OI-codes/S2OJ/661/data/flower5.out

57
46
49
49
45
59
43
57
54
44
50
42
30
21
39
41
23
43
37
38
30
39
37
71
46
17
30
43
24
43
28
24
39
36
36
36
28
39
28
34
28
27
28
32
53
27
25
18
28
29
37
23
36
24
31
27
37
32
23
27
33
25
45
31
22
24
21
21
20
38
26
23
22
34
41
24
10
35
19
19
28
22
31
23
27
22
19
37
17
42
28
18
24
34
22
23
25
28
27
23
20
21
15
23
18
30
26
27
19
21
16
20
14
21
27
38
30
25
24
28
19
41
23
20
18
31
25
36
25
19
19
24
18
27
23
18
16
33
28
17
24
27
25
20
14
11
17
22
33
20
24
15
15
26
15
24
29
27
14
13
22
25
22
20
10
28
28
20
19
18
14
28
28
31
21
18
11
14
12
17
21
8
17
12
9
19
20
19
18
17
14
20
15
21
18
23
15
25
22
21
16
19
25
12
12
20
16
17
17
34
10
14
28
26
28
22
25
15
13
10
13
19
20
11
16
20
16
25
15
16
34
15
14
17
25
22
28
18
52
15
19
9
20
17
17
16
21
25
18
13
30
17
11
29
15
9
12
20
16
12
23
9
9
25
18
14
19
17
32
20
22
15
9
13
11
19
16
23
10
13
13
13
15
14
19
15
14
10
21
22
22
20
20
12
41
9
13
17
19
19
13
18
14
14
19
24
13
11
22
19
17
19
18
24
15
16
16
6
14
8
8
24
22
18
5
27
12
23
24
23
12
13
11
22
17
13
15
9
13
16
24
17
29
8
18
10
11
18
30
28
20
25
21
17
14
15
19
14
8
19
24
15
13
15
8
11
7
19
7
16
13
12
12
17
12
12
15
15
13
11
12
19
8
22
9
25
23
10
10
10
16
13
14
25
12
16
12
11
15
11
12
9
10
11
18
27
12
20
28
14
17
25
16
10
20
33
15
8
25
19
7
11
47
15
12
7
20
14
8
34
8
14
8
12
17
26
16
14
19
14
12
17
17
4
14
31
20
14
12
8
10
27
16
14
22
19
11
16
15
13
9
15
12
13
12
10
18
16
19
12
20
17
25
13
17
8
7
20
20
12
11
14
27
21
27
9
24
20
12
24
5
11
9
20
12
15
16
16
14
11
18
15
7
13
13
17
16
11
8
10
14
8
28
23
8
21
10
7
15
8
13
8
18
12
18
13
12
12
27
13
10
8
5
12
9
8
16
9
14
15
10
10
14
19
17
11
18
17
6
11
12
20
19
11
19
9
21
20
19
12
5
23
14
16
14
7
11
13
19
15
15
13
14
14
12
22
19
13
15
14
11
6
14
15
15
11
20
13
18
16
22
9
9
11
17
17
14
9
14
9
7
20
17
11
20
17
28
6
11
17
8
5
13
31
23
8
12
15
15
16
10
15
7
9
10
13
10
9
8
13
8
10
17
11
6
9
12
12
10
7
16
9
8
12
9
7
9
12
9
11
3
10
13
17
11
14
4
19
12
10
10
15
12
28
7
7
17
15
16
14
14
17
7
10
8
10
15
13
6
11
7
16
17
10
13
15
12
8
13
10
17
11
12
16
13
15
8
13
10
16
8
7
7
6
19
10
16
13
18
9
11
7
13
6
7
16
14
8
8
12
12
26
13
10
13
11
9
20
10
7
9
10
13
12
11
5
13
11
12
11
18
14
30
5
15
9
8
7
6
17
16
4
8
9
7
10
9
6
7
14
11
16
10
17
6
12
4
14
19
12
26
28
24
21
12
11
14
12
11
13
12
21
17
10
8
15
29
7
4
18
9
10
7
10
22
4
3
8
10
12
14
18
15
3
11
10
10
5
6
13
14
5
8
13
12
16
11
13
12
19
12
8
13
20
11
10
14
7
12
6
11
17
7
5
9
14
13
10
6
4
21
18
11
10
14
15
7
11
7
14
8
6
9
8
6
13
8
7
15
7
7
8
7
6
11
18
12
11
7
11
14
11
9
12
6
9
7
8
10
12
12
21
20
9
7
7
11
3
10
9
12
12
4
13
5
18
14
25
14
8
7
10
25
22
29
10
11
8
4
12
10
14
3
6
10
8
6
14
12
30
6
9
20
10
8
16
8
9
6
11
13
6
10
10
7
10
9
15
20
15
6
19
10
15
16
10
10
17
8
33
11
6
11
12
8
10
7
7
8
7
16
4
3
10
10
12
12
8
6
6
12
10
5
24
7
15
16
18
15
6
32
29
10
9
13
11
12
10
11
5
6
17
11
7
10
8
12
11
12
5
9
14
17
18
8
11
5
11
6
7
5
13
6
14
13
8
13
6
9
5
10
6
10
12
7
17
5
15
10
4
5
8
22
11
10
3
10
5
9
18
10
11
5
15
12
10
8
10
14
6
24
9
13
11
5
14
21
7
13
12
8
8
13
16
5
10
11
10
12
18
10
9
15
14
5
10
26
10
14
15
4
17
7
11
8
17
3
12
5
8
12
9
5
12
14
20
9
13
10
4
12
19
11
5
8
9
7
4
5
14
5
5
6
4
23
6
5
5
15
3
12
2
3
11
4
3
10
15
14
6
4
13
7
5
21
2
8
10
18
4
9
10
15
8
9
3
2
11
8
12
3
7
4
11
10
17
7
2
8
18
5
6
2
18
14
13
8
10
6
10
8
10
7
8
3
14
5
20
8
4
17
17
10
8
14
10
17
22
7
14
8
3
11
16
6
5
10
9
7
5
5
6
7
5
8
10
7
9
8
17
10
15
16
21
9
11
5
11
15
10
5
6
13
4
18
7
7
8
6
7
20
10
11
9
5
18
13
7
4
10
10
5
9
5
11
17
7
16
8
5
11
4
15
7
19
8
15
8
9
12
6
5
12
8
16
7
10
15
10
9
6
7
11
7
5
5
9
8
5
10
5
7
7
9
10
12
7
13
2
11
7
11
2
14
12
7
6
10
8
7
8
17
12
7
15
12
7
15
9
18
9
9
16
11
7
11
5
4
4
7
8
8
6
9
7
25
11
14
6
5
7
13
10
6
9
9
10
9
11
4
6
4
8
16
7
4
12
13
4
8
11
13
11
17
5
4
8
6
8
11
9
3
10
6
5
10
9
10
5
6
9
10
7
12
29
6
12
13
9
10
6
12
5
14
5
8
2
13
10
15
17
4
6
5
13
10
11
9
12
8
11
2
10
10
8
5
17
15
8
10
11
7
9
11
12
24
2
10
2
15
7
4
1
8
14
8
13
8
3
5
10
7
8
8
5
4
5
7
10
9
9
9
20
10
9
10
10
10
8
14
7
6
17
8
7
4
6
14
4
11
10
2
10
8
7
17
7
6
10
11
9
9
7
10
13
8
9
6
4
8
8
8
14
3
8
6
3
4
9
8
9
6
12
8
6
6
9
5
4
12
20
10
17
6
6
8
19
5
12
8
17
9
6
4
9
13
5
10
3
6
10
4
27
6
5
6
3
9
13
6
3
7
25
9
9
28
8
4
8
7
6
3
5
8
3
0
6
12
7
9
6
6
9
14
11
6
15
12
15
7
4
7
5
5
8
4
6
7
5
6
9
12
3
6
9
13
2
9
4
3
8
5
11
13
11
5
5
9
3
3
10
15
8
6
4
10
10
6
7
3
2
11
6
9
9
5
3
6
8
19
6
3
10
9
9
7
5
2
4
14
4
15
10
13
6
6
5
6
10
9
9
8
9
5
7
3
14
7
5
6
4
7
13
9
19
6
13
5
4
6
10
13
5
5
3
4
2
11
4
11
14
8
2
5
5
4
8
11
30
4
6
18
10
9
6
3
2
8
21
4
19
6
8
11
3
6
12
7
9
5
6
4
7
4
10
8
4
5
4
10
10
10
6
7
6
8
3
6
3
9
2
4
9
12
3
6
7
1
5
9
4
11
9
13
4
16
13
4
2
5
6
8
5
8
16
8
7
5
10
7
8
4
13
7
5
8
3
5
9
7
5
7
12
3
6
9
6
17
3
5
7
8
13
5
9
7
4
10
17
5
6
10
11
6
9
9
9
12
2
9
4
9
6
12
2
7
9
10
6
8
14
9
7
4
12
6
12
13
4
10
4
5
10
12
4
8
3
5
13
3
14
9
8
7
6
12
9
3
4
4
10
8
5
7
12
9
14
3
3
8
9
5
8
1
5
16
9
4
13
7
10
16
9
4
8
10
2
5
9
10
5
13
22
5
20
6
11
5
5
5
10
6
6
9
14
8
10
9
13
4
5
10
7
5
7
8
12
9
6
3
9
5
6
7
3
11
9
14
15
6
8
7
13
8
8
6
21
1
8
6
5
24
2
15
7
9
6
7
6
3
15
6
13
11
13
5
8
6
9
5
14
11
6
3
12
11
9
14
9
9
8
9
15
10
4
10
4
8
3
5
1
9
1
11
7
7
8
8
7
4
8
10
3
5
3
8
1
5
3
9
4
4
12
14
11
8
11
8
1
6
24
7
3
4
4
4
5
8
24
10
18
7
20
6
6
19
5
6
8
5
7
6
14
5
7
5
14
9
11
10
7
3
14
7
8
8
9
5
6
16
6
19
8
8
6
4
7
13
8
6
4
13
11
7
6
3
7
9
9
9
14
14
6
7
3
5
6
10
5
7
11
6
10
9
9
11
7
8
6
4
4
7
6
6
15
5
9
7
5
5
6
12
8
3
24
9
1
2
1
10
6
2
24
6
6
7
2
15
7
5
4
5
6
21
10
13
7
7
5
5
10
7
6
5
5
10
4
6
3
3
6
14
4
4
10
7
1
5
8
5
8
9
4
6
3
4
20
4
2
7
3
13
17
4
20
3
9
10
2
8
8
14
7
8
8
6
5
12
3
17
10
5
4
6
8
10
3
8
5
8
5
1
14
7
10
6
12
13
5
13
11
8
9
9
8
6
7
5
3
5
5
6
3
6
9
6
10
4
6
5
8
11
9
6
7
6
5
5
11
6
7
11
5
9
11
8
7
5
0
8
3
12
17
3
4
6
13
6
5
9
4
1
5
6
5
13
10
2
5
6
7
14
4
7
5
6
13
6
4
5
5
7
11
9
4
9
6
12
6
5
11
1
9
9
3
10
5
5
15
11
6
6
10
2
6
3
8
8
6
5
6
17
14
3
4
10
19
3
5
4
4
5
10
8
6
2
7
13
8
6
6
6
15
4
19
9
2
6
7
3
5
6
6
5
6
15
3
7
4
7
8
7
5
5
9
7
10
8
5
11
5
10
10
15
14
17
5
10
3
6
3
8
5
8
7
10
5
7
3
4
7
11
22
11
20
6
4
6
8
4
5
7
5
3
8
8
6
6
3
2
5
8
7
11
5
6
2
9
3
7
5
7
7
9
5
3
6
5
11
6
13
12
6
10
12
8
8
4
7
18
18
3
8
10
1
10
13
10
7
1
7
3
7
11
7
4
3
3
4
6
2
9
5
5
5
4
5
5
7
6
5
7
5
7
9
13
9
15
14
17
6
11
3
3
7
3
10
4
3
5
7
6
11
7
10
14
4
5
4
6
7
3
1
18
7
3
5
3
1
5
13
9
19
2
7
7
8
3
4
7
9
7
6
4
4
13
8
2
8
2
24
10
8
5
8
9
8
4
5
7
11
5
3
5
10
5
18
2
4
1
7
10
9
3
8
7
4
6
8
6
7
6
25
12
10
6
7
4
8
2
4
8
8
4
4
18
10
4
20
3
11
15
4
11
3
6
13
6
7
17
5
8
2
2
3
8
7
7
3
6
6
1
7
3
3
5
7
4
5
9
4
4
7
9
4
3
4
3
4
13
4
4
9
8
3
4
5
9
24
3
3
13
9
5
12
7
4
4
3
7
5
8
1
4
4
4
5
6
7
11
12
9
9
13
5
11
4
9
4
8
3
2
3
12
5
8
5
7
4
3
5
3
6
4
5
3
7
3
3
3
3
6
3
1
5
2
9
8
12
4
3
4
3
8
6
5
3
5
7
6
4
3
18
5
7
3
5
7
7
7
1
10
6
9
7
6
6
5
12
7
5
5
1
15
6
4
6
5
8
7
3
7
4
3
6
6
7
5
4
4
11
7
24
6
6
10
5
4
7
5
8
2
3
4
2
5
7
3
4
9
3
10
3
9
6
7
6
2
4
4
6
4
9
9
4
8
5
4
4
3
4
3
7
6
3
6
2
2
6
4
5
18
5
5
4
10
3
7
8
6
2
2
5
4
2
12
3
2
5
8
4
3
7
4
11
7
5
1
11
0
20
7
3
1
2
5
4
3
4
6
1
2
6
3
7
5
7
7
7
6
7
13
12
6
10
8
16
2
6
10
2
3
8
7
5
16
5
9
6
3
18
6
5
3
3
9
3
6
13
6
6
12
6
5
9
5
6
8
5
6
10
7
11
9
0
3
6
11
5
12
7
10
3
7
7
2
4
3
4
9
5
10
22
8
4
2
4
2
7
5
7
3
6
6
4
14
8
10
7
5
3
6
7
6
7
10
7
9
1
14
8
7
2
4
1
5
7
3
3
4
6
3
6
7
3
4
10
3
11
6
4
6
5
5
11
5
8
15
7
5
4
5
8
4
11
9
5
3
6
6
7
4
2
12
2
15
4
3
8
3
4
6
9
7
6
10
9
12
5
10
3
3
7
11
8
4
3
6
12
8
1
5
5
7
1
2
7
17
0
4
2
7
6
11
4
4
4
6
5
4
6
10
6
6
5
2
7
6
3
6
7
3
2
10
19
8
3
9
4
8
17
10
2
6
3
5
5
6
3
4
4
10
7
6
6
5
20
3
2
5
7
13
9
4
5
6
2
7
6
1
4
8
7
4
3
20
8
2
4
4
6
2
2
3
3
8
8
7
5
6
4
6
3
6
4
1
5
3
5
5
13
5
6
1
2
7
1
9
8
16
1
5
6
5
7
5
11
3
1
3
4
9
6
7
5
4
4
6
6
10
9
7
9
16
0
0
5
7
3
3
8
5
6
4
9
3
0
5
5
5
3
4
4
12
6
3
7
15
3
1
3
4
5
25
7
3
5
3
14
13
2
8
5
3
3
3
6
5
9
4
3
7
4
8
4
9
6
7
1
5
9
6
4
16
4
4
6
2
8
6
12
4
8
6
9
17
2
4
5
7
3
6
11
18
2
4
6
7
1
10
8
4
11
4
6
4
4
2
2
11
7
2
11
3
6
5
5
7
8
10
4
9
10
6
3
4
6
1
5
10
8
9
7
12
4
2
8
4
6
2
2
14
2
12
5
2
6
4
5
9
3
2
2
1
6
9
10
11
3
5
5
8
8
5
5
3
5
6
8
8
7
2
1
8
4
8
7
5
3
2
10
6
6
7
2
3
5
9
5
5
3
6
5
4
5
4
3
1
10
6
4
2
3
9
1
6
4
1
10
3
6
5
6
11
3
5
3
20
11
8
5
2
5
4
4
3
4
9
12
9
12
9
4
3
7
5
7
3
4
6
3
4
12
0
6
6
10
4
2
3
4
11
3
6
2
7
5
8
9
15
6
2
6
6
9
2
4
2
7
3
8
6
27
15
2
11
3
4
2
12
6
4
5
4
4
6
3
1
4
1
3
4
9
16
8
5
7
11
27
8
4
5
2
4
3
3
7
5
6
6
8
7
6
5
3
3
12
5
3
6
11
8
2
9
3
5
3
12
2
9
6
4
5
4
5
9
3
1
8
18
6
2
6
7
2
9
5
3
3
0
12
5
4
2
4
6
4
6
19
5
2
1
2
3
12
7
10
9
6
4
0
11
4
2
5
12
8
2
14
5
5
17
10
8
5
5
5
3
2
7
13
3
3
6
4
5
4
6
11
7
4
12
11
3
6
6
6
5
2
3
7
2
3
9
5
20
2
3
3
4
3
5
3
2
4
5
4
4
4
2
10
1
3
7
6
18
2
6
8
6
5
6
5
5
3
5
2
5
5
9
5
4
6
2
9
9
2
9
7
11
3
3
1
4
8
9
6
4
3
5
2
6
8
5
3
6
5
6
3
2
8
2
7
6
2
5
4
6
3
4
3
13
9
2
5
6
2
9
1
6
4
15
5
9
2
10
4
8
6
1
12
3
5
5
10
6
7
3
5
5
4
3
2
3
3
3
6
13
2
8
4
5
11
5
6
2
7
5
2
1
6
3
4
5
7
6
2
6
10
3
10
12
2
7
5
9
9
3
9
3
8
11
6
4
3
4
5
6
3
7
4
5
7
3
14
10
9
3
9
5
5
8
5
6
8
9
6
9
4
8
15
6
2
9
12
3
4
12
9
16
17
3
6
15
7
5
2
0
2
3
5
3
5
4
2
5
2
6
2
2
15
5
5
5
2
4
7
6
6
4
8
2
4
6
5
5
4
2
1
13
1
5
13
2
6
17
7
2
4
4
14
14
3
4
7
13
4
5
6
7
6
6
4
5
11
5
3
3
4
4
2
10
1
7
4
5
14
2
10
6
21
7
9
4
4
6
3
5
3
8
6
4
7
15
7
9
5
2
4
4
4
2
3
6
9
4
6
4
3
4
4
6
3
4
10
7
10
4
5
6
7
8
12
5
5
5
3
3
16
4
1
2
0
8
3
11
3
4
5
1
6
2
15
2
4
6
20
1
4
5
7
8
6
2
8
8
5
3
4
5
5
5
2
10
12
3
5
3
1
2
5
8
2
4
3
7
6
1
5
9
2
5
4
6
7
3
6
1
6
2
4
3
2
8
2
10
8
3
8
2
2
9
3
1
4
6
8
6
9
5
4
7
7
4
5
4
2
5
4
7
7
4
0
2
7
6
4
6
4
7
10
9
3
5
7
3
6
1
8
2
9
7
6
2
0
5
1
7
17
5
2
16
11
7
1
6
3
2
6
12
2
8
2
10
5
6
4
4
16
4
13
6
9
8
14
3
10
2
6
6
7
12
6
4
10
5
4
5
3
1
3
22
11
6
6
4
3
5
5
3
5
0
4
6
6
4
1
9
4
5
8
4
6
16
8
2
2
4
2
4
6
10
4
7
5
3
4
3
2
5
3
3
5
3
6
3
4
3
19
19
2
3
4
12
4
1
4
5
6
3
5
4
6
8
4
1
2
4
2
6
1
2
2
4
9
8
1
3
3
10
9
8
6
4
4
2
6
18
3
6
4
10
4
13
3
2
2
4
5
4
2
1
5
7
2
5
2
3
3
5
11
3
1
7
7
11
9
5
10
5
8
17
9
7
27
9
6
3
1
5
6
9
6
7
5
10
2
8
4
5
2
2
6
5
12
3
8
6
2
5
7
3
3
5
12
8
5
2
2
7
7
4
5
0
4
4
10
5
9
15
3
8
2
4
2
2
8
5
6
3
5
4
4
10
3
4
5
2
4
4
3
15
2
9
11
5
5
9
9
6
6
3
0
7
3
5
3
3
6
3
4
3
4
4
4
3
6
4
3
2
7
9
8
6
4
2
8
7
5
7
7
4
9
5
5
9
4
3
8
3
5
7
9
7
7
9
5
2
10
5
4
16
4
3
1
7
4
4
2
6
4
3
5
4
1
4
6
13
5
2
4
4
2
7
3
4
8
10
5
4
5
5
7
11
1
2
4
6
3
4
10
1
4
6
3
5
5
1
4
13
2
8
3
5
2
4
2
3
4
4
4
8
5
3
8
4
4
4
7
7
6
10
9
4
4
7
4
1
4
4
3
10
7
3
1
5
4
4
10
2
19
3
5
3
12
6
5
6
4
7
2
3
2
7
5
6
17
11
11
1
0
0
3
4
10
3
4
2
1
3
4
2
3
2
2
2
3
0
3
2
8
2
2
4
4
2
5
16
3
5
22
3
17
3
5
3
7
11
9
6
2
3
5
1
3
14
12
5
7
3
16
2
4
14
5
19
2
9
3
8
3
5
5
1
4
7
1
3
12
7
2
2
3
5
4
10
3
2
6
5
4
7
9
1
6
6
6
5
4
5
3
5
3
2
9
3
1
3
10
3
1
5
7
7
4
3
4
2
8
6
3
5
8
0
6
1
3
3
5
4
1
4
5
12
2
4
7
3
2
13
15
4
2
1
5
4
2
2
7
3
4
7
5
9
3
3
10
4
9
3
5
2
3
5
9
7
1
5
4
4
7
6
17
11
1
6
3
1
6
5
6
5
5
5
4
6
1
13
4
9
5
3
4
9
1
3
5
4
4
7
7
2
2
2
3
4
8
3
6
4
3
3
6
4
6
4
5
3
4
3
6
2
5
2
5
8
5
6
1
6
8
5
5
12
6
6
1
2
5
8
3
4
2
1
2
1
7
5
10
11
16
4
4
1
5
5
1
5
4
2
3
4
6
3
6
1
3
6
4
3
5
5
4
4
3
7
7
3
3
0
7
2
2
6
3
1
4
5
5
1
3
2
4
5
9
12
6
13
6
10
5
11
5
3
7
6
4
5
3
1
7
2
3
5
3
3
2
0
2
2
6
5
5
1
1
3
1
3
3
4
1
7
7
5
1
5
3
4
0
3
10
5
16
3
1
13
1
2
4
5
10
8
3
2
4
1
9
5
6
5
3
7
3
0
3
4
5
7
4
4
6
4
1
3
4
5
9
4
4
5
3
6
2
2
2
7
6
22
3
4
4
3
6
3
1
18
3
2
2
3
2
3
2
1
4
9
1
3
4
2
3
11
2
9
3
3
5
15
1
4
3
2
5
5
2
6
2
3
10
6
5
3
2
3
3
6
3
4
7
4
4
5
5
2
5
0
5
0
5
3
5
19
1
3
7
2
5
1
10
0
2
3
5
0
0
1
8
2
3
6
15
4
7
5
2
3
1
4
6
5
6
6
6
21
3
4
2
1
16
2
2
1
8
6
6
4
11
3
4
2
9
7
1
3
3
8
2
6
4
4
5
2
1
5
2
4
7
1
6
5
1
4
2
2
3
10
3
7
6
6
6
8
6
3
2
4
4
4
2
4
3
4
2
3
0
9
6
5
14
3
6
2
7
3
4
7
7
7
12
3
7
3
5
3
7
10
2
3
7
2
2
2
6
2
1
4
7
7
5
6
3
2
4
8
3
14
2
17
5
1
6
3
4
4
3
3
0
6
5
5
0
10
4
2
4
4
8
3
5
3
1
3
3
6
5
4
5
10
2
6
1
2
4
8
4
1
8
3
2
3
11
1
5
2
1
3
5
2
2
4
21
4
1
15
6
17
4
4
0
3
3
3
3
3
8
2
5
2
3
4
3
1
3
14
3
3
4
3
8
2
5
8
8
2
11
5
23
2
2
3
8
8
2
5
3
5
4
2
5
6
5
1
1
0
4
1
13
3
4
3
4
5
3
1
2
6
1
0
7
7
7
3
1
11
2
3
2
3
12
5
3
9
6
5
2
2
5
1
0
6
8
4
8
5
12
3
6
4
1
6
8
3
4
3
0
3
4
3
3
3
5
6
2
2
3
2
8
4
2
1
4
5
2
3
3
4
5
6
1
5
2
3
4
2
4
1
4
2
6
3
7
2
9
4
15
2
3
4
2
6
5
1
4
9
5
5
5
5
2
3
12
1
5
5
3
2
2
1
2
2
2
5
2
8
3
1
4
1
9
4
1
4
15
6
15
8
6
6
6
3
5
5
2
6
3
1
5
4
2
6
4
7
2
3
1
1
5
6
3
3
2
2
3
1
3
1
3
5
2
2
3
6
5
5
2
3
3
3
9
2
4
4
6
5
4
8
3
3
2
2
5
2
14
5
3
7
2
6
8
1
4
8
2
3
3
2
2
6
7
5
4
2
2
8
4
3
6
6
2
2
4
3
6
5
3
5
3
11
2
7
4
5
3
2
4
9
6
1
3
3
3
3
4
3
3
1
3
11
18
6
2
1
2
2
1
1
2
1
3
3
2
8
4
0
5
12
3
1
5
6
0
1
8
5
4
6
4
4
6
2
2
4
2
3
1
5
1
7
2
8
2
1
8
2
2
6
5
3
2
3
2
1
8
5
11
3
4
4
4
7
11
3
2
4
3
4
1
4
5
7
6
4
5
10
3
5
4
3
4
2
2
2
1
13
4
4
7
5
7
3
1
3
10
0
4
3
19
5
0
5
9
3
5
1
2
1
14
3
4
7
2
5
8
7
5
5
5
6
3
6
2
5
4
8
6
8
2
5
3
2
4
4
6
2
8
1
11
9
2
1
3
4
4
2
3
3
3
1
9
4
6
4
2
2
4
3
11
7
5
2
5
6
2
14
3
7
1
5
12
4
2
6
2
0
3
2
3
8
8
5
2
8
6
4
2
3
5
1
2
4
2
3
1
1
3
4
4
2
7
2
1
4
1
7
6
1
5
2
5
4
4
4
2
5
4
1
5
3
3
3
11
2
5
4
5
4
3
3
3
2
7
4
4
10
5
10
4
10
2
4
8
3
1
15
2
1
2
2
4
4
4
2
4
4
4
11
2
5
2
6
9
3
2
5
2
8
9
4
2
6
6
3
18
3
5
3
3
4
4
2
6
4
16
3
13
1
8
4
5
1
2
2
6
2
4
1
3
6
5
15
1
3
2
9
2
10
3
3
6
1
2
2
5
1
0
7
13
7
5
9
2
3
5
4
3
4
6
2
3
5
2
5
5
2
6
3
6
2
1
2
2
0
3
2
5
2
1
3
7
7
5
6
4
7
12
3
5
7
1
1
3
2
4
7
2
14
1
1
2
1
3
9
5
1
14
3
2
1
18
6
15
3
2
5
2
4
16
1
5
7
8
4
5
3
9
9
3
4
7
4
5
5
3
4
3
10
4
3
1
8
2
4
2
1
7
6
5
1
2
10
10
3
6
3
2
4
6
2
4
2
1
2
2
1
1
2
3
11
5
2
2
3
2
3
2
1
6
0
7
1
7
3
5
5
5
2
8
7
2
5
5
5
1
1
3
3
5
18
3
3
2
3
4
4
4
3
4
1
3
7
0
3
1
1
3
0
3
5
4
2
0
5
2
4
0
2
0
1
6
3
2
1
11
6
1
4
12
4
1
2
3
1
6
5
4
2
5
8
2
6
3
7
2
1
8
5
6
4
3
5
4
4
2
1
2
2
2
4
0
5
3
2
8
5
0
6
3
6
2
4
3
1
8
4
3
1
4
3
5
0
2
3
1
4
1
5
8
2
5
15
4
4
1
7
6
3
1
6
3
5
2
0
2
3
0
4
0
2
8
3
6
3
13
4
0
5
2
5
4
2
2
0
2
0
6
3
7
4
3
1
2
3
8
3
5
2
3
4
6
10
3
2
2
3
1
7
1
5
11
2
5
6
1
5
4
0
4
2
8
7
6
2
3
3
2
2
1
3
5
6
7
2
2
3
5
3
4
5
3
2
2
2
2
3
6
4
3
6
4
4
4
3
3
1
3
11
3
3
9
3
2
3
2
7
5
1
5
2
4
14
4
4
2
4
6
1
0
9
5
18
4
1
3
4
2
3
2
9
5
1
2
2
1
1
24
2
3
5
6
6
1
3
0
5
2
3
3
1
6
2
5
1
4
1
4
2
6
5
2
4
1
1
4
3
3
8
3
6
6
3
5
1
2
2
3
3
11
2
2
4
0
1
6
1
2
8
7
10
8
1
4
6
1
1
2
2
3
3
11
2
2
7
3
1
8
3
2
0
6
0
4
3
4
7
8
4
4
4
3
2
4
7
2
5
3
3
4
3
7
4
4
6
2
2
5
5
2
3
2
3
3
4
6
1
9
2
6
5
1
2
4
1
8
2
10
15
1
4
1
4
5
17
1
4
3
4
1
4
4
3
2
2
4
10
3
2
8
1
2
9
1
2
7
5
4
6
3
4
2
5
10
1
2
2
2
7
6
4
4
4
1
5
3
5
2
3
2
2
1
2
6
4
3
2
8
2
5
4
4
4
2
2
4
5
11
3
1
5
8
5
2
2
7
3
3
3
3
2
3
2
4
5
3
4
5
8
3
4
3
3
2
16
1
1
3
6
7
12
1
5
4
3
5
3
1
15
4
2
4
10
1
3
2
9
1
6
4
4
1
9
2
3
30
4
3
0
2
6
3
3
2
2
2
2
2
5
2
3
8
7
2
4
12
0
4
4
1
2
1
4
2
1
9
3
2
2
2
1
3
0
5
4
1
13
2
6
2
7
2
3
2
1
2
3
7
1
3
14
3
2
3
5
1
3
10
6
4
3
5
3
3
3
3
3
3
2
8
6
6
2
2
6
4
2
3
4
5
8
1
5
4
3
3
3
0
2
5
2
5
4
4
6
15
1
3
3
2
2
4
0
2
3
4
2
3
4
5
4
3
4
0
6
1
2
11
20
5
5
3
1
3
3
3
3
2
1
3
1
0
3
3
3
3
5
8
3
2
2
1
3
2
11
4
3
2
4
1
2
5
4
2
9
2
1
3
2
1
3
2
7
7
3
2
1
3
6
3
6
3
2
4
8
6
3
9
5
2
21
7
5
5
3
1
2
0
3
4
4
0
2
13
11
2
4
4
4
2
3
5
1
6
4
3
1
5
0
4
3
18
6
3
0
4
4
8
4
3
2
4
1
8
5
5
1
1
2
17
2
3
4
2
5
3
6
2
4
0
2
2
8
2
3
4
1
1
4
5
3
3
4
3
1
8
3
4
6
10
6
4
4
3
1
2
3
4
5
5
1
2
3
7
7
2
3
7
2
1
6
3
3
1
6
3
4
4
0
4
0
4
9
3
1
2
7
1
2
7
4
2
2
3
5
5
3
3
3
3
1
2
3
4
5
4
3
3
2
1
3
5
4
2
2
3
3
6
12
1
2
2
1
2
2
2
4
4
7
3
3
8
3
1
3
2
1
2
6
1
1
4
1
5
5
1
4
2
1
1
2
2
6
0
2
6
8
3
18
5
4
2
3
3
0
4
3
8
5
5
3
5
0
3
1
3
5
2
4
4
5
16
0
3
2
4
3
2
6
3
7
1
1
3
1
4
4
6
7
3
2
0
4
4
6
14
6
4
0
0
2
5
1
4
1
8
0
3
2
4
1
1
4
4
8
3
0
1
4
1
2
3
7
1
1
7
1
15
4
5
8
2
3
4
2
0
4
2
2
8
3
5
3
3
7
2
1
2
1
3
4
2
4
7
1
1
1
8
4
4
4
0
4
3
2
1
4
5
4
0
3
18
1
2
5
1
5
2
1
3
1
6
4
1
3
5
3
3
3
9
4
3
1
5
6
2
4
3
4
2
3
5
4
1
3
3
16
3
1
6
5
3
3
1
6
1
3
2
0
9
0
1
4
1
5
3
2
2
5
1
5
2
4
2
0
2
2
0
2
3
8
2
3
1
15
14
2
1
5
1
6
2
2
4
4
2
2
2
7
3
4
4
2
5
1
6
4
12
4
4
4
3
8
4
3
4
2
4
2
6
4
1
1
2
1
3
1
3
0
1
1
2
5
6
3
3
2
2
2
4
3
0
5
1
1
3
0
3
4
5
5
1
7
3
4
8
8
7
9
2
2
1
4
5
6
5
8
9
3
3
7
4
5
3
4
3
1
3
1
19
1
4
3
3
2
1
4
1
5
3
12
1
2
2
6
4
3
11
1
2
1
3
1
3
3
3
8
5
5
4
5
3
4
2
3
2
3
1
6
3
7
21
3
2
2
0
2
4
0
6
1
5
4
3
2
2
4
2
1
7
2
2
8
3
4
3
3
5
3
1
1
2
8
2
5
1
5
4
3
7
4
4
5
1
2
3
2
1
2
1
3
4
1
3
2
4
7
0
12
4
1
4
1
3
3
6
2
13
1
23
2
4
2
0
3
3
7
1
8
0
3
3
7
9
5
2
3
3
3
2
10
9
4
5
3
11
2
6
2
3
3
8
3
4
0
3
3
2
4
5
3
1
4
2
1
5
2
0
15
4
3
17
3
1
5
3
2
1
0
3
7
3
9
5
2
8
4
7
5
3
6
0
1
3
6
0
3
4
5
14
11
7
5
1
5
4
14
2
2
2
4
3
1
1
5
3
5
2
2
4
5
1
4
8
3
1
1
2
0
2
5
4
4
4
3
14
2
7
1
2
5
3
7
4
2
3
2
1
3
3
1
3
2
4
7
6
4
2
5
2
3
3
6
10
1
3
0
9
3
1
2
2
1
1
3
0
5
4
8
7
2
7
5
3
3
3
1
3
1
4
3
2
1
5
4
1
2
3
1
8
5
2
2
3
4
2
2
0
5
2
0
3
0
0
1
11
4
8
3
3
0
4
6
3
5
3
5
2
5
3
5
2
3
3
2
4
4
14
4
3
2
1
3
3
3
4
1
3
0
5
2
6
3
1
7
4
4
9
3
9
2
4
8
2
5
0
4
0
6
11
2
1
0
4
3
4
2
4
3
5
2
1
2
5
3
6
3
1
1
4
4
11
2
0
1
1
6
5
0
3
5
8
5
6
4
0
3
2
4
5
2
8
4
2
2
3
0
1
13
3
1
9
1
1
5
2
2
3
3
2
10
4
4
3
4
5
5
1
0
6
2
3
2
0
1
3
14
3
4
2
5
7
7
5
8
5
0
3
2
4
6
1
4
0
4
1
5
1
2
6
7
1
3
1
4
13
0
3
3
3
4
0
1
0
8
1
5
5
0
5
3
2
1
1
1
1
3
1
2
4
1
2
1
2
0
4
2
3
5
1
3
3
2
7
2
5
2
0
4
8
4
6
1
6
10
1
3
6
4
2
3
4
6
3
2
2
5
4
1
3
1
5
3
1
5
2
2
0
3
5
4
2
2
0
11
2
5
2
5
5
3
1
12
3
0
3
2
2
0
5
2
3
1
0
6
2
3
2
4
2
2
4
8
3
3
3
1
2
2
6
5
5
4
2
0
11
2
9
5
3
4
5
3
1
1
3
1
2
5
6
6
4
6
3
1
1
6
1
2
5
4
3
3
3
4
2
3
3
1
3
1
2
4
4
4
0
1
2
1
10
7
7
3
4
4
4
3
9
1
4
6
4
7
0
2
5
2
6
5
3
5
3
3
2
2
5
4
1
3
4
6
0
2
1
7
2
0
4
7
4
1
8
1
5
2
5
9
8
0
3
3
0
8
0
2
0
6
3
13
2
0
3
0
4
3
5
0
5
3
0
4
3
2
7
2
1
1
3
3
1
1
7
6
6
2
3
6
4
7
7
4
5
1
0
3
2
2
3
1
3
4
1
2
1
2
1
0
3
3
1
3
4
9
3
1
2
3
3
2
10
6
1
1
3
1
3
1
3
2
4
9
3
2
2
0
4
4
7
4
0
2
10
1
2
6
5
3
4
1
4
0
2
3
6
2
2
2
5
1
0
2
2
2
2
3
1
1
2
3
3
0
4
3
4
3
4
5
6
5
1
2
1
3
8
3
1
3
6
5
2
2
3
2
4
6
7
2
1
4
3
3
1
3
1
7
2
2
1
3
5
4
11
2
2
4
2
2
2
2
4
3
15
7
4
4
3
2
0
1
1
6
8
3
0
2
2
2
0
2
3
16
10
1
4
0
2
2
7
0
2
1
3
10
2
0
11
6
2
2
5
1
3
15
2
4
2
2
2
3
2
0
4
3
2
5
5
2
3
2
3
3
4
2
2
8
3
3
2
5
3
3
9
3
3
2
3
2
2
2
3
9
5
4
1
2
2
2
1
4
5
0
4
2
5
3
3
4
2
8
4
2
2
7
2
1
2
3
4
0
1
3
2
2
2
1
5
0
6
2
7
5
0
7
3
3
4
3
2
1
2
6
1
0
6
3
5
2
4
4
4
2
5
2
2
2
1
4
0
4
2
3
2
7
4
0
5
0
3
6
0
1
2
5
2
8
15
8
11
8
2
0
3
2
1
2
6
4
3
2
2
3
4
4
2
2
4
2
3
1
1
1
0
5
1
2
4
1
2
3
7
3
3
1
3
12
2
0
2
4
4
6
3
3
4
1
3
7
2
1
7
1
4
2
2
2
2
0
6
1
2
3
1
4
1
3
4
2
2
3
0
7
2
9
2
2
5
4
8
2
3
5
0
4
10
1
3
4
5
5
2
0
2
4
4
3
6
2
3
3
4
5
3
0
3
1
5
7
5
8
0
2
1
2
4
3
6
6
1
3
1
3
0
1
3
3
2
3
2
1
10
4
2
1
7
1
0
1
2
2
1
2
6
7
2
7
1
6
5
1
2
2
2
3
4
2
6
9
3
2
4
3
12
4
0
0
1
7
2
2
3
6
1
2
3
2
2
2
3
0
2
2
3
3
3
1
8
2
16
6
3
2
4
2
4
7
3
2
4
3
2
2
1
7
2
2
2
1
3
3
1
8
3
2
17
4
1
0
3
2
2
4
1
2
1
3
1
7
4
5
2
3
0
0
5
6
1
4
1
3
3
0
7
2
9
2
2
2
4
2
3
2
1
7
4
1
2
3
4
1
3
7
7
1
6
1
3
4
3
3
2
10
1
1
2
3
15
1
5
2
4
6
2
2
3
6
3
0
4
2
0
2
1
2
0
5
6
1
1
1
2
2
4
1
1
5
1
2
1
4
1
1
1
1
2
3
1
6
5
6
4
2
5
2
2
6
2
2
3
3
4
0
2
1
6
2
1
0
3
4
0
1
2
1
3
5
1
1
1
1
3
3
1
4
5
1
11
2
3
2
3
4
4
1
2
7
1
3
1
4
1
9
3
0
5
1
0
6
2
1
3
2
3
4
4
1
4
4
2
12
2
3
13
1
6
2
1
6
0
2
1
2
5
6
10
3
3
7
3
3
5
2
3
2
3
1
4
2
0
2
4
3
8
2
3
3
3
7
4
9
7
4
2
1
3
3
6
1
9
1
6
1
7
6
10
2
4
3
2
2
0
0
2
1
3
4
3
3
5
2
3
1
1
1
1
2
1
5
0
3
1
5
2
3
16
6
1
7
1
21
3
4
2
1
2
4
2
4
14
3
2
3
1
11
3
2
4
2
4
3
2
4
3
1
2
3
1
4
1
1
3
3
2
3
5
3
3
7
5
2
2
3
2
3
5
2
5
1
2
3
1
2
0
5
6
4
3
1
1
7
4
2
4
1
0
0
2
3
2
2
2
10
3
6
3
5
3
3
1
1
0
8
5
1
1
3
6
0
7
1
1
1
2
2
2
0
3
1
3
4
10
1
3
2
2
3
4
2
5
1
3
1
2
5
5
6
2
7
1
6
4
3
2
3
0
4
4
4
5
3
6
21
4
1
2
3
3
3
1
6
2
3
1
1
2
3
10
1
1
5
4
2
3
0
3
4
6
2
2
0
15
3
5
2
3
2
1
3
4
2
5
2
3
2
2
0
2
2
5
1
4
3
2
1
2
2
10
1
3
1
6
5
2
6
0
3
1
1
3
1
4
2
1
2
1
4
2
12
4
2
3
7
7
7
1
3
1
2
1
0
3
2
2
3
0
2
4
3
2
12
2
2
7
1
2
3
3
2
2
1
5
3
9
9
4
6
2
2
2
6
3
4
1
9
1
8
1
11
8
1
3
3
1
1
5
1
1
0
3
3
2
0
6
2
2
2
2
1
1
3
2
1
1
3
1
0
5
5
0
4
2
2
5
1
3
2
2
3
8
2
1
2
4
2
9
3
7
0
1
3
4
6
5
3
1
6
1
1
3
2
0
1
4
0
3
5
8
3
2
3
6
1
2
1
1
1
3
5
1
2
3
0
1
0
4
2
4
3
3
1
3
1
2
3
2
8
1
6
3
2
2
2
2
7
1
4
7
2
2
3
1
2
5
2
11
2
2
2
6
2
1
2
0
2
3
2
4
2
3
3
3
4
0
1
3
2
4
2
1
1
2
3
2
1
1
1
6
2
4
2
1
3
5
1
4
2
3
4
2
0
4
2
2
2
2
5
3
5
2
4
17
1
4
1
2
1
2
2
2
1
7
1
4
1
3
2
6
1
4
2
2
3
2
5
8
2
0
1
0
2
16
1
1
6
6
3
1
2
2
4
1
4
3
3
2
10
0
6
2
3
10
5
21
2
1
0
6
0
0
2
4
1
7
1
4
4
3
1
0
5
3
2
1
1
2
0
2
0
7
1
2
8
3
2
2
3
4
0
1
1
1
1
2
5
5
1
6
2
5
3
2
2
3
1
0
3
1
5
5
4
5
8
2
3
4
6
1
0
3
1
3
5
3
3
3
2
2
2
0
5
2
2
2
9
4
1
1
0
2
0
1
4
2
3
5
1
2
4
4
4
4
3
2
2
1
2
0
1
0
4
2
2
1
2
4
3
1
4
3
2
4
2
1
4
2
2
0
1
2
1
1
4
8
5
2
12
2
0
1
4
2
4
2
2
17
5
1
5
5
1
0
2
3
3
4
5
3
3
6
0
2
1
2
5
2
7
3
1
2
2
2
0
2
6
5
7
1
4
11
9
1
2
1
5
3
3
2
0
2
0
3
0
1
2
4
1
1
3
1
3
1
2
7
3
1
4
3
3
4
0
11
1
1
1
5
3
4
4
2
0
2
5
3
2
4
4
2
1
0
12
4
17
4
3
6
1
1
2
7
16
6
2
5
0
2
9
2
3
3
1
4
3
4
2
3
4
2
6
1
1
1
1
2
2
3
5
3
4
2
1
2
2
3
4
7
1
1
3
3
0
1
0
2
1
4
6
3
4
5
9
1
1
0
3
1
0
0
2
0
1
4
16
2
14
3
4
4
3
3
2
0
1
1
11
3
5
2
2
3
1
3
4
2
3
2
4
2
4
2
0
3
3
2
1
4
7
2
1
2
0
2
0
2
1
10
3
2
3
2
1
3
2
5
1
2
1
5
2
5
7
6
0
2
3
4
1
1
2
4
1
1
1
3
0
0
4
2
1
5
10
4
3
2
0
0
3
1
2
3
0
2
4
4
3
10
2
3
1
5
1
2
1
6
3
1
3
3
2
1
4
1
3
1
1
2
1
2
3
1
2
2
8
2
2
6
20
0
2
11
2
2
2
4
4
1
0
1
1
7
2
5
1
3
4
1
3
0
3
1
1
0
1
3
1
1
1
2
1
1
7
2
1
8
2
1
4
2
0
3
2
2
3
2
3
5
3
4
5
1
5
3
0
3
0
0
2
4
2
2
2
2
0
2
5
5
0
3
1
3
1
1
1
13
3
2
5
5
4
3
1
2
2
2
4
1
3
1
2
8
2
2
1
1
1
5
6
0
0
2
1
1
3
3
1
0
2
2
1
3
3
3
3
1
3
4
1
2
1
4
3
0
7
2
1
3
3
5
5
1
2
0
4
1
1
0
4
5
9
1
18
0
1
3
2
13
3
1
2
1
0
4
2
3
1
1
2
4
0
2
3
2
2
1
7
9
5
14
23
2
2
4
1
5
2
1
0
3
1
3
1
3
1
2
0
1
7
2
7
3
1
3
3
2
3
1
3
2
3
2
3
2
6
5
12
2
2
2
4
4
1
2
5
1
2
1
3
1
2
2
0
2
0
2
5
3
8
1
3
3
3
2
2
2
6
2
5
6
1
0
4
3
2
1
3
3
4
2
6
12
0
2
2
1
2
2
2
2
2
3
14
3
3
8
6
5
12
1
6
1
1
2
5
2
3
1
1
2
3
1
4
5
0
2
1
1
1
3
1
7
1
1
3
2
1
3
1
4
2
4
0
2
4
11
14
2
2
1
0
2
5
1
4
3
2
3
4
0
3
2
0
5
2
3
2
0
2
1
1
2
1
2
2
3
0
6
6
0
5
3
5
5
3
3
4
1
3
1
1
11
2
2
2
2
7
4
5
4
3
0
4
1
1
3
7
1
2
0
5
3
1
0
2
4
2
13
1
6
2
2
1
1
2
4
1
0
2
1
3
0
2
4
2
0
5
3
4
0
3
2
0
5
2
2
8
3
4
3
0
0
4
1
3
2
3
2
4
0
2
2
14
1
1
7
2
18
5
2
3
0
6
2
7
12
1
2
0
2
3
7
4
4
4
2
0
1
3
4
0
1
4
2
1
1
5
2
2
5
3
1
3
1
5
4
5
4
3
5
2
7
1
3
3
2
1
0
5
2
2
0
0
4
2
2
0
2
3
3
1
5
1
4
4
1
4
0
2
4
3
2
3
4
4
3
10
1
5
7
2
4
2
2
4
1
2
9
1
5
3
3
2
7
1
3
2
7
3
1
1
9
3
3
3
3
0
2
1
5
5
3
5
2
2
3
4
2
3
2
10
1
2
3
1
1
2
2
3
5
3
4
4
2
4
9
2
1
0
1
2
3
0
0
3
0
3
0
5
3
1
8
0
1
3
3
4
1
2
5
2
2
3
2
1
2
3
3
1
0
1
3
3
3
4
1
2
4
4
7
5
3
4
2
4
1
4
3
1
1
0
4
1
1
0
3
4
1
2
0
1
3
4
0
1
6
1
4
2
3
1
2
0
3
3
0
4
4
3
4
4
1
3
1
0
1
4
5
0
2
1
4
4
15
3
3
1
2
2
0
2
1
1
3
1
0
0
2
1
7
3
2
1
5
5
3
2
1
2
2
4
1
2
3
3
4
15
3
4
5
2
1
2
4
5
1
1
3
3
1
5
7
11
0
0
2
2
2
10
1
2
3
5
1
1
2
1
3
0
2
2
10
2
0
3
2
1
0
2
4
5
2
1
2
1
4
0
2
1
3
2
2
1
1
3
1
6
1
6
0
3
2
1
3
1
0
7
3
2
0
3
6
1
1
2
0
1
4
2
1
11
8
1
4
3
2
7
3
6
11
0
2
0
0
2
4
2
2
0
3
0
2
0
2
0
3
8
3
1
1
2
2
0
2
2
2
3
3
3
3
3
1
6
3
1
5
0
3
4
3
2
2
3
0
0
4
4
1
2
3
3
7
3
3
0
3
1
0
3
0
1
0
3
2
1
1
2
2
3
2
1
8
0
2
1
1
0
1
0
0
6
6
2
8
1
3
1
2
2
0
15
2
3
6
2
3
4
5
2
2
3
5
5
4
1
11
1
2
1
1
4
0
6
0
1
5
1
3
8
1
0
2
2
2
0
3
1
3
1
0
2
13
2
3
3
0
3
0
2
3
1
4
3
0
2
2
1
0
1
6
5
0
23
5
1
2
1
1
4
0
0
4
0
1
4
3
3
1
3
1
3
4
4
4
0
3
3
4
1
6
4
0
0
2
5
2
1
7
2
3
5
1
1
1
6
4
1
3
11
3
1
0
0
2
2
6
9
2
3
3
9
1
2
1
4
2
3
7
2
2
3
2
8
3
2
2
4
8
3
1
1
2
11
2
0
2
0
2
2
2
0
3
0
3
0
2
4
1
2
2
0
1
6
2
0
3
5
4
0
3
3
4
1
1
10
4
1
0
3
1
2
1
4
2
2
7
7
7
4
1
11
2
1
0
6
2
15
9
0
1
4
1
1
3
6
0
7
4
2
2
4
1
3
2
6
11
3
1
6
2
3
7
1
2
0
0
1
3
2
0
2
3
12
1
5
4
3
4
1
5
2
3
3
2
0
2
1
0
0
1
1
1
1
0
8
1
0
0
3
0
2
4
2
1
6
2
4
0
0
2
1
5
3
0
1
6
7
1
1
1
5
2
3
0
1
2
4
4
2
2
3
0
1
1
13
2
1
1
5
2
0
2
5
5
1
1
5
1
3
2
1
4
0
0
4
3
3
4
7
7
0
0
4
2
5
2
0
1
2
4
2
1
2
1
3
3
5
2
1
3
2
2
10
4
0
6
1
1
1
3
0
2
1
6
0
14
1
12
0
7
1
2
2
1
2
1
4
0
2
1
3
5
2
1
2
2
1
5
3
3
2
1
5
0
2
3
1
5
3
4
1
1
1
1
3
1
1
1
1
0
7
3
4
5
4
1
1
13
1
7
4
6
2
4
0
2
3
0
2
5
5
2
9
2
1
1
3
1
6
1
3
2
3
1
0
1
0
1
2
4
0
1
2
5
2
4
18
5
1
0
5
6
2
0
4
1
2
1
2
0
5
2
3
1
1
0
0
4
2
2
3
3
2
2
3
2
2
1
2
15
1
1
3
0
0
3
2
0
2
4
1
1
0
3
0
4
1
2
4
3
7
2
6
6
1
0
2
0
2
4
0
2
1
1
2
2
3
15
5
3
3
1
3
2
1
2
3
0
1
1
2
0
2
2
5
1
1
1
1
3
6
4
2
4
2
3
3
1
1
5
1
1
1
0
1
2
3
1
3
2
1
1
1
3
3
3
11
5
1
0
3
3
1
4
1
2
4
0
0
2
4
1
2
0
1
3
0
4
3
2
0
1
1
4
1
1
1
3
1
4
0
1
5
2
3
2
2
2
1
2
3
0
0
3
1
2
4
0
3
2
3
1
0
3
3
4
3
1
3
2
3
1
1
7
1
1
3
2
0
1
0
3
3
4
1
2
2
0
3
1
3
5
2
5
0
1
1
2
1
1
9
6
4
2
2
1
4
1
2
1
0
2
0
1
2
7
0
7
0
3
2
4
3
2
0
1
2
1
2
0
4
1
3
0
5
0
3
1
19
2
8
1
2
2
2
0
10
0
3
3
1
2
0
2
3
3
5
5
2
3
3
2
1
1
1
4
3
1
2
1
3
0
3
2
2
10
3
2
1
3
4
3
1
0
1
3
3
3
2
2
4
1
3
0
1
2
2
3
3
3
13
0
1
1
4
1
0
2
3
3
1
2
4
3
3
1
4
0
5
9
3
0
0
3
0
3
1
3
5
3
1
0
5
4
1
2
1
0
1
0
0
5
1
5
2
3
1
2
5
3
2
4
5
0
0
1
1
2
1
1
1
0
2
2
3
3
1
3
2
2
2
9
2
3
2
4
0
2
1
2
3
1
2
17
5
2
3
0
4
4
0
1
2
1
1
0
1
1
2
7
1
5
1
3
1
2
0
7
0
4
2
1
1
3
1
8
0
3
1
1
13
1
2
0
1
4
1
1
6
3
1
8
5
1
3
3
14
1
0
1
1
4
2
5
0
1
2
1
1
3
0
1
3
0
1
3
0
3
1
2
0
1
3
5
2
0
2
1
3
2
1
5
3
3
3
0
2
2
4
3
1
1
3
4
0
3
4
0
4
0
1
3
6
0
2
3
5
2
1
2
4
2
0
1
3
3
2
1
1
2
0
0
1
2
13
13
6
7
0
0
2
3
0
2
2
1
9
3
2
3
2
1
1
2
3
1
2
2
0
2
4
8
0
1
0
2
2
4
4
2
1
4
1
4
3
5
2
0
2
3
3
2
1
2
2
13
2
2
0
3
0
1
2
0
1
1
0
3
0
3
2
1
2
2
1
3
3
2
2
1
2
4
1
2
1
9
8
1
0
1
3
0
2
2
1
0
2
2
0
2
1
2
4
3
2
5
0
2
4
0
2
1
2
1
1
2
7
2
3
4
3
2
0
1
3
5
2
1
3
3
1
2
1
0
1
2
0
1
2
1
1
1
8
3
2
4
1
2
3
1
0
2
2
4
1
1
0
11
2
4
1
3
5
2
1
0
2
9
3
3
12
1
2
2
5
1
2
1
1
4
1
4
7
0
3
0
4
0
1
2
3
0
1
1
2
3
10
0
1
12
1
8
0
6
4
0
0
2
10
1
12
0
2
1
2
2
1
2
3
1
3
1
9
1
1
2
2
10
2
2
3
0
2
2
10
4
2
3
3
1
1
4
8
2
3
3
0
4
2
2
0
4
1
2
2
1
6
5
2
1
0
11
3
1
0
4
1
4
1
0
19
2
2
5
1
0
5
3
5
4
2
3
1
1
2
1
3
2
2
2
9
6
4
1
2
4
2
5
7
4
2
0
7
2
0
0
6
7
4
1
4
0
2
0
2
4
1
5
1
2
3
2
6
1
2
9
5
5
2
5
1
0
10
0
2
1
1
1
4
2
3
3
6
3
1
4
2
1
1
1
2
3
2
5
1
5
0
2
2
1
3
0
3
3
2
4
1
1
8
4
2
0
1
2
0
1
7
3
2
0
1
3
5
1
2
2
1
3
2
1
3
3
3
5
1
5
0
3
1
1
1
1
1
7
5
0
2
4
7
2
1
1
1
2
2
2
2
3
2
2
3
1
3
4
1
1
2
2
4
0
1
1
4
1
0
4
1
1
2
0
3
1
3
9
3
0
1
2
7
2
0
1
1
1
1
1
1
1
1
1
5
1
2
1
1
1
0
0
11
12
2
0
1
3
0
0
5
4
1
0
1
1
0
1
2
3
0
1
3
1
3
9
2
0
2
1
0
3
1
15
2
2
1
5
1
1
1
0
2
1
2
2
1
1
2
0
2
5
3
2
0
1
0
3
1
5
2
1
1
2
0
1
3
2
1
0
7
3
0
3
2
3
5
0
1
2
5
2
1
3
10
1
1
2
3
4
1
5
2
0
2
3
2
2
3
3
2
1
1
4
0
6
0
2
3
0
4
4
0
2
1
0
1
5
1
1
7
0
1
2
6
3
1
3
20
6
1
0
2
1
10
3
1
8
0
8
0
3
2
6
1
1
0
3
1
1
8
1
3
0
2
1
1
1
3
1
2
1
4
2
0
1
4
2
3
1
3
0
5
1
1
4
1
3
3
2
0
0
1
5
0
1
3
1
1
4
6
2
6
1
0
1
1
1
1
0
3
2
2
1
0
3
2
2
1
0
3
2
2
1
5
4
0
3
2
1
1
3
3
2
3
2
3
1
1
4
0
1
13
1
2
1
2
2
1
2
2
1
4
4
21
2
3
2
5
2
3
2
2
0
0
1
5
0
3
2
6
1
3
3
5
1
1
2
6
0
4
1
2
4
2
1
2
2
3
4
1
1
7
3
0
2
0
3
1
2
5
0
10
6
3
2
2
1
1
1
4
3
1
3
0
1
2
0
1
1
7
1
2
2
4
0
2
4
0
2
4
10
3
5
0
1
2
4
7
0
2
1
0
2
1
1
2
1
3
2
0
3
5
4
1
1
0
1
1
3
10
1
0
1
4
4
3
2
0
2
0
2
2
6
2
2
1
8
2
2
3
0
1
1
3
2
3
6
1
2
5
3
2
2
1
2
3
16
0
2
1
2
3
2
12
3
3
1
1
1
0
5
2
0
1
5
2
1
2
3
10
2
14
4
1
1
3
2
4
4
2
1
7
3
3
0
2
1
3
3
2
0
16
2
4
3
2
4
4
1
1
1
2
1
3
1
1
0
1
1
2
2
3
1
1
2
1
1
1
1
0
1
4
1
10
4
4
11
3
2
1
0
5
0
1
6
7
4
0
0
2
7
2
1
0
4
2
1
2
2
1
6
1
2
0
11
1
7
2
3
1
0
2
1
1
3
1
1
0
3
1
0
1
0
4
0
2
1
3
2
1
2
2
1
2
0
4
1
1
4
1
1
4
1
0
1
1
1
1
1
2
4
3
6
0
0
2
2
2
3
3
9
2
2
2
2
0
2
1
2
2
0
1
2
1
4
0
2
4
5
2
1
1
0
9
0
5
2
1
2
1
1
1
1
1
2
6
2
0
2
5
4
1
4
1
1
2
3
1
1
0
6
2
2
1
1
0
3
8
2
0
5
3
2
3
0
3
1
1
0
2
0
5
2
2
1
5
2
7
3
1
1
2
0
2
2
5
3
1
1
5
1
4
2
2
1
2
3
2
2
5
3
0
3
0
2
0
2
3
7
2
2
1
1
0
10
2
1
2
0
1
3
5
0
4
3
1
2
2
1
3
1
9
1
2
1
1
7
5
0
2
0
2
1
0
2
6
3
4
2
0
0
3
3
2
1
5
5
2
1
2
3
3
2
3
1
1
1
5
1
3
3
5
0
2
5
1
1
1
1
2
2
0
5
1
0
0
1
1
1
1
3
0
2
1
1
2
1
5
0
3
1
2
2
2
0
2
0
4
2
0
0
0
4
2
0
1
0
5
1
5
1
2
1
3
3
4
5
2
2
3
5
4
4
9
1
1
1
1
0
0
4
0
1
0
0
5
2
3
0
1
3
9
1
3
2
2
2
2
8
0
1
2
3
4
2
1
0
2
3
1
2
1
4
1
2
2
3
0
2
1
2
2
1
4
2
1
3
1
1
2
2
5
4
0
3
1
2
3
0
4
2
3
2
0
2
1
2
0
2
4
1
3
1
0
2
0
2
2
2
0
2
1
1
0
1
1
3
1
1
1
2
8
1
1
2
6
2
2
4
4
4
1
2
2
1
4
2
0
0
0
1
0
3
4
2
1
1
2
3
2
6
1
3
2
3
1
4
3
0
0
2
3
7
2
2
2
1
3
4
1
0
1
1
1
1
1
1
2
1
1
2
0
10
3
1
3
4
2
1
27
4
1
1
0
5
2
2
1
2
2
2
2
2
2
1
4
4
2
1
5
2
1
5
1
3
0
3
4
1
1
0
0
2
1
1
2
4
2
2
1
0
2
1
3
0
1
3
2
1
0
2
0
1
3
4
7
0
3
4
1
4
1
3
0
3
4
1
1
1
2
2
1
4
0
1
2
3
2
1
0
0
1
1
1
1
1
5
2
3
1
4
0
1
0
1
8
1
2
7
2
1
6
1
1
2
1
0
1
1
0
3
1
1
0
9
0
0
0
2
0
6
1
1
3
5
2
0
0
1
3
2
2
3
0
8
1
1
1
0
1
2
6
1
2
1
2
4
2
2
5
4
7
2
0
3
4
9
1
0
3
4
3
2
2
3
1
1
3
11
3
0
2
4
0
0
2
1
1
5
2
1
3
5
0
1
0
0
1
2
2
0
3
2
0
1
9
2
1
0
1
1
2
3
1
0
2
3
1
1
2
2
2
2
1
2
2
4
1
2
1
1
5
3
2
1
1
1
2
2
2
0
4
2
1
4
4
1
2
1
2
1
2
0
1
2
3
5
13
2
2
1
1
1
11
11
3
1
0
0
0
1
2
1
2
3
0
1
1
1
0
2
1
6
3
0
2
2
0
2
2
2
0
0
1
2
0
2
1
1
3
9
3
3
0
2
1
1
2
2
3
2
4
4
1
0
2
2
1
1
1
1
0
1
3
1
3
9
4
0
6
2
1
1
1
5
3
2
2
1
3
4
1
6
4
0
0
1
1
8
1
1
3
4
1
2
3
1
2
0
1
2
1
4
1
11
0
0
0
2
2
0
1
2
6
2
2
1
6
0
2
15
6
0
3
0
2
0
1
1
1
1
0
1
2
4
0
14
0
2
3
0
2
2
4
1
0
2
2
2
0
1
5
2
1
0
2
4
2
1
4
1
0
0
1
1
1
1
1
3
2
1
1
4
5
0
8
0
2
1
1
1
1
5
14
1
8
5
3
2
0
1
2
0
0
2
1
0
1
2
3
4
2
4
2
0
2
9
1
2
8
1
2
0
0
1
1
12
0
1
1
2
3
0
0
1
4
5
1
3
1
3
3
1
0
1
0
1
0
1
2
4
1
1
0
4
3
2
3
5
2
0
2
2
2
0
13
1
1
2
3
3
1
1
1
1
1
2
0
1
1
2
2
1
5
4
0
1
3
0
2
2
0
1
1
1
2
1
3
4
3
0
0
0
4
0
2
1
3
2
2
4
3
2
0
2
1
1
1
4
1
1
0
3
1
2
2
1
2
1
3
0
0
1
0
2
2
2
2
4
2
0
0
0
1
4
0
1
0
1
2
6
1
2
4
3
5
12
1
0
2
2
0
3
0
0
1
0
2
0
0
0
2
1
2
2
4
1
2
3
2
2
2
8
1
0
1
5
2
2
1
2
0
0
0
8
1
3
1
1
3
2
2
0
11
2
2
1
0
2
1
2
9
2
1
3
1
3
0
3
1
0
4
0
1
1
3
4
5
0
0
2
3
1
0
2
6
1
1
1
0
2
1
1
1
1
1
1
3
1
1
0
0
0
1
0
2
2
3
1
1
1
2
1
0
2
2
1
1
1
1
2
1
2
3
1
4
2
0
2
0
0
1
2
0
3
2
0
7
2
0
0
2
3
1
2
1
3
3
2
8
2
2
2
0
2
1
1
0
0
1
5
8
3
3
3
0
3
0
3
2
1
2
2
1
2
1
2
2
0
3
4
2
3
2
1
1
3
0
0
3
2
1
2
0
2
3
3
0
0
1
2
5
0
3
3
0
1
1
0
1
1
0
2
0
1
3
1
1
3
0
2
0
2
1
4
8
1
0
0
1
1
1
2
4
2
4
0
12
2
2
2
0
1
0
0
0
1
3
3
2
3
1
2
3
3
0
3
0
0
1
3
2
0
0
2
2
1
0
2
1
0
3
0
3
2
2
2
1
4
3
0
4
1
1
2
0
1
2
1
2
0
1
0
0
2
1
2
0
2
2
0
1
3
2
6
4
0
1
3
0
1
1
0
3
0
1
5
1
1
1
0
0
2
1
1
1
7
8
0
3
2
3
0
0
0
0
11
2
2
2
1
3
1
4
2
2
1
3
2
2
2
1
2
0
2
4
0
1
6
1
0
3
2
2
2
0
1
2
4
0
0
0
2
4
1
0
0
4
1
0
2
10
3
1
1
2
1
2
0
4
4
2
14
1
7
0
5
0
2
2
4
3
0
2
2
2
1
1
0
1
4
1
0
0
1
2
2
13
2
11
8
2
11
1
1
2
0
0
2
3
2
1
1
3
1
1
5
0
1
3
3
0
1
1
1
1
3
2
2
3
1
2
3
0
4
1
0
2
2
1
12
4
1
2
0
1
3
0
2
1
0
2
1
2
1
1
0
0
1
2
1
0
2
1
8
1
1
2
0
1
1
0
0
11
3
2
1
0
1
0
0
3
0
0
1
0
2
1
1
2
1
3
3
4
0
2
1
0
7
2
2
0
1
1
4
2
0
0
10
1
1
1
0
3
1
0
2
1
1
1
2
1
12
2
3
5
2
0
2
3
1
3
2
0
0
0
3
1
0
1
3
1
3
2
0
1
1
2
4
0
1
2
4
2
2
1
1
3
1
0
9
2
4
0
3
0
5
2
0
0
2
4
1
0
1
0
1
2
0
1
2
3
1
3
3
3
1
2
2
0
2
0
3
0
1
1
1
1
1
1
1
0
1
2
0
4
1
1
2
6
2
3
1
0
1
9
1
2
1
2
2
0
1
5
3
0
0
0
6
0
1
1
1
2
1
1
2
2
0
3
1
2
3
1
3
2
1
5
1
1
0
6
2
3
7
1
1
4
1
0
0
0
1
2
3
0
2
3
2
2
1
2
1
2
0
1
0
2
15
1
2
0
5
10
7
6
0
3
0
1
2
3
4
2
1
2
3
5
1
3
3
1
2
0
2
2
2
2
0
2
6
1
0
3
4
1
1
1
3
2
2
1
2
12
2
5
0
1
0
0
2
2
0
1
0
0
5
0
0
3
2
1
4
3
1
1
4
3
0
0
3
0
6
2
1
2
10
3
6
6
3
2
0
2
2
0
1
1
6
1
1
1
0
1
1
1
0
10
4
2
1
0
4
3
2
1
3
6
2
1
0
2
2
1
0
1
1
1
2
2
3
1
3
1
1
1
3
2
0
0
0
1
0
2
0
1
1
0
1
6
0
1
0
0
0
2
0
3
1
2
1
8
0
8
3
2
0
3
2
2
1
0
0
1
1
1
2
2
5
3
0
1
1
1
1
0
0
1
2
3
3
3
3
1
1
1
2
1
1
3
2
3
1
0
4
2
1
3
0
3
3
2
0
1
2
1
1
2
2
2
0
1
3
2
0
2
2
0
3
0
0
2
1
1
2
3
7
1
2
2
1
2
3
2
1
3
2
2
1
1
0
3
1
0
1
0
1
2
2
1
2
5
0
2
2
0
4
2
0
3
2
1
0
1
1
1
2
1
1
2
3
6
7
0
2
2
1
2
1
2
1
3
1
1
0
1
1
0
2
1
2
1
4
2
3
0
1
2
7
0
1
1
1
0
1
1
3
5
2
0
4
2
1
1
0
2
2
5
0
1
3
2
1
0
2
2
2
3
1
5
0
1
1
2
3
4
1
0
6
1
1
2
1
3
2
2
3
2
2
3
1
6
2
1
0
1
1
1
5
3
8
2
1
0
6
3
2
2
1
3
1
0
3
1
2
0
2
2
1
1
1
3
5
0
4
1
0
2
1
1
0
0
2
3
1
1
0
0
1
2
1
0
2
0
1
1
5
1
2
2
2
1
0
3
2
3
1
1
0
1
0
2
3
2
2
0
0
1
1
2
1
4
2
6
3
2
2
0
6
1
7
1
0
6
1
2
0
3
4
0
3
6
1
0
2
1
1
13
10
1
2
0
1
1
2
3
1
1
2
3
1
2
2
2
3
1
2
3
15
0
1
1
0
1
3
0
2
3
4
0
1
2
2
3
0
1
0
0
3
3
2
2
1
0
2
0
2
2
0
2
1
1
3
5
2
2
1
1
1
2
1
0
0
0
1
1
5
2
2
0
0
2
2
1
0
3
5
1
2
0
2
1
1
1
1
0
3
2
3
2
1
1
1
0
1
0
1
5
2
3
4
3
1
2
1
4
1
1
1
2
1
7
0
1
1
0
0
7
3
0
4
0
0
1
1
0
1
0
0
1
0
6
0
1
4
1
2
1
1
1
0
1
0
1
1
1
1
4
0
1
2
1
1
3
1
1
1
2
2
2
1
1
3
2
0
1
3
1
1
0
1
0
1
0
1
2
2
0
0
15
2
1
0
5
1
10
2
2
1
2
5
0
0
2
1
2
0
1
10
2
1
4
2
2
2
1
8
1
1
3
0
11
1
0
1
1
1
0
5
2
2
3
0
0
1
1
1
3
2
2
1
2
4
0
3
0
2
0
1
3
2
2
1
2
4
0
1
0
2
3
1
3
1
4
0
0
1
1
1
2
4
4
0
3
4
0
1
1
1
2
3
2
1
6
1
8
3
0
0
2
0
2
2
2
2
1
2
0
1
1
3
6
0
5
1
1
3
1
0
0
11
2
0
2
1
1
1
8
4
0
1
2
0
0
1
2
3
1
1
1
1
2
1
0
3
2
3
4
1
1
1
1
0
1
3
4
0
1
0
0
3
2
5
3
0
2
6
4
0
2
3
0
2
5
0
2
3
0
0
4
0
0
8
2
4
2
5
0
7
0
0
1
0
0
8
0
3
2
2
4
1
3
3
0
2
1
1
2
1
1
0
5
2
0
5
2
2
0
12
2
0
2
0
1
1
1
1
0
2
1
3
1
0
3
2
0
1
0
1
2
2
1
1
1
2
1
1
0
2
0
3
1
0
3
1
6
2
3
0
0
1
0
5
1
1
2
0
6
4
1
1
0
0
1
0
3
0
1
1
4
1
2
1
0
2
5
0
2
2
0
0
1
0
8
0
8
1
2
1
2
0
0
1
3
1
3
2
3
1
2
1
0
1
0
0
2
2
5
1
2
2
2
1
2
0
4
2
1
0
2
2
0
3
1
3
1
2
2
1
1
1
0
1
1
3
1
0
3
2
1
5
0
0
3
0
4
0
2
1
1
6
1
4
1
3
1
4
0
0
2
2
0
1
10
3
2
3
5
0
2
3
2
1
2
0
6
1
3
0
2
3
1
0
2
4
4
1
3
6
1
0
1
3
2
1
1
2
2
4
1
2
1
2
1
1
3
8
2
1
1
0
0
0
0
3
0
1
2
2
2
1
0
3
5
1
3
0
0
0
2
8
1
1
0
0
1
2
2
0
4
2
3
1
0
1
2
4
0
1
2
4
1
1
1
2
5
2
0
3
2
1
1
2
3
1
2
1
2
1
0
0
1
1
1
2
2
2
1
0
1
1
3
3
2
1
3
1
0
4
0
2
1
3
0
3
2
2
3
2
2
0
3
2
2
2
3
0
2
2
0
1
1
1
1
2
2
2
0
0
0
0
8
2
11
3
2
0
1
2
1
5
1
0
2
1
2
2
0
1
1
1
2
2
3
4
0
10
1
1
0
1
0
1
5
1
0
0
1
3
3
1
1
5
1
2
1
2
2
3
1
0
0
1
0
4
2
3
5
0
3
1
1
1
0
1
2
0
1
0
1
0
0
1
4
1
0
2
1
0
1
0
2
2
0
0
1
5
0
0
5
1
1
0
2
3
2
2
1
4
1
1
0
3
1
0
3
0
1
1
1
2
5
3
1
5
1
3
0
3
7
3
0
2
1
0
4
1
1
2
1
0
0
2
4
0
1
1
1
0
0
0
0
5
4
0
1
1
1
1
2
1
0
1
0
0
1
1
0
1
3
1
0
0
0
4
1
0
0
0
2
6
1
2
2
3
1
2
1
1
2
2
3
4
0
1
0
0
2
3
2
1
1
0
2
1
1
0
3
0
7
1
0
0
0
2
2
11
0
5
3
2
0
0
1
7
0
3
1
2
1
0
1
1
1
0
1
3
1
0
0
0
1
0
4
1
1
0
2
0
0
3
0
3
0
1
1
13
1
2
1
2
1
0
1
1
2
3
2
1
5
1
0
0
8
2
10
2
0
1
2
1
5
1
1
2
4
1
1
1
4
0
0
1
0
2
2
0
1
0
1
3
1
5
0
2
0
3
1
0
0
1
0
0
1
3
2
0
1
2
2
5
1
1
1
4
0
1
2
3
1
2
1
1
0
1
0
2
2
4
3
1
2
0
4
2
0
4
2
3
1
4
1
3
1
1
2
0
4
1
1
4
1
0
1
3
8
0
2
2
0
0
0
0
2
1
1
1
0
2
1
3
0
3
0
0
1
0
0
0
1
2
0
2
3
0
4
4
1
2
3
1
1
1
2
2
5
3
1
6
1
2
1
1
4
1
2
0
3
3
4
0
0
0
1
2
0
2
1
1
1
0
3
2
1
1
1
0
2
6
0
1
5
1
0
2
3
0
1
4
0
3
0
1
3
0
3
1
0
1
3
0
2
0
0
7
2
0
0
0
3
2
2
0
3
7
2
3
2
2
0
1
1
1
1
0
2
0
1
0
3
4
2
3
0
1
2
1
2
0
1
3
1
2
3
0
0
0
2
0
3
1
0
0
3
2
0
1
0
0
3
2
2
0
1
1
1
0
0
1
3
0
1
2
1
1
0
2
2
0
2
3
2
1
0
0
2
2
1
1
3
1
2
0
13
3
1
1
1
1
1
0
0
2
1
3
1
1
1
0
1
1
13
2
3
5
4
3
2
4
2
1
0
4
1
1
3
2
1
1
1
0
1
0
4
2
9
1
1
2
1
2
2
1
0
1
1
0
0
0
4
0
2
0
2
0
2
1
0
2
1
0
0
2
1
2
1
0
1
1
0
2
0
6
2
2
3
9
4
9
3
1
0
4
2
1
1
1
1
1
2
5
0
8
1
0
1
0
0
1
1
4
0
3
0
0
0
1
5
1
0
1
0
3
1
4
1
2
1
2
0
2
0
2
2
1
2
1
5
1
0
0
1
1
3
1
0
0
1
2
1
1
2
1
0
0
4
1
0
1
2
0
2
2
3
7
0
0
1
0
0
1
1
3
2
1
3
1
2
0
1
2
2
2
2
3
1
2
1
2
1
0
10
1
0
8
0
3
1
0
2
2
1
3
4
1
5
1
4
0
3
0
1
9
4
1
2
1
5
1
5
0
3
2
2
2
2
0
3
4
2
1
2
2
4
0
1
0
1
3
1
5
1
1
1
1
0
2
3
0
0
0
1
2
2
1
3
1
2
0
1
4
0
1
1
1
2
4
1
0
2
1
1
2
1
4
3
1
2
0
1
0
2
1
1
0
1
1
0
1
2
1
2
0
0
1
0
3
1
0
1
0
3
1
0
1
2
4
2
0
1
0
3
0
1
2
2
1
0
2
2
0
2
1
1
0
1
4
0
4
2
2
0
0
1
8
1
2
0
1
0
0
2
2
2
1
0
1
0
1
2
1
5
0
1
2
0
3
3
1
0
1
1
0
1
2
3
10
0
2
2
1
2
11
2
0
1
4
1
1
1
1
2
3
1
4
0
0
0
1
3
2
1
1
1
1
3
0
0
5
7
1
0
0
1
2
1
3
1
1
1
0
2
0
0
1
1
1
2
0
0
1
0
0
0
5
1
0
0
0
8
2
0
2
0
2
6
0
0
1
1
2
0
0
1
2
1
0
3
2
1
2
0
1
1
1
3
0
3
1
5
0
1
1
3
2
3
4
0
2
0
1
0
1
1
3
2
0
2
4
3
0
0
2
0
2
0
2
2
2
1
3
2
3
1
0
0
1
0
1
1
1
2
3
3
2
4
12
2
1
1
1
0
2
4
8
11
1
0
1
2
0
1
3
3
0
1
2
0
3
0
2
1
0
2
1
1
0
1
9
2
2
1
6
2
0
3
3
0
2
0
2
0
1
1
1
1
2
1
0
0
2
3
1
0
5
2
3
2
3
2
1
4
1
1
0
2
2
1
1
4
0
0
0
1
2
1
4
3
0
1
2
6
5
1
2
10
3
1
2
0
2
3
0
1
3
3
2
4
1
1
2
0
2
4
1
1
3
9
1
1
2
0
2
1
1
3
4
2
0
0
1
0
0
3
2
0
0
1
2
1
0
3
11
2
1
1
0
2
1
1
1
1
0
1
1
3
0
2
0
0
2
0
3
1
4
0
0
4
2
1
0
3
0
0
1
5
0
4
1
2
0
1
2
1
0
1
1
2
0
1
1
2
4
2
0
1
2
1
0
2
1
2
1
5
1
0
3
3
2
4
4
1
4
0
2
0
1
8
1
0
3
0
1
0
1
3
1
1
1
2
1
0
0
2
1
1
1
2
1
2
2
3
2
3
1
2
1
3
1
2
1
1
3
1
2
1
3
2
3
1
2
1
1
2
2
1
0
0
0
0
14
3
4
2
2
1
1
0
0
0
0
2
3
0
0
1
1
2
1
0
7
1
5
2
2
1
1
2
1
1
1
2
2
1
1
3
4
2
1
0
1
11
1
1
1
3
7
0
0
1
1
1
1
4
1
9
0
3
1
12
2
0
0
1
1
1
7
1
1
1
1
0
1
1
3
1
0
1
4
3
2
2
2
1
1
0
1
4
0
1
1
2
4
1
1
1
2
3
3
1
0
1
3
1
5
0
3
1
5
2
1
2
4
1
2
0
3
1
1
1
1
0
1
0
9
1
2
2
0
4
0
2
5
4
8
1
2
1
3
6
2
0
1
1
2
0
1
2
1
0
1
2
1
0
1
1
4
1
1
0
1
1
0
3
0
0
3
1
3
0
2
3
0
1
1
0
1
1
2
1
0
0
1
2
2
3
0
1
0
3
0
5
4
1
1
2
1
3
2
6
2
1
0
1
2
0
4
1
0
1
1
4
8
0
1
4
0
3
3
0
5
0
1
0
1
0
2
0
2
1
0
0
4
0
0
6
2
8
1
2
1
1
0
2
0
8
1
0
2
0
3
3
2
0
1
1
0
1
11
2
3
0
5
1
1
1
4
4
1
1
2
0
14
5
0
2
1
2
1
1
0
2
3
5
1
2
1
0
1
5
1
6
3
2
6
2
0
3
0
0
0
0
3
1
0
0
2
0
5
8
1
1
1
1
0
2
1
1
1
3
1
1
1
0
0
2
2
0
1
2
1
1
1
3
3
2
1
2
0
0
2
0
1
1
0
2
1
13
2
1
1
1
0
1
2
0
3
1
0
1
1
1
1
2
0
0
2
1
1
1
3
2
3
0
1
0
7
2
0
2
2
0
0
2
5
2
0
0
1
2
2
1
2
7
1
2
0
3
2
0
2
1
1
0
3
1
0
3
2
1
3
0
16
0
0
0
0
5
0
1
3
0
2
0
2
0
0
1
1
0
3
0
3
0
4
2
3
2
1
6
1
4
0
3
3
0
2
2
2
1
1
1
2
0
4
1
1
0
2
1
2
3
0
0
6
3
0
2
14
1
5
2
0
0
0
3
0
0
3
0
0
3
1
0
3
0
14
2
1
0
3
1
0
0
2
3
5
1
3
3
1
1
2
0
0
2
0
0
2
1
2
1
2
1
1
1
5
1
1
0
3
2
1
2
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
16
1
1
2
3
2
0
2
1
1
1
1
4
1
0
1
3
4
0
1
9
3
1
0
1
1
2
5
4
1
1
0
0
4
1
2
0
3
0
0
3
2
2
0
2
0
4
2
0
0
0
1
0
1
0
0
0
1
2
1
1
3
2
5
2
0
1
4
0
2
2
2
0
2
1
3
3
2
3
1
2
1
2
2
1
1
2
1
2
0
1
0
0
1
0
2
1
2
1
0
1
2
0
2
3
2
1
1
0
2
0
3
0
1
1
0
0
2
1
0
0
0
3
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
0
3
4
2
1
1
2
2
1
2
3
3
1
1
0
2
1
3
2
2
1
0
1
2
0
1
1
5
2
1
1
2
1
1
2
1
0
3
2
0
0
1
1
0
2
0
1
2
1
2
2
1
1
1
2
0
1
0
1
0
2
2
2
0
2
9
0
4
1
0
0
1
2
3
3
0
1
1
4
3
0
1
2
1
1
2
3
2
1
1
2
1
1
0
7
0
1
1
1
1
0
0
1
1
2
2
3
2
4
0
2
3
4
2
2
4
0
1
2
2
1
1
1
2
3
4
1
4
0
2
1
1
1
1
0
1
0
1
1
2
1
2
2
2
1
1
2
0
2
9
1
2
2
1
1
5
3
1
1
0
2
2
1
0
3
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
3
2
3
2
0
0
0
4
2
3
1
1
1
0
1
2
0
6
13
1
1
0
2
1
0
0
0
2
0
1
0
1
0
2
2
1
2
2
1
0
1
0
3
1
4
0
0
5
3
0
5
2
0
1
1
3
1
5
1
1
1
0
1
2
1
0
1
2
5
1
2
1
1
0
2
0
2
0
1
2
0
1
0
0
2
1
3
2
1
2
0
1
2
2
0
0
0
0
1
0
2
0
1
1
4
0
0
1
3
0
1
2
1
2
2
1
1
2
1
2
0
1
1
1
3
2
1
0
0
2
2
1
1
1
2
0
3
1
0
1
3
1
0
3
0
0
1
1
3
8
3
0
0
0
1
2
3
1
1
2
1
0
0
3
3
1
2
0
1
6
0
1
0
0
1
3
0
2
6
0
1
2
1
2
2
1
3
2
3
2
0
5
2
8
0
1
1
0
0
1
2
5
3
2
8
2
3
2
0
1
0
0
1
2
2
3
1
1
0
0
1
1
1
0
1
0
1
2
0
6
1
2
12
0
0
0
1
2
2
2
0
2
3
0
1
7
1
4
0
0
0
1
0
1
0
0
0
2
0
0
3
0
3
0
2
3
0
4
0
0
0
3
2
3
3
0
1
1
4
1
3
0
0
0
1
0
0
3
1
0
1
3
0
1
1
2
2
2
2
4
0
1
4
2
1
0
2
0
3
1
4
0
0
2
2
1
2
2
0
2
1
1
1
3
1
1
2
0
3
3
0
3
1
1
2
1
2
2
4
0
1
1
0
5
1
4
0
0
2
3
2
2
9
1
1
6
2
1
2
0
2
0
2
3
2
1
0
2
6
1
0
2
1
2
3
1
0
0
2
0
2
4
0
4
1
2
2
0
2
0
1
1
1
2
0
0
1
0
1
1
4
1
0
1
3
0
2
0
2
2
1
1
1
1
0
0
2
10
1
7
0
0
0
2
2
0
0
0
0
2
0
1
0
0
3
4
0
0
7
3
0
2
4
0
3
2
0
0
0
1
1
1
0
1
0
0
4
3
1
1
1
1
3
1
0
0
1
3
0
1
1
2
3
7
1
2
1
0
1
1
2
1
1
2
1
1
2
1
2
3
1
1
1
1
1
3
3
2
1
0
9
0
1
0
1
6
0
2
2
0
1
6
1
1
1
1
1
5
13
0
0
0
1
1
1
0
12
0
1
0
1
1
1
2
1
0
0
2
1
1
2
2
1
2
2
2
0
3
1
0
0
1
7
3
2
0
3
0
1
2
1
0
2
1
1
1
0
2
0
2
1
1
0
0
2
2
1
2
2
2
1
3
2
2
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
0
1
3
2
0
0
0
0
1
1
1
1
3
1
2
1
4
1
1
0
0
0
0
2
1
1
1
1
1
2
3
2
2
1
2
0
1
1
2
0
0
3
0
1
3
2
1
1
2
1
5
2
0
1
2
1
0
2
1
0
0
4
2
0
2
1
0
1
1
2
3
0
2
1
8
2
0
1
1
1
0
3
1
0
2
1
0
7
1
1
2
4
0
8
0
8
9
1
2
0
1
2
1
0
2
3
7
4
1
0
2
2
6
3
1
0
1
0
0
1
1
0
1
1
1
3
2
0
0
10
0
5
0
1
1
1
3
1
3
3
4
0
3
0
2
0
5
2
1
0
2
1
0
3
3
0
0
1
2
2
1
1
0
4
2
1
1
10
1
1
0
1
1
1
1
0
1
1
1
1
9
1
1
1
0
0
1
0
0
1
2
0
6
0
2
2
2
0
2
1
4
0
0
1
1
1
0
0
0
6
1
1
0
16
2
0
0
1
1
1
11
6
0
3
3
2
1
0
0
1
2
3
1
3
2
0
1
0
1
3
1
2
1
0
0
5
2
6
0
1
2
1
4
1
0
0
1
0
0
1
1
0
1
0
1
2
1
2
1
1
0
1
3
2
1
0
2
1
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
2
1
4
1
2
2
4
0
2
3
0
2
0
0
1
2
0
0
1
0
0
1
1
1
2
2
0
0
3
1
1
1
0
0
0
2
10
2
3
2
0
1
0
0
0
0
0
0
1
0
0
2
2
3
2
0
0
1
0
1
2
3
0
1
1
2
4
1
1
2
1
7
0
1
2
0
1
0
1
3
9
4
2
0
2
2
1
1
1
0
3
2
0
3
2
0
0
2
1
1
2
0
2
1
1
2
1
0
1
1
1
1
3
1
1
8
1
1
1
0
2
1
2
1
0
2
1
0
2
3
0
1
0
3
0
0
0
2
3
1
1
1
1
1
1
0
6
3
1
1
3
1
2
1
1
0
2
1
4
1
4
2
1
0
0
1
0
1
1
1
0
1
2
0
0
1
1
0
2
1
3
0
2
5
0
7
0
1
4
2
0
3
4
1
2
1
0
0
0
4
0
0
2
0
2
1
0
2
1
1
2
1
2
0
2
5
5
2
1
0
0
2
1
0
0
0
1
4
1
1
2
1
2
2
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
5
4
3
4
0
1
0
2
0
1
0
2
1
6
2
0
1
2
3
1
1
1
4
2
0
0
0
2
0
2
1
1
0
3
0
3
1
1
0
3
1
4
1
0
1
0
0
1
2
0
2
16
1
1
0
0
4
2
1
1
0
0
1
4
1
1
1
1
1
4
0
1
12
1
0
2
1
1
0
2
1
0
1
2
1
1
1
0
1
8
0
0
0
1
0
2
3
2
1
1
1
0
1
0
2
2
11
0
8
3
0
2
1
1
1
3
1
2
1
4
1
1
2
2
2
1
2
3
2
0
1
2
1
1
1
1
2
0
1
1
0
1
1
0
0
3
1
1
0
1
6
0
2
1
0
2
2
3
2
0
27
2
0
0
0
0
0
0
2
1
0
2
0
5
2
1
1
0
2
2
1
1
1
3
2
4
1
1
1
0
1
2
5
1
0
3
1
3
1
0
3
0
1
1
0
0
1
1
1
0
1
2
1
0
0
1
4
2
1
0
2
0
1
0
0
3
4
1
0
2
2
1
0
1
2
1
1
0
2
2
0
2
1
2
1
2
1
1
0
2
0
0
0
3
3
1
1
2
2
1
0
4
6
2
0
2
0
0
0
5
1
1
1
0
0
0
0
1
13
0
1
0
1
1
1
1
1
0
3
11
4
0
4
1
0
0
1
1
2
0
0
3
1
1
0
0
4
0
1
3
0
3
2
5
3
1
2
2
1
0
0
0
2
2
0
2
1
15
0
0
1
0
0
1
2
1
3
2
0
1
2
3
1
0
0
2
7
3
0
0
1
0
7
2
2
2
1
3
1
0
0
0
1
0
1
6
3
0
0
0
2
0
3
1
1
1
0
2
2
3
0
6
0
0
2
2
3
1
0
1
2
0
2
2
3
2
1
2
1
1
1
0
0
2
4
1
0
1
0
0
0
2
3
2
3
1
1
2
1
1
0
1
2
0
1
3
0
1
1
0
1
0
2
2
1
1
2
0
5
0
0
1
1
0
1
0
0
0
0
0
5
0
0
0
1
0
0
4
4
4
0
2
0
2
1
0
1
0
2
1
0
3
1
3
1
2
1
2
6
2
2
1
8
0
0
0
1
0
0
3
0
2
2
0
0
2
0
0
2
0
0
0
2
0
2
0
1
1
0
1
2
1
0
2
5
0
0
1
0
1
1
2
1
0
1
1
3
0
0
2
4
1
1
0
2
0
12
0
1
0
2
0
0
1
1
1
3
1
1
2
1
1
1
4
1
2
5
0
0
0
0
1
6
2
0
1
1
3
1
1
0
4
0
0
1
0
1
1
0
2
1
5
0
0
1
2
1
0
2
5
0
2
0
3
1
0
3
2
2
0
3
0
1
1
0
1
0
1
2
1
3
3
1
1
0
0
4
0
4
1
0
4
2
0
0
5
1
0
1
0
0
2
0
2
1
4
10
1
1
0
2
6
1
0
1
1
1
2
1
3
2
2
1
2
0
2
0
1
2
1
8
0
0
1
1
1
0
1
1
2
0
2
2
3
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
1
0
0
1
0
1
0
1
2
1
3
2
2
3
2
0
0
1
2
0
2
3
0
0
1
0
1
1
0
1
1
2
2
0
0
1
2
0
1
0
0
1
0
0
2
1
0
2
1
1
1
1
2
0
1
1
1
0
4
2
0
0
1
2
1
1
0
0
0
2
1
9
0
0
0
0
6
2
0
0
3
1
1
2
5
1
1
2
3
0
5
1
0
1
0
1
1
1
3
0
0
2
1
1
0
1
3
1
2
1
0
0
1
0
0
2
0
0
0
3
1
1
2
1
3
1
0
2
1
1
1
2
2
0
2
2
0
1
6
0
2
1
2
0
0
1
0
1
2
0
2
1
2
0
4
1
1
0
1
0
1
1
2
0
0
2
2
3
2
1
2
2
1
1
2
0
1
0
1
3
1
2
3
2
1
2
0
0
1
4
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
10
2
0
3
0
1
0
3
1
2
3
1
2
0
2
1
0
0
1
1
1
2
3
1
3
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
2
0
1
0
7
2
0
1
1
1
1
3
4
2
0
2
2
2
1
2
0
3
1
3
2
2
1
2
1
0
1
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
0
2
1
2
0
2
0
2
1
0
0
15
1
1
1
1
1
2
4
4
2
1
1
1
0
1
3
0
0
1
1
1
4
0
0
1
2
1
1
1
0
0
1
6
0
2
2
0
2
3
0
1
1
2
4
0
3
0
2
1
1
2
0
1
2
1
0
0
0
0
1
0
1
2
0
0
2
1
1
2
0
2
1
2
1
5
1
2
1
1
0
2
2
1
2
2
1
0
7
0
0
4
0
0
1
1
0
0
1
0
2
1
0
0
0
2
0
2
0
7
4
0
3
1
1
0
2
0
0
0
0
1
0
0
3
0
2
1
1
1
0
1
2
3
9
3
4
1
1
0
2
1
0
2
0
5
0
2
0
3
0
1
0
2
1
5
2
1
1
2
0
3
3
0
1
3
2
17
1
5
0
1
1
0
0
1
0
2
0
4
1
2
0
1
1
0
2
0
0
2
2
0
1
1
1
1
0
2
1
4
1
4
2
3
2
2
0
3
0
1
1
2
0
0
0
0
2
1
0
4
4
0
1
0
1
2
0
1
1
0
1
0
1
5
0
0
0
4
1
4
1
0
2
0
0
1
1
1
2
1
5
0
1
2
1
3
2
2
2
2
0
0
0
1
9
0
2
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
3
2
0
1
1
0
3
0
2
2
2
1
1
0
1
0
7
0
0
1
1
1
2
1
0
0
2
6
0
1
1
1
4
1
2
1
1
0
1
0
0
3
0
1
3
0
1
0
5
1
7
1
3
1
0
1
0
8
2
1
1
2
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
1
1
5
1
0
9
0
1
1
1
3
1
0
0
1
1
2
3
1
2
5
5
2
1
0
3
12
1
0
0
1
0
1
0
5
1
0
2
1
1
2
1
1
1
0
0
2
1
1
0
2
1
2
1
2
1
2
0
2
0
0
1
0
1
1
6
1
0
0
4
2
0
0
1
1
2
1
2
1
1
1
0
2
1
0
1
2
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
2
0
2
2
2
0
1
1
0
1
1
0
0
0
0
0
2
3
0
2
1
1
0
0
0
2
1
0
1
1
2
1
3
1
1
0
0
0
2
0
2
2
0
0
4
0
0
1
0
0
0
2
1
1
0
1
1
6
0
1
3
1
0
1
1
1
2
4
1
1
1
2
0
2
0
0
4
0
1
0
1
1
2
0
1
2
0
1
1
0
0
0
1
2
0
1
0
2
5
0
8
0
1
0
11
1
7
0
0
1
0
1
2
2
2
0
2
1
1
2
2
0
2
1
1
3
1
1
2
1
0
0
7
1
0
1
0
7
1
8
1
1
0
1
1
0
1
11
0
1
6
2
5
1
1
1
0
0
0
0
0
1
2
2
1
0
1
3
0
3
0
1
0
1
0
0
0
3
2
1
4
2
2
1
2
1
0
2
0
2
0
0
2
1
0
0
0
1
1
1
2
0
1
0
2
2
2
1
3
0
5
3
2
0
0
0
0
1
1
1
0
0
7
0
0
2
2
0
0
0
3
2
1
1
0
0
0
2
0
0
1
1
3
0
1
1
0
0
4
1
0
5
0
1
2
1
0
1
1
0
2
0
0
1
1
2
0
1
1
2
0
4
0
0
0
7
1
0
0
2
2
2
2
1
0
0
0
0
3
0
2
0
2
0
0
3
1
1
1
2
0
3
3
3
7
1
10
0
0
0
0
1
1
3
2
1
0
1
2
3
0
1
1
0
0
1
1
0
1
3
1
1
2
1
0
0
4
0
0
1
4
2
6
2
0
1
0
0
2
0
3
3
0
4
1
1
1
1
1
2
3
0
0
1
1
3
2
0
3
1
1
1
0
3
0
0
0
1
0
3
2
1
0
1
0
1
1
7
2
1
0
0
1
4
1
0
2
0
1
1
1
0
2
2
3
3
1
0
0
2
1
3
1
1
0
0
0
2
2
1
2
0
1
2
2
2
4
0
1
1
0
0
6
2
1
2
2
0
0
0
2
2
0
1
0
2
2
0
0
1
1
2
7
3
1
6
4
3
0
3
1
2
0
1
0
2
0
2
1
1
0
5
0
3
1
1
1
1
3
2
2
0
0
2
0
3
3
1
0
3
0
4
0
3
1
0
4
1
0
2
1
0
3
0
2
1
2
3
1
1
0
2
3
1
1
1
0
0
2
1
1
0
1
2
0
2
2
1
0
0
0
3
1
2
2
0
0
0
0
1
1
4
3
1
1
0
1
0
2
1
2
1
0
0
2
1
0
2
0
1
1
2
2
2
2
3
1
0
4
1
2
1
1
1
0
0
2
1
0
2
1
1
0
0
0
1
1
1
0
0
3
0
1
0
2
1
1
0
0
1
1
1
0
1
1
3
1
1
0
2
0
1
2
2
1
0
0
1
2
0
0
3
0
2
1
0
1
0
1
0
0
1
0
5
0
0
2
1
12
4
0
1
0
2
1
0
1
1
0
0
0
1
2
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
0
1
1
4
1
1
1
3
0
2
0
1
0
1
1
1
2
3
1
0
2
2
3
1
1
2
1
0
0
1
1
2
2
3
2
1
0
0
1
0
1
1
4
0
1
2
0
0
1
1
1
0
0
0
2
0
1
2
2
2
0
2
1
0
2
1
0
1
4
0
2
0
1
0
1
0
0
0
0
0
0
1
6
3
2
2
1
1
1
0
0
2
1
2
2
0
0
1
1
1
0
0
2
0
0
0
1
2
4
0
2
1
12
0
1
1
1
1
3
3
1
0
1
2
0
0
1
1
0
1
0
1
0
6
0
1
0
2
1
1
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
1
3
2
2
10
0
1
3
0
1
3
2
0
0
1
0
0
1
2
3
2
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
2
1
2
0
0
0
1
2
3
1
0
0
1
1
0
0
1
3
1
2
0
3
6
0
2
1
2
0
0
2
2
0
0
1
0
1
0
0
2
1
12
2
0
1
0
1
1
0
0
1
2
1
4
2
1
2
1
0
2
2
1
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
4
1
1
3
0
0
0
0
0
1
6
8
6
0
1
2
1
2
0
3
3
1
0
1
0
2
1
0
2
2
0
1
3
1
1
0
0
0
1
3
1
1
2
1
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
2
0
0
1
2
3
1
1
1
1
0
1
1
0
0
2
0
2
4
0
2
0
2
2
0
0
1
0
0
1
1
2
0
2
1
3
0
0
0
0
0
1
1
1
0
3
0
0
1
1
3
0
0
1
2
0
3
0
1
2
1
1
0
1
2
1
2
3
1
0
1
0
0
2
4
0
1
1
0
0
2
0
6
1
2
0
0
0
0
0
7
2
2
0
2
1
1
0
1
2
2
1
0
1
4
0
2
3
2
0
0
1
1
2
2
0
2
0
0
4
1
1
1
1
7
2
0
1
0
1
0
1
0
1
1
0
2
2
0
2
0
2
2
1
0
2
1
0
2
0
1
0
1
3
2
2
1
1
2
5
0
2
0
0
1
0
1
1
2
0
0
0
3
0
5
1
5
2
0
1
0
0
2
1
0
0
1
0
0
4
0
0
11
0
0
0
1
1
1
4
0
2
3
2
0
1
2
0
1
3
4
1
0
0
1
1
0
0
0
2
1
2
1
1
0
1
2
3
3
1
1
2
0
1
0
0
10
0
0
2
1
0
1
1
3
0
0
3
1
7
0
0
0
2
7
1
5
2
6
1
0
0
0
0
2
1
1
2
1
1
1
3
0
0
0
2
2
2
1
4
1
1
0
0
0
2
2
3
1
0
0
1
0
1
0
1
2
3
0
2
0
0
1
1
1
6
4
1
1
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
0
2
1
1
0
2
1
0
3
1
1
3
0
0
0
1
2
0
0
1
1
0
1
1
0
1
0
2
5
0
1
0
0
1
3
0
0
0
1
2
1
2
1
0
1
5
0
0
0
0
1
0
1
0
1
8
0
3
2
0
0
1
1
0
1
3
0
1
0
1
2
1
0
0
1
1
1
0
1
0
2
1
1
1
1
2
0
0
1
1
1
1
5
0
1
0
4
0
1
1
0
1
1
2
0
1
0
2
1
0
2
0
4
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
1
1
2
0
0
0
1
2
0
1
1
1
2
1
1
1
1
0
0
1
2
0
5
1
5
0
0
0
2
2
1
1
1
0
0
2
0
1
0
1
0
1
0
2
1
0
0
2
0
1
1
2
0
1
0
2
0
1
0
1
3
2
1
2
0
0
7
1
0
1
3
0
0
0
1
2
2
1
2
2
1
0
0
0
0
0
1
1
2
0
0
1
0
3
2
0
0
1
0
1
6
0
0
3
0
1
1
0
1
1
2
0
5
2
1
2
0
1
1
0
1
2
1
0
1
1
0
2
1
1
1
2
0
3
1
1
4
1
0
1
1
1
0
0
2
1
1
1
0
1
14
0
1
0
2
9
0
0
2
0
1
0
2
3
1
0
0
4
2
2
0
0
1
0
1
0
3
0
1
3
1
0
0
2
0
1
0
2
0
1
2
1
0
1
1
0
2
1
1
0
1
0
0
2
1
1
1
1
3
3
0
8
8
2
1
1
9
2
3
0
0
1
0
0
0
1
2
1
3
0
1
1
2
1
2
1
1
2
0
1
1
3
0
1
1
2
0
1
0
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
1
0
1
1
0
3
1
4
2
0
1
0
1
2
0
0
1
2
0
0
0
1
2
0
0
3
1
2
10
0
1
4
2
10
0
1
0
1
1
0
5
1
3
1
0
3
2
1
0
1
0
1
1
3
0
2
1
1
0
2
1
10
1
1
1
0
2
0
1
0
0
1
0
0
1
0
4
0
0
1
0
0
6
1
3
0
1
0
2
0
1
0
1
1
0
2
0
2
0
1
0
1
0
0
0
1
1
3
0
0
1
0
2
1
0
0
0
8
1
2
3
1
2
1
0
1
0
2
2
0
1
0
1
0
2
0
1
1
4
1
3
0
0
2
2
0
1
1
3
0
1
2
1
1
3
0
3
5
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
2
1
1
1
0
1
1
1
0
0
1
2
3
0
2
2
0
2
3
1
1
2
3
1
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
4
0
1
0
1
1
1
1
0
2
1
0
1
1
1
2
2
1
0
4
2
1
0
0
2
1
0
1
0
0
2
1
0
5
0
1
5
1
1
1
12
2
1
1
0
1
0
1
1
3
0
0
4
0
1
0
0
1
0
0
0
0
0
4
0
0
2
1
0
3
2
0
1
0
1
1
2
1
2
1
4
2
3
0
0
1
0
0
2
0
0
0
0
0
1
5
0
1
2
1
1
2
3
1
2
1
1
2
1
5
0
0
1
0
2
1
1
0
0
4
0
1
0
1
0
1
0
0
0
0
2
3
1
0
0
2
2
1
0
0
0
1
1
0
0
1
1
0
0
3
1
1
0
0
2
0
2
0
2
1
0
0
2
1
5
1
0
1
2
0
0
0
2
1
1
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
9
1
1
1
0
3
2
2
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
2
5
8
1
0
3
0
0
1
1
3
0
2
0
0
0
1
15
1
2
0
0
6
5
3
0
4
1
0
1
1
1
2
1
1
2
1
6
0
2
0
0
0
2
1
3
1
2
1
1
1
2
1
0
0
1
1
0
2
2
0
2
0
0
1
5
0
1
1
1
2
1
1
0
0
0
0
1
1
0
1
2
0
0
3
0
2
0
2
1
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
1
0
9
2
0
1
1
7
0
1
4
3
2
2
2
0
6
0
6
0
1
0
0
0
3
1
1
2
2
1
1
0
2
3
0
0
0
1
0
2
2
1
1
1
0
0
0
1
0
1
0
0
6
1
3
1
1
1
0
1
1
0
1
3
4
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
1
1
1
1
0
0
1
0
2
1
0
2
0
0
0
1
1
1
1
2
1
0
2
14
1
2
1
3
0
0
0
0
0
1
2
0
1
2
2
1
2
0
1
1
1
0
0
0
0
0
6
2
0
0
3
2
2
0
4
1
1
1
1
1
2
1
1
0
2
0
1
0
1
1
1
0
1
2
0
1
1
1
0
2
2
2
0
0
1
0
0
1
0
1
2
1
4
0
0
2
7
1
3
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
1
1
6
0
1
0
0
0
1
1
1
1
2
6
2
1
2
1
2
1
1
0
0
7
0
1
2
1
0
2
1
3
0
0
0
2
0
0
4
1
0
0
5
1
0
1
2
0
0
0
0
1
0
1
0
0
3
0
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
1
0
0
1
0
2
0
1
1
0
0
2
2
0
1
1
1
0
0
1
1
0
2
0
2
0
0
2
2
0
2
1
0
0
1
1
1
9
0
0
0
1
0
1
0
0
0
2
0
4
2
1
3
0
0
0
0
0
0
0
0
0
3
1
3
3
1
2
2
0
0
0
0
3
1
0
0
0
2
6
0
1
4
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
1
2
4
2
1
2
0
1
0
0
0
9
0
1
1
1
4
0
1
1
0
8
1
1
0
0
1
2
1
0
0
1
0
1
0
1
4
1
0
1
0
0
1
1
2
1
1
1
2
1
0
1
0
1
3
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
8
0
0
1
1
0
1
1
1
0
1
0
0
0
2
2
1
0
0
1
8
0
0
1
9
0
1
0
0
1
0
10
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
9
2
2
1
9
1
1
1
1
0
3
0
1
0
1
1
1
1
0
2
4
0
6
2
0
0
0
3
2
2
3
1
1
4
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
2
1
1
0
1
2
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
4
2
0
1
1
2
0
0
0
2
5
0
2
0
1
3
0
0
2
0
4
0
0
0
4
4
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
2
1
1
0
0
1
1
2
0
0
1
0
1
3
0
2
1
0
1
9
1
3
1
0
3
0
1
1
1
2
0
0
0
0
1
1
0
1
1
0
0
5
2
0
0
2
4
2
1
1
0
0
0
0
1
0
0
3
0
4
0
2
0
0
0
1
2
0
5
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
7
1
1
0
0
2
0
1
0
1
0
1
0
0
1
1
8
0
0
6
0
1
0
1
1
1
13
2
1
0
0
0
3
0
4
0
1
1
0
2
1
1
0
1
2
0
6
0
0
2
4
1
1
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
5
1
2
1
1
2
0
0
1
3
1
2
0
2
1
1
0
2
1
2
7
0
1
1
2
1
0
4
0
4
1
0
1
2
3
1
0
0
0
1
5
1
1
1
1
1
7
1
2
0
3
1
0
2
0
0
0
1
0
1
2
0
0
4
0
1
0
0
3
2
3
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
2
2
1
1
0
1
2
0
0
0
0
0
0
3
1
2
1
2
0
4
0
0
1
0
4
1
1
1
0
2
0
0
0
0
0
3
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
3
0
3
2
4
1
0
1
0
1
3
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
14
0
1
2
1
2
1
2
2
0
1
2
1
0
0
1
1
2
1
0
0
1
5
0
2
3
0
2
1
2
1
0
7
1
2
0
0
2
1
3
0
0
0
0
2
6
0
0
0
2
0
2
1
0
0
1
2
0
2
0
2
12
2
0
1
1
0
0
0
1
1
0
1
1
1
2
6
1
0
3
2
0
0
0
0
0
3
2
4
3
1
0
1
0
1
1
1
2
1
1
0
2
0
0
2
1
1
0
1
2
1
2
0
2
0
0
0
1
1
0
4
2
0
1
0
2
0
0
1
1
1
8
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
2
1
1
0
1
3
1
0
0
2
2
1
0
1
0
0
0
1
1
3
1
1
2
0
2
1
1
1
0
0
3
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
2
3
1
0
0
2
0
0
0
2
2
2
0
1
0
12
2
0
0
1
0
1
0
2
1
0
0
0
2
0
2
1
0
0
2
0
2
2
2
0
0
0
2
1
0
1
0
3
1
5
0
1
16
4
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
6
1
2
1
0
0
2
0
0
2
0
0
0
1
7
1
5
1
0
1
1
2
1
1
0
0
1
1
2
0
0
3
1
1
1
2
1
0
1
0
10
3
2
3
1
0
1
0
2
0
0
1
1
1
2
2
0
0
1
0
0
0
0
1
1
2
1
3
3
0
0
0
1
1
0
0
7
0
0
1
1
0
2
0
1
0
1
1
0
1
2
1
1
3
1
0
0
2
0
2
1
1
0
0
1
2
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
3
1
0
1
2
0
0
1
2
0
0
1
0
1
2
0
0
1
0
1
0
1
1
0
1
1
3
1
1
5
0
0
2
1
0
0
0
0
1
1
2
2
1
7
3
0
1
2
0
2
1
1
0
2
1
1
0
0
3
0
1
3
0
0
0
0
1
3
1
0
3
2
0
1
0
0
0
1
4
0
1
0
4
2
0
0
0
5
1
4
0
2
0
3
2
1
0
3
1
1
2
0
1
1
1
3
2
0
1
1
0
0
2
0
1
0
0
0
3
7
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
4
1
0
1
1
2
0
2
2
0
1
4
3
0
2
2
1
2
1
3
1
0
1
0
1
2
1
1
1
1
0
2
0
0
1
0
1
1
1
1
1
1
0
0
2
0
6
1
0
1
1
0
1
0
0
1
7
1
1
0
1
3
0
0
15
0
0
0
1
1
1
0
0
0
2
0
0
1
0
4
0
2
0
13
2
2
0
0
4
0
0
1
0
0
0
0
1
0
2
1
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
3
0
2
0
2
3
1
3
0
1
1
1
0
0
0
3
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
2
4
0
6
2
0
2
1
0
6
1
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
3
1
0
0
0
1
4
2
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
4
1
0
1
1
1
2
0
1
1
2
0
1
0
0
1
2
0
1
1
1
2
1
1
0
2
0
0
1
0
0
3
0
1
0
1
4
3
1
7
0
1
1
0
0
1
6
1
0
1
0
0
1
0
2
1
0
0
1
5
2
0
1
2
1
1
0
0
0
3
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
4
2
3
4
1
0
1
0
4
2
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
4
1
0
0
1
1
3
0
2
1
0
0
1
0
0
0
3
3
1
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
4
0
2
0
0
4
0
2
2
2
0
0
1
2
0
1
1
2
3
0
0
0
2
1
0
2
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
1
0
3
0
0
3
0
0
0
2
3
0
1
1
1
0
1
0
2
1
1
0
3
0
0
1
2
2
1
1
1
1
1
2
2
2
0
0
1
3
1
1
2
1
2
1
0
1
0
0
3
2
0
0
1
0
0
11
2
0
0
0
1
0
4
0
1
1
0
0
0
3
0
1
0
0
0
0
2
1
1
0
1
1
1
2
2
4
0
2
2
0
1
0
1
1
0
4
1
0
0
0
0
1
1
0
0
1
3
1
0
2
1
1
8
1
0
1
1
6
2
0
0
0
1
0
1
1
1
1
1
0
0
0
8
2
0
0
0
0
0
0
0
7
1
2
0
1
0
0
0
1
10
1
4
0
2
0
1
1
0
4
2
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
1
4
1
2
0
0
0
0
1
0
0
2
0
1
1
0
3
0
0
1
0
2
1
0
3
1
0
0
1
0
0
0
2
2
3
0
2
1
1
0
1
3
1
0
1
0
2
1
1
0
0
2
2
2
0
0
1
3
1
1
1
1
0
1
1
0
0
1
0
11
1
1
2
2
0
1
1
4
1
0
0
0
1
2
1
6
1
0
1
0
0
0
0
6
1
1
0
0
2
0
0
4
1
1
1
0
1
1
11
0
2
2
0
1
1
1
1
1
1
1
1
1
4
5
0
0
3
6
0
3
0
0
2
0
0
5
0
1
1
2
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
2
1
7
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
1
3
0
0
0
0
2
0
3
0
1
0
3
1
1
0
1
0
1
1
2
3
0
2
3
0
1
0
1
1
0
0
1
0
0
0
1
11
1
7
1
3
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
5
4
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
2
1
0
1
1
0
4
0
2
0
2
1
1
4
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
3
0
0
3
0
0
4
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
0
2
1
0
1
0
2
3
1
1
2
3
1
1
0
1
1
0
0
8
1
0
0
1
0
0
2
2
1
0
0
0
0
4
0
0
0
0
4
1
1
11
1
1
0
1
8
0
0
3
1
0
1
7
1
0
0
1
0
0
8
3
0
2
0
0
5
3
1
0
0
2
3
0
0
6
0
0
0
0
0
2
1
10
0
1
1
1
1
0
1
0
0
1
0
0
1
0
2
1
0
0
4
0
2
2
1
1
2
0
3
2
0
1
2
11
0
1
1
0
1
1
2
0
0
6
0
0
2
0
2
1
1
2
1
2
1
0
0
0
1
1
1
3
1
1
2
2
2
2
2
0
0
0
1
1
0
2
0
0
3
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
2
16
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
3
2
1
1
0
2
0
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
0
1
1
0
2
1
5
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
2
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
3
2
0
0
1
1
0
0
1
4
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
0
0
3
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
1
0
2
0
0
1
0
1
1
2
1
0
0
2
2
1
1
1
0
1
0
4
1
0
0
2
0
7
1
1
1
0
0
1
0
0
7
0
1
0
7
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
4
1
0
1
0
0
3
2
0
6
1
0
2
0
1
1
0
0
0
1
0
0
2
1
1
2
0
2
0
1
0
3
0
1
0
4
2
0
8
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
5
0
2
0
1
1
1
1
3
1
1
0
1
0
4
0
0
0
0
1
1
0
1
0
1
1
0
1
4
0
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
1
0
0
1
2
2
4
1
1
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
2
2
1
1
0
1
0
0
0
3
0
1
0
1
8
2
1
2
0
0
0
0
0
2
3
3
2
1
0
2
1
0
1
1
1
2
1
1
3
0
0
0
0
0
1
6
1
0
0
0
0
2
0
0
0
1
1
2
4
1
0
1
1
0
1
0
1
1
13
5
0
2
1
3
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
2
0
1
2
1
1
1
1
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
2
1
1
0
0
0
0
1
0
2
0
0
8
1
0
2
0
2
2
0
1
1
0
0
3
1
1
0
0
0
1
2
2
1
0
0
0
0
1
1
1
1
2
1
1
1
0
0
5
1
0
0
0
1
1
1
2
1
2
0
0
2
1
0
1
4
2
0
0
1
0
2
0
8
0
2
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
8
2
4
0
1
1
1
6
0
0
0
0
2
4
0
1
0
1
0
5
1
0
1
4
0
0
2
0
1
1
2
0
1
0
0
2
3
1
0
1
1
3
1
2
0
4
0
0
0
0
0
1
1
1
1
0
1
1
0
6
0
0
3
1
3
0
1
0
10
2
0
0
3
7
0
1
1
1
1
3
4
1
0
0
1
1
1
0
1
1
3
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
3
1
0
0
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
0
8
1
1
0
0
0
0
0
0
1
0
0
3
0
2
1
0
1
1
0
0
0
2
1
3
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
1
2
0
0
1
0
2
2
0
0
0
0
0
1
1
1
3
4
0
1
2
0
0
1
3
0
1
1
1
0
0
0
0
2
1
1
0
0
1
1
0
1
2
0
1
0
0
3
0
2
0
0
0
1
1
2
1
1
3
1
5
0
5
0
4
1
0
0
2
0
0
0
1
1
0
1
1
1
1
2
2
1
1
0
0
0
1
0
1
2
1
1
0
1
3
0
0
6
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
1
0
1
0
0
2
0
3
0
3
0
1
1
1
1
2
0
0
3
2
0
0
0
2
2
2
1
1
1
2
1
2
0
0
1
1
0
0
3
2
0
1
0
0
0
1
1
0
1
0
2
1
2
0
0
1
0
1
1
0
3
0
1
2
1
1
1
0
1
1
0
2
0
2
0
0
1
2
0
0
2
0
2
0
2
0
1
0
0
0
1
0
3
0
1
0
0
1
2
0
1
0
1
2
1
0
1
1
0
2
1
1
0
1
0
2
0
4
1
2
1
1
1
2
0
0
0
2
2
1
0
1
2
0
1
2
0
3
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
4
0
2
2
1
1
0
0
1
1
0
1
1
0
0
2
0
2
1
1
2
0
3
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
4
0
0
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
0
1
2
2
1
1
2
1
1
1
0
1
0
2
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
3
0
0
1
0
0
0
1
0
1
0
1
1
1
4
3
3
1
2
2
2
0
1
0
6
1
1
0
0
0
1
1
3
1
1
0
1
0
1
2
2
4
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
3
1
1
0
0
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
8
2
1
3
1
0
0
0
1
0
0
1
0
1
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
0
0
0
0
3
0
1
1
1
0
0
0
1
0
0
2
1
0
6
1
0
0
1
0
2
2
1
1
1
1
2
1
0
1
1
0
2
0
0
11
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
2
1
0
1
1
1
2
1
2
0
0
0
1
5
0
0
0
0
1
1
2
4
0
1
1
1
1
0
2
2
1
1
0
1
1
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
3
2
0
0
0
0
1
3
0
1
6
1
0
2
0
1
0
0
0
8
0
2
0
0
1
0
1
0
0
0
3
0
0
4
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
1
1
0
0
3
1
7
0
1
1
0
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
5
0
0
1
1
1
1
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
0
3
0
2
4
0
0
0
2
0
2
1
1
0
1
4
0
0
2
2
0
0
0
0
9
2
0
0
0
0
1
0
0
1
2
1
1
0
0
1
1
0
0
6
3
0
1
2
7
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
3
0
0
1
2
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
1
1
4
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
3
0
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
2
3
2
0
16
6
0
0
2
0
4
3
0
0
0
1
3
1
2
0
1
2
0
1
0
0
1
1
2
1
1
0
0
0
0
1
5
1
1
1
7
0
0
1
1
1
2
6
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
1
0
4
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
1
0
0
2
0
0
0
5
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
3
1
0
0
0
1
0
0
0
1
1
2
5
2
2
1
2
2
5
1
0
0
0
0
0
2
0
3
0
0
2
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
1
1
0
2
0
1
0
4
1
1
0
1
1
0
2
0
0
1
0
1
2
0
3
2
0
0
1
2
1
0
0
1
5
2
0
7
2
2
1
2
0
0
0
2
0
0
3
7
2
0
1
0
1
1
0
0
1
2
5
1
1
0
0
0
1
2
2
0
1
2
1
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
1
10
2
0
0
1
0
1
1
1
3
0
2
1
0
0
0
1
1
4
2
1
0
1
1
1
2
1
1
1
0
2
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
5
2
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
2
0
0
2
0
1
1
3
0
1
0
14
0
0
0
0
1
3
1
0
0
1
0
3
2
0
1
0
0
1
1
1
3
1
1
1
0
0
2
2
0
0
1
1
0
0
0
2
1
0
2
0
15
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
0
2
0
2
1
1
0
3
0
1
3
1
1
1
0
0
0
1
0
1
2
1
1
0
1
5
1
5
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
3
1
1
0
0
1
3
1
0
0
0
0
0
2
0
1
0
1
1
1
3
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
4
0
0
0
0
3
0
1
0
2
0
0
0
1
1
1
1
0
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
1
2
0
2
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
1
1
0
1
1
0
0
0
2
1
1
3
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
3
0
0
1
1
2
0
0
0
1
0
1
0
0
1
5
2
0
1
1
1
1
1
0
1
0
1
1
3
1
0
1
1
0
0
1
1
0
0
1
0
3
0
0
0
1
1
1
1
1
1
2
1
0
1
0
0
0
2
0
1
1
0
0
10
0
0
0
1
0
2
0
1
7
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
2
1
2
0
4
2
1
0
0
0
1
4
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
1
9
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
0
2
2
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
12
4
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
2
0
2
1
1
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
3
2
0
2
0
0
3
2
5
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
9
0
0
1
1
1
5
0
1
1
0
0
1
1
1
2
0
1
0
0
2
0
6
0
0
0
0
3
10
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
22
1
2
0
1
7
0
3
1
0
1
1
1
3
0
2
2
2
1
0
0
1
6
0
1
0
0
0
0
2
9
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
1
0
3
2
0
0
1
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
1
1
0
0
1
1
2
0
1
1
2
3
0
1
0
0
0
0
1
1
0
1
0
1
1
2
0
1
0
1
0
3
0
0
1
1
1
0
1
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
3
1
1
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
2
9
1
1
1
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
1
0
0
2
6
1
0
0
1
2
0
2
0
0
1
0
1
0
0
1
6
0
3
0
1
0
2
2
0
0
0
1
2
0
3
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
3
0
2
2
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
0
7
0
1
0
1
1
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
0
3
0
2
1
0
1
0
0
0
0
0
1
1
1
2
0
0
6
0
0
1
0
8
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
1
0
2
0
2
0
0
3
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
3
1
0
1
1
2
1
0
0
1
0
1
1
10
0
0
1
0
1
2
1
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
1
1
2
0
0
1
2
0
1
0
2
1
0
0
0
1
2
0
3
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
2
0
0
1
0
2
2
0
1
0
0
0
1
5
0
2
2
0
0
0
1
0
1
1
0
1
0
0
1
0
3
1
0
1
0
0
3
1
2
0
2
1
1
0
5
0
2
2
3
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
2
0
1
1
0
1
1
1
2
2
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
7
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
2
1
1
0
2
0
0
1
1
1
3
0
2
1
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
1
0
0
0
4
0
2
1
1
0
4
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
2
0
3
1
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
0
1
0
0
2
2
2
3
0
0
0
2
1
2
2
0
1
2
0
0
0
0
1
1
0
0
1
3
0
12
0
1
0
1
0
1
1
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
1
2
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
3
0
0
3
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
5
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
7
1
0
1
0
0
1
1
2
1
1
0
1
2
1
1
0
6
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
1
4
0
2
0
1
1
0
1
1
1
0
0
2
0
1
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
16
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
0
1
0
1
4
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
3
1
0
1
1
1
2
1
1
0
5
2
2
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
4
2
0
0
0
1
1
0
1
0
1
1
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
3
0
1
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
4
2
0
2
0
0
0
1
0
3
0
0
1
0
0
0
8
1
0
0
0
1
0
0
0
0
0
0
0
5
1
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
3
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
18
5
1
1
1
0
3
0
3
0
0
0
0
3
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
7
8
0
1
0
0
1
0
0
0
0
0
0
0
0
2
8
0
1
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
4
0
0
0
0
1
3
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
5
1
0
0
1
3
1
3
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
2
0
1
1
1
2
2
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
0
2
1
1
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
0
3
0
0
0
2
0
1
3
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
3
8
1
0
7
0
1
2
1
0
4
2
1
0
2
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
4
0
0
0
3
1
0
0
8
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
1
0
1
0
1
6
2
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
1
2
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
9
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
0
2
0
1
1
9
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
1
1
0
1
0
0
0
7
0
0
1
0
1
1
3
1
0
1
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
1
1
0
1
0
1
0
0
1
0
0
0
4
1
1
2
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
2
0
1
1
1
1
0
0
0
4
0
0
1
0
2
1
0
0
3
2
0
2
1
0
1
1
1
0
1
1
1
0
1
1
2
0
0
0
0
10
0
2
0
0
0
3
0
0
1
1
1
2
1
0
0
0
3
2
0
1
0
1
2
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
1
0
7
2
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
9
1
1
0
0
2
0
0
0
8
0
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
1
2
0
0
0
0
1
2
3
0
3
0
1
0
0
0
0
0
0
2
0
0
0
7
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
1
0
0
1
2
2
0
0
1
0
1
1
0
9
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
1
1
2
0
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
3
0
1
2
0
2
1
1
0
0
0
0
2
0
1
1
1
0
2
1
0
0
2
1
0
0
1
0
1
3
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
2
0
1
2
0
0
0
0
0
7
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
1
0
1
1
0
3
1
1
2
2
1
0
1
0
2
0
1
2
1
0
1
0
0
1
1
0
1
0
2
2
1
1
0
0
1
2
0
1
2
1
1
0
1
1
0
0
1
1
0
0
1
0
3
0
2
2
3
0
0
0
0
3
4
1
0
19
1
3
1
5
0
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
1
0
0
2
1
1
3
0
0
0
1
0
1
1
1
1
1
2
1
0
0
0
0
0
2
0
1
2
3
0
0
0
1
0
0
0
0
1
1
3
1
0
0
0
2
1
0
3
1
1
0
1
0
0
1
0
1
0
4
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
5
1
4
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
4
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
2
2
1
0
0
1
1
0
0
9
1
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
4
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
13
0
3
1
0
1
1
0
1
1
0
0
1
2
2
0
0
0
0
6
1
1
0
4
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
7
1
1
2
2
0
2
1
1
0
1
0
1
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
1
1
0
0
0
3
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
1
2
0
0
5
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
1
1
7
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
3
0
0
1
2
1
1
0
2
4
0
1
1
2
0
1
1
1
0
5
1
1
0
0
0
3
0
0
0
1
2
1
1
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
3
0
0
0
1
16
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
5
0
0
1
1
1
0
2
2
1
0
0
0
2
0
1
3
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
1
3
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
0
0
0
0
0
1
0
4
1
0
0
1
1
2
0
1
0
0
0
9
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
4
1
1
0
0
1
0
1
2
9
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
2
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
9
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
6
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
7
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
1
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
3
1
1
1
1
0
3
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
2
0
8
1
1
1
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
1
2
0
0
3
0
0
0
3
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
1
2
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
5
1
0
1
0
0
0
0
1
1
4
1
6
1
1
0
1
3
2
1
7
0
4
2
1
0
2
1
0
0
3
0
0
0
0
2
2
0
1
1
0
1
0
1
1
0
2
2
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
4
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
5
1
0
0
1
1
1
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
3
0
2
0
0
0
0
0
2
0
1
0
2
0
5
4
0
1
1
1
0
0
7
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
3
3
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
5
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
3
0
0
0
0
6
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
2
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
1
0
1
1
2
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
1
0
1
1
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
6
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
2
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
4
1
1
0
0
1
0
0
2
6
0
3
1
2
1
1
0
0
0
1
0
0
0
0
1
2
3
2
4
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
3
1
1
0
0
1
0
2
1
0
1
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
2
7
0
1
0
1
5
0
3
1
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
8
1
0
1
0
1
2
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
4
0
0
0
0
0
1
1
1
2
1
1
1
0
1
0
2
1
1
2
0
0
1
0
1
2
3
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
7
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
3
1
3
0
0
0
1
0
0
0
0
0
0
10
1
0
14
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
3
2
0
2
1
1
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
2
0
2
3
1
0
1
2
6
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
3
3
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
11
0
0
2
0
2
0
0
1
1
9
0
0
4
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
3
2
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
1
0
2
1
0
5
0
1
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
3
1
0
0
1
1
1
1
0
0
0
0
0
0
3
1
1
2
0
0
0
0
5
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
6
1
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
1
1
2
1
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
2
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
8
0
0
0
0
0
0
1
0
1
2
2
1
1
0
1
1
1
2
2
0
1
2
1
0
1
1
1
1
0
2
1
0
2
0
4
1
0
0
1
0
0
0
1
1
1
13
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
3
1
0
0
0
1
0
0
1
1
1
1
2
0
0
0
1
1
1
0
3
2
0
1
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
2
4
0
0
0
1
1
2
1
0
0
1
4
1
1
1
0
0
0
0
3
0
1
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
4
0
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
5
1
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
1
1
7
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
5
1
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
12
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
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
1
0
1
2
0
1
0
8
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
3
1
0
0
1
5
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
5
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
3
1
4
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
2
0
3
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
3
0
3
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
2
5
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
8
12
0
1
1
0
0
0
1
11
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
9
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
3
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
3
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
0
1
2
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
3
0
0
2
0
0
0
2
1
0
1
2
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
7
1
1
0
0
1
0
0
2
2
0
1
3
4
1
1
12
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
6
1
0
2
1
0
1
0
0
1
0
1
0
4
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
2
1
0
0
1
1
1
0
0
2
1
0
0
1
1
1
0
1
1
0
0
0
2
1
2
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
1
1
1
0
15
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
13
1
2
0
1
0
0
0
0
0
0
0
3
0
0
4
0
0
0
1
2
2
0
1
0
0
2
0
0
0
7
0
0
2
0
0
0
0
1
3
0
1
0
0
4
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
8
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
2
0
0
0
4
0
0
0
1
1
1
0
0
1
1
1
4
0
0
1
1
0
0
1
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
13
0
0
0
1
0
0
0
0
1
1
3
6
0
2
0
0
0
3
0
0
0
1
0
1
1
2
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
8
1
0
2
0
1
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
4
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
2
0
1
1
2
0
1
0
0
0
0
0
2
5
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
3
0
0
6
0
1
4
0
1
0
0
0
0
2
0
0
0
0
1
0
5
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
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
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
1
3
1
1
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
1
2
0
1
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
4
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
2
1
0
1
5
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
8
1
0
0
0
0
1
0
0
1
0
21
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
6
0
0
0
1
0
1
2
0
1
1
0
0
1
2
3
0
1
2
0
0
12
0
0
1
0
0
0
1
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
4
0
1
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
6
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
1
0
1
0
0
7
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
1
6
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
1
2
2
1
2
0
1
2
5
0
1
0
0
0
0
0
0
0
1
0
0
2
0
10
0
1
0
0
1
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
7
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
1
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
1
1
0
1
0
0
2
2
1
1
0
0
2
1
0
0
0
9
1
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
6
0
0
2
0
2
7
0
0
0
1
1
1
0
1
1
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
15
1
0
0
0
0
1
1
0
0
0
0
1
8
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
0
2
0
1
0
0
3
1
2
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
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
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
5
0
1
0
2
2
0
2
0
1
0
7
0
2
1
2
1
0
1
2
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
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
5
3
1
1
0
1
2
0
0
1
0
4
0
0
0
1
2
4
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
4
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
7
1
1
0
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
10
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
4
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
12
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
1
0
1
3
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
1
1
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
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
3
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
7
1
0
0
0
0
0
0
2
0
0
8
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
7
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
1
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
1
0
1
1
0
0
2
1
2
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
0
2
1
3
2
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
4
1
0
1
0
3
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
5
1
1
0
0
1
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
3
0
0
0
2
1
0
0
0
4
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
2
2
1
0
1
0
0
0
1
2
1
0
1
2
0
0
1
1
1
1
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
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
1
0
0
1
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
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
2
0
1
0
1
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
3
1
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
6
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
11
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
5
1
0
0
0
2
0
0
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
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
1
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
6
0
2
1
1
0
0
2
0
5
1
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
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
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
1
0
1
1
2
0
1
0
0
0
1
1
6
0
0
1
1
4
0
0
0
2
1
4
0
1
1
0
0
1
0
1
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
1
0
0
1
0
1
6
0
0
0
0
1
1
1
0
0
0
0
0
1
0
9
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
1
0
8
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
2
1
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
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
12
0
2
1
0
0
1
0
2
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
1
1
4
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
15
1
0
0
3
0
5
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
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
2
0
0
1
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
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
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
4
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
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
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
6
1
0
1
0
1
0
0
5
1
1
0
0
1
0
0
0
0
1
0
0
0
0
8
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
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
1
0
1
0
1
0
0
0
13
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
5
0
0
1
0
0
7
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
3
2
1
9
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
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
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
7
0
0
0
0
0
0
0
0
1
2
0
1
3
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
4
4
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
1
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
1
4
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
1
1
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
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
5
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
1
1
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
16
0
1
0
0
0
1
0
0
1
0
0
0
1
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
1
4
0
0
0
0
3
0
0
0
1
3
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
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
1
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
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
6
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
2
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
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
1
1
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
12
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
2
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
4
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
4
0
1
1
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
3
0
0
1
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
4
0
1
1
0
1
0
0
0
0
5
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
4
0
0
2
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
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
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
1
0
0
0
0
2
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
1
1
2
1
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
0
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
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
6
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
3
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
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
9
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
12
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
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
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
3
0
0
1
0
1
0
0
1
1
0
0
0
1
2
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
2
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
2
0
1
0
0
8
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
4
2
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
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
1
1
0
1
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
0
1
0
1
0
0
1
3
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
4
1
1
0
0
0
0
6
0
1
0
1
0
1
1
1
1
0
0
3
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
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
3
0
1
2
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
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
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
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
6
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
4
1
0
1
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
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
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
3
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
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
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
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
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
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
8
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
16
0
0
1
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
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
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
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
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
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
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
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
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
0
1
4
2
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
3
1
1
0
0
0
1
13
0
0
0
0
0
11
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
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
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
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
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
0
0
0
1
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
3
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
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
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
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
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
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
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
1
4
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
5
0
0
0
1
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
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
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
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
1
0
0
0
1
0
0
0
1
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
7
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
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
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
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
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
1
4
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
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
2
1
13
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
9
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
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
1
0
2
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
5
1
1
0
0
0
2
0
0
3
0
0
1
1
0
1
0
1
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
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
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
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
3
0
8
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
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
1
0
0
2
1
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
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
1
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
3
1
0
1
0
0
0
1
6
1
1
0
1
0
2
1
0
0
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
4
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
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
3
0
1
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
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
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
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
1
0
3
0
0
0
0
1
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
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
5
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
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
1
0
0
0
0
1
0
2
0
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
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
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
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
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
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
1
0
0
0
1
0
1
0
1
0
0
0
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
4
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
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
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
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
1
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
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
0
0
1
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
1
0
0
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
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
1
0
0
0
0
0
1
2
0
0
0
17
0
0
0
0
0
1
0
0
0
1
2
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
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
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
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
5
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
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
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
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
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
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
1
0
0
1
11
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
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
1
1
0
0
0
0
1
0
1
0
1
0
5
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
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
1
1
4
0
2
1
1
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
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
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
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
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
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
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
1
0
0
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
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
1
1
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
0
0
0
0
0
1
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
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
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
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
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
1
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
1
2
3
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
5
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
1
0
1
1
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
0
0
1
0
0
0
1
1
0
3
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
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
1
1
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
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
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
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
0
0
0
0
0
0
0
0
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
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
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
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
1
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
1
0
0
0
1
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
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
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
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
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
1
0
0
0
1
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
0
0
0
1
2
1
0
0
1
1
0
0
3
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
0
1
0
2
0
0
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
1
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
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
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
1
1
1
0
1
0
0
0
0
1
6
0
1
1
0
1
0
0
0
0
1
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
1
0
0
0
0
1
1
0
0
0
0
1
0
7
1
0
0
0
7
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
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
1
0
0
0
0
0
0
0
0
0
0
0
16
1
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
1
0
1
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
4
0
0
0
0
0
0
1
0
0
0
1
1
0
4
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
1
0
0
0
0
0
0
1
1
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
0
0
0
0
1
0
0
0
0
0
0
0
1
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
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
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
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
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
6
1
0
0
1
0
0
1
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
0
0
0
0
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
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
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
5
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
1
1
0
0
1
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
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
2
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
3
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
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
15
0
0
0
3
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
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
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
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
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
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
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
0
0
3
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
1
1
0
0
0
0
0
0
1
1
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
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
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
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
1
1
0
1
1
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
0
1
0
0
0
0
0
0
2
0
1
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
1
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
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
3
1
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
0
1
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
2
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
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
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
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
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
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
6
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
0
0
0
0
0
2
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
4
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
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
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
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
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
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
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
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
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
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
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
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
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
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
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
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
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
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
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
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
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
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
2
0
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
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
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
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
1
0
0
0
0
2
0
0
0
0
0
0
0
2
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
1
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
1
0
0
0
1
0
0
1
1
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
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
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
2
0
1
0
2
1
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
6
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
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
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
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
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
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
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
2
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
1
0
0
0
0
2
0
0
0
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
1
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
0
0
1
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
0
0
0
2
1
0
0
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
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
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
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
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
0
1
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
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
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
1
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
1
0
0
0
3
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
1
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
12
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
1
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
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
1
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
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
1
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
1
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
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
1
0
0
0
1
1
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
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
1
0
0
2
0
1
0
1
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
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
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
1
0
1
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
1
0
0
1
0
1
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
1
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
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
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
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
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
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
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
1
1
1
0
0
1
0
0
0
0
0
0
0
5
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
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
1
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
1
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
0
0
0
1
0
0
0
0
0
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
0
0
0
0
1
0
0
0
0
1
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
1
0
0
1
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
0
0
0
0
0
2
1
0
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
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
0
0
1
0
0
0
0
0
0
0
0
1
0
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
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
0
0
0
0
2
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
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
5
1
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
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
1
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
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
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
4
0
1
0
1
0
0
0
1
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
1
0
1
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
0
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
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
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
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
1
1
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
1
0
0
0
0
5
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
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
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
6
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
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
0
0
0
4
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
1
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
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
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
12
0
0
0
0
0
1
1
0
0
0
1
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
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
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
1
1
0
0
3
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
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
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
1
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
0
0
0
0
1
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
1
0
1
1
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
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
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
1
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
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
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
1
0
0
0
0
0
0
2
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
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
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
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
1
0
0
2
0
0
0
0
0
0
0
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
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
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
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
1
1
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
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
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
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
1
1
1
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
0
0
1
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
1
0
0
0
1
1
0
0
0
0
0
1
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
1
0
0
0
1
7
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
1
0
0
0
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
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
1
2
0
0
0
0
0
1
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
0
0
1
0
1
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
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
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
1
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
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
1
0
0
0
0
0
0
0
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
1
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
3
0
0
0
0
0
0
1
2
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
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
1
0
0
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
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
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
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
3
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
2
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
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
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
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
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
1
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
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
1
0
0
0
0
0
0
0
0
0
3
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
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
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
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
0
0
3
0
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
0
0
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
0
0
0
0
0
0
0
0
0
0
1
0
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
0
0
1
0
0
1
1
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
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
2
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
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
1
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
0
0
0
0
0
7
1
0
0
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
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
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
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
1
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
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
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
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
1
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
13
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
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
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
0
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
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
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
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
1
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
0
0
0
0
0
0
0
0
1
2
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
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
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
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
1
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
1
0
0
1
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
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
1
0
0
0
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
1
0
1
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
0
0
0
0
0
0
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
1
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
1
0
0
0
0
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
3
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
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
5
0
1
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
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
0
0
0
0
0
0
0
0
0
0
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
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
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
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
7
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
1
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
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
1
0
0
0
0
0
0
0
0
1
0
0
1
5
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
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
0
0
0
0
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
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
1
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
1
0
0
0
1
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
2
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
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
3
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
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
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
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
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
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
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
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
6
0
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
1
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
1
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
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
2
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
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
1
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
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
1
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
2
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
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
1
0
0
0
12
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
1
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
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
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
0
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
1
0
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
0
0
0
1
0
0
0
0
0
2
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
0
0
0
0
0
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
1
0
0
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
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
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
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
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
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
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
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
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
0
0
1
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
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
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
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
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
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
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
1
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
1
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
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
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
1
0
0
1
0
0
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
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
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
0
0
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
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
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
1
4
0
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
0
0
0
0
0
0
0
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
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
3
0
0
0
0
2
0
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
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
4
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
1
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
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
0
0
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
0
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
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
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
2
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
0
0
1
0
0
0
1
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
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
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
1
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
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
0
0
0
0
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
1
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
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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
15
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
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
6
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
1
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
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
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
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
1
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
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
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
4
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
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
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
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
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
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
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
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
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
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
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
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
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
1
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
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
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
8
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
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
0
0
2
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
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
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
1
0
0
0
0
0
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
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
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1