
5
0
1
2
0
1
0
2
1
1
0
0
2
3
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
3
0
1
4
0
1
1
0
2
1
5
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
1
2
0
0
0
1
1
5
0
1
1
2
0
0
6
0
18
0
0
0
1
0
0
0
1
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
2
3
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
1
1
4
2
0
1
1
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
3
2
2
1
2
1
1
0
1
0
0
0
3
1
1
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
1
2
3
0
4
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
2
0
7
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
2
1
1
2
1
0
1
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
1
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
9
0
0
0
0
0
0
0
0
1
3
0
1
1
0
4
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
1
0
0
2
5
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
3
2
0
3
0
0
1
1
0
0
0
1
0
2
0
0
0
5
1
1
0
0
0
0
3
1
2
0
0
0
2
5
0
0
0
0
1
1
0
1
0
0
1
2
0
1
3
2
0
1
0
0
2
2
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
0
1
1
0
11
0
0
1
2
1
0
1
0
1
0
0
2
0
0
1
0
0
4
0
10
0
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
1
4
0
1
2
0
1
0
0
1
1
3
0
1
0
0
2
0
0
0
1
3
0
0
1
1
1
0
1
0
1
2
1
0
0
1
1
0
0
1
1
1
1
1
2
0
0
3
0
0
0
0
0
2
1
3
2
0
0
0
2
0
0
2
1
0
1
1
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
14
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
4
0
1
2
0
0
1
0
0
0
0
1
1
9
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
3
11
1
1
0
2
1
0
0
10
1
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
12
1
0
0
0
0
0
3
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
18
0
0
2
1
0
0
0
1
1
1
0
2
1
0
1
0
1
0
3
0
1
1
2
0
1
0
1
0
1
0
0
4
0
13
0
5
5
2
0
0
0
1
8
0
1
0
1
1
0
1
0
1
0
0
0
0
10
0
3
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
4
1
0
5
1
6
1
0
0
1
4
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
2
1
3
1
0
1
1
1
1
0
0
1
1
0
5
1
0
0
1
1
0
0
0
2
0
4
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
11
0
1
0
0
2
1
0
0
0
1
0
1
2
1
2
3
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
1
1
0
0
6
0
1
1
0
0
0
0
1
0
0
0
1
6
1
1
0
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
1
1
1
1
3
1
0
1
2
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
3
1
1
0
2
0
1
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
10
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
5
0
0
12
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
2
0
1
1
1
0
0
1
5
1
3
1
0
1
0
0
0
1
1
0
1
3
0
0
1
0
0
0
1
0
0
3
0
0
0
4
1
5
0
2
0
2
1
1
2
0
0
2
1
0
9
0
1
1
0
0
2
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
1
1
1
0
0
0
0
1
7
1
1
1
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
3
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
1
1
2
0
1
1
0
0
0
3
0
3
1
3
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
0
2
1
0
1
0
3
0
0
0
0
0
1
0
1
1
1
0
1
1
1
3
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
2
5
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
1
0
2
0
1
1
3
1
1
2
0
2
1
0
2
1
1
0
0
0
0
0
3
4
0
0
3
1
1
0
1
1
0
0
0
0
0
0
1
1
1
3
0
1
0
6
0
2
1
0
1
1
0
0
1
0
1
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
1
1
0
1
0
4
1
1
0
1
0
0
1
2
0
1
0
1
2
1
0
1
1
0
1
0
0
2
0
2
0
0
0
1
2
1
0
0
2
2
0
1
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
2
1
0
0
10
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
13
0
1
0
0
0
2
2
3
0
8
8
0
6
0
3
3
0
1
0
0
0
1
2
1
0
1
0
1
3
0
1
0
0
1
0
0
1
1
0
1
1
2
1
1
0
0
4
1
5
0
0
2
0
0
1
1
5
1
0
1
1
1
7
0
2
5
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
3
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
6
1
1
0
0
1
3
0
0
1
3
3
1
0
2
0
2
0
1
1
0
0
2
0
1
2
0
0
4
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
1
1
1
0
1
1
0
0
6
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
1
1
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
2
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
2
4
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
4
1
0
9
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
3
1
0
0
0
9
0
0
1
1
0
0
0
0
1
1
0
1
0
4
0
0
2
1
1
1
0
0
1
1
3
0
0
5
1
1
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
0
5
2
0
0
2
0
11
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
1
1
0
0
2
3
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
3
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
1
3
2
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
1
1
0
0
1
2
0
0
2
2
0
1
0
3
0
5
1
9
0
0
2
3
0
0
2
1
0
0
0
0
0
0
1
1
3
0
3
0
0
0
2
0
0
1
2
1
0
1
0
1
1
3
4
1
3
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
2
1
0
1
0
0
1
4
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
3
1
2
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
0
1
3
2
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
1
2
0
0
0
3
1
0
2
0
2
0
2
0
2
1
1
0
0
1
0
3
1
0
1
0
1
0
2
3
0
1
0
0
1
1
0
1
2
2
1
0
0
1
1
0
1
1
7
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
2
3
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
2
1
0
0
1
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
1
0
1
0
5
5
1
2
0
1
0
1
0
1
8
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
1
2
0
1
0
1
1
0
0
0
2
0
0
0
0
4
1
2
1
1
0
0
1
0
5
1
0
0
1
1
1
3
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
0
2
1
1
1
0
1
2
1
1
9
1
2
1
0
5
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
16
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
3
0
8
0
0
0
1
0
0
0
1
0
1
0
0
1
1
8
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
8
1
0
0
0
0
0
0
0
1
1
0
1
6
1
1
1
0
2
2
1
0
1
0
2
1
0
1
0
1
1
5
3
1
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
4
2
1
0
0
0
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
3
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
1
1
1
0
1
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
2
0
1
2
0
3
0
0
1
0
1
1
2
0
1
0
1
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
1
1
7
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
3
0
2
0
0
0
1
0
0
3
0
4
0
1
0
0
0
0
0
1
2
1
1
4
0
0
2
3
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
1
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
1
1
2
1
2
0
1
0
3
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
3
0
1
1
0
1
1
0
0
3
1
1
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
1
0
1
3
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
8
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
4
0
1
0
0
2
1
1
0
3
0
1
0
5
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
4
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
4
0
0
0
1
1
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
7
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
4
1
0
1
1
1
0
1
0
1
0
2
1
4
0
0
1
0
0
1
0
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
7
1
0
1
1
0
0
1
0
1
2
1
0
0
1
1
2
1
0
2
7
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
0
2
1
0
5
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
3
1
0
1
1
1
0
6
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
2
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
3
1
0
0
0
1
1
4
0
0
0
1
0
2
14
0
0
1
0
1
0
1
1
1
3
0
0
0
0
0
4
0
0
0
1
0
0
0
1
3
0
1
2
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
3
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
1
1
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
6
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
4
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
3
0
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
3
0
0
0
2
0
1
2
0
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
6
1
1
0
1
1
2
2
1
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
2
2
1
1
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
1
0
1
7
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
0
3
1
1
0
1
1
0
0
2
1
1
0
4
1
1
0
1
1
0
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
3
0
2
1
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
1
2
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
4
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
1
2
1
0
1
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
3
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
2
1
1
0
1
1
0
3
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
4
0
0
0
1
9
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
8
0
0
1
9
0
1
0
1
0
0
0
9
0
1
0
2
1
0
1
2
1
1
0
0
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
1
1
1
9
4
2
0
1
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
5
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
3
1
2
0
0
1
0
6
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
7
1
1
1
0
2
1
1
0
3
0
0
0
3
0
0
0
1
1
3
0
0
7
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
2
1
0
2
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
6
0
1
1
1
0
1
0
0
0
0
0
1
1
1
2
1
1
1
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
3
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
4
0
1
0
0
0
0
1
0
0
1
1
3
0
1
2
1
1
0
1
0
1
0
0
0
2
8
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
1
1
0
5
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
1
7
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
6
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
1
0
8
0
1
0
3
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
1
2
2
1
0
0
1
0
0
1
4
1
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
2
2
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
3
0
1
0
0
3
0
6
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
2
1
3
0
0
2
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
2
1
2
0
0
1
0
0
1
1
2
0
0
0
0
4
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
3
0
0
1
1
1
2
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
3
1
1
0
0
0
0
0
0
7
1
0
0
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
3
6
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
2
5
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
4
1
1
1
0
0
0
0
0
0
0
1
0
4
1
0
1
1
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
2
0
0
0
3
2
0
2
1
1
0
1
3
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
3
3
1
2
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
1
0
1
0
2
0
1
3
0
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
0
2
2
0
9
0
0
0
1
0
1
0
1
0
1
1
1
1
1
2
0
0
0
0
2
0
0
0
1
0
0
9
5
1
2
0
1
1
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
0
1
12
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
2
2
1
1
0
2
1
2
0
1
0
0
1
0
0
1
1
1
8
7
1
1
0
0
0
2
2
1
0
5
2
1
0
0
0
0
0
8
1
1
0
1
0
1
0
0
0
7
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
7
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
3
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
1
1
0
0
1
0
0
2
1
8
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
2
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
11
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
1
2
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
4
1
0
1
2
0
1
1
1
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
1
7
1
1
1
1
1
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
6
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
0
0
6
0
1
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
6
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
1
3
0
4
4
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
8
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
4
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
3
0
1
0
1
1
2
0
2
0
2
3
0
0
0
0
1
1
1
2
0
1
0
1
1
2
0
0
0
0
1
3
0
1
7
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
1
1
0
2
0
2
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
1
8
1
0
0
1
1
0
1
1
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
6
1
1
1
0
5
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
4
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
0
1
1
0
0
4
4
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
1
0
2
0
1
0
1
7
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
3
0
2
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
4
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
6
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
2
1
2
0
8
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
11
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
8
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
5
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
8
0
5
0
1
1
0
0
1
0
0
1
1
0
0
0
0
5
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
7
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
1
6
1
3
0
2
1
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
1
4
0
0
0
1
0
0
14
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
13
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
10
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
3
4
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
8
0
0
2
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
2
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
3
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
1
1
2
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
4
1
2
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
6
0
4
2
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
0
0
1
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
3
0
1
3
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
7
1
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
6
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
6
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
13
0
0
0
2
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
5
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
16
0
1
1
0
1
0
1
0
1
0
1
0
0
4
1
0
0
0
1
0
0
0
2
1
1
1
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
3
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
1
1
0
0
1
3
0
0
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
4
3
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
8
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
1
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
5
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
1
2
3
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
6
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
1
0
1
3
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
9
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
7
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
9
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
1
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
1
0
3
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
8
1
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
12
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
6
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
12
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
4
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
7
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
4
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
6
7
2
2
0
0
0
1
1
0
3
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
8
0
3
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
1
0
0
4
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
7
0
1
1
0
0
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
13
0
0
0
0
1
7
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
4
0
0
2
1
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
0
0
0
1
0
2
0
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
6
0
0
0
0
6
1
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
1
2
0
8
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
10
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
4
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
3
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
5
0
1
0
0
0
0
0
5
0
0
1
0
0
1
0
7
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
13
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
5
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
5
0
1
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
4
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
3
0
1
0
0
0
1
0
1
1
0
0
4
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
6
0
0
0
0
0
0
0
1
0
5
1
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
5
0
0
0
0
0
1
0
4
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
3
0
1
0
5
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
1
15
0
0
0
1
1
1
0
1
0
0
0
0
0
0
5
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
1
4
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
10
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
8
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
4
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
8
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
5
0
0
0
0
0
0
3
0
0
1
0
1
5
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
5
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
4
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
1
12
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
7
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
7
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
8
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
13
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
9
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
7
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
7
0
1
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
1
1
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
14
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
1
1
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
1
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
12
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
1
0
2
0
0
1
1
0
0
5
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
4
0
0
4
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
5
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
2
2
1
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
4
2
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
1
0
7
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
8
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
11
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
11
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
11
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
15
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
4
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
3
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
4
0
0
0
9
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
11
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
11
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
9
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
12
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12