52
36
29
31
44
40
29
28
42
31
41
47
38
40
27
52
27
33
25
34
33
24
34
22
38
30
25
50
28
26
19
20
28
22
23
22
19
33
34
13
21
29
22
26
25
27
26
39
28
32
19
29
28
37
24
32
26
19
21
16
21
30
23
24
23
16
16
31
16
17
18
20
23
22
18
19
26
29
11
24
24
31
19
13
22
26
22
22
21
25
17
18
28
20
12
42
19
20
19
18
27
40
21
20
29
19
11
21
18
20
15
30
23
45
14
31
23
24
15
18
17
17
18
23
17
8
24
15
21
15
9
22
23
23
28
16
26
16
14
17
15
22
15
12
25
13
20
15
19
21
26
16
17
15
10
22
13
16
12
13
28
20
22
12
9
15
33
27
15
18
20
19
12
16
19
20
14
14
28
11
40
18
13
25
12
18
21
18
11
19
8
16
21
17
11
22
11
22
10
12
43
38
18
29
12
17
19
22
14
12
19
12
10
20
19
11
11
26
11
9
13
8
22
16
13
15
19
8
12
10
12
14
8
19
16
19
10
12
11
14
14
12
9
18
16
23
10
29
20
12
13
18
8
11
8
9
15
28
6
16
6
11
11
17
14
17
19
22
21
16
12
12
12
12
7
10
17
8
8
26
10
13
8
25
11
11
13
13
16
6
13
6
10
11
24
9
19
13
16
32
14
14
12
6
16
13
19
8
24
11
20
14
9
13
24
10
12
12
17
13
15
8
10
18
7
10
13
9
9
19
22
11
10
14
20
8
8
11
31
10
4
11
8
8
7
7
8
6
12
8
16
8
11
9
11
7
4
15
9
13
17
14
24
5
28
12
13
24
6
9
9
7
13
14
5
13
16
10
7
8
12
12
18
5
12
8
11
18
12
9
18
13
20
16
7
8
14
10
12
2
10
14
14
14
5
15
10
7
10
12
16
13
10
3
8
8
14
21
7
19
11
8
19
12
12
16
8
9
11
9
11
7
10
14
22
11
31
12
11
13
12
6
9
21
21
12
9
19
26
16
9
12
6
17
9
20
11
15
12
5
24
7
14
10
16
13
23
22
15
14
8
8
6
15
27
5
9
10
16
5
11
15
3
11
16
12
8
11
10
16
17
8
8
14
12
13
15
20
15
4
4
10
8
8
19
15
12
11
19
8
11
12
19
9
15
10
10
4
8
6
11
10
14
17
14
6
14
5
15
14
10
9
7
7
12
14
6
22
15
11
20
6
14
15
5
15
14
23
7
2
7
21
9
15
10
10
5
4
6
17
17
13
6
9
7
20
6
7
4
10
21
8
16
11
6
6
5
3
17
7
8
12
19
17
6
14
17
9
17
8
9
17
8
10
8
7
14
9
11
5
7
13
7
3
5
7
6
13
11
10
13
10
2
5
9
10
27
11
14
16
7
5
9
12
5
9
13
11
15
7
11
9
7
9
4
8
9
6
7
9
7
12
15
10
10
5
4
5
13
18
11
9
14
7
3
10
7
3
12
9
4
4
9
6
9
6
12
9
4
8
14
9
9
14
11
11
14
18
14
19
11
9
12
7
6
8
7
8
11
6
9
14
23
7
31
10
6
8
7
10
4
9
9
5
5
16
7
10
7
14
16
7
5
16
6
14
7
10
10
14
13
17
15
9
6
21
11
10
10
17
18
17
25
7
10
15
11
12
13
10
9
11
8
11
6
10
8
12
16
7
7
6
4
9
9
17
7
8
13
12
10
5
7
9
13
6
10
3
10
6
14
9
10
6
8
29
7
15
13
7
5
11
7
17
12
19
13
7
10
9
8
5
11
5
6
4
15
13
15
15
14
3
10
8
10
7
9
7
17
6
5
16
7
12
8
16
4
4
8
7
7
8
17
8
11
9
6
4
7
3
12
9
6
9
19
17
5
17
11
8
10
9
7
6
10
11
10
8
6
7
7
28
8
6
12
12
11
6
13
13
10
13
10
9
11
8
8
22
13
12
4
21
4
3
9
20
9
11
6
8
12
7
7
24
7
6
7
9
3
6
12
3
6
8
10
2
9
6
6
10
4
5
16
7
7
3
9
6
7
7
10
4
4
6
10
10
11
8
8
7
7
16
5
12
11
10
11
9
6
4
6
10
7
17
9
15
10
7
6
10
16
5
9
6
12
4
10
5
10
15
14
8
7
8
5
14
8
2
11
6
12
7
8
3
7
11
15
13
15
17
6
5
2
2
6
4
10
5
4
5
7
15
13
6
9
17
6
7
3
10
7
12
1
7
19
13
9
10
5
20
9
10
4
6
7
9
8
17
9
4
4
4
12
3
10
16
10
14
3
15
7
8
3
4
9
7
7
10
8
8
4
32
5
12
3
11
6
2
11
13
2
16
14
12
6
4
5
16
4
13
11
11
9
13
3
15
10
11
8
6
9
6
6
9
10
4
7
3
9
11
8
4
9
8
5
2
22
12
2
5
6
22
10
3
5
5
7
14
6
4
6
7
7
7
1
7
10
5
15
12
4
4
8
4
12
8
14
8
7
11
5
3
9
5
6
8
12
18
19
11
10
4
5
8
3
13
4
5
5
5
15
9
7
3
8
7
13
5
3
19
7
11
5
2
6
5
1
4
20
7
2
3
4
7
26
7
5
4
10
8
10
9
9
7
2
13
11
4
17
9
2
22
7
7
6
5
1
13
6
16
4
8
5
4
22
4
8
1
4
3
6
6
5
6
6
8
5
7
9
15
13
9
5
10
5
8
8
5
8
9
4
8
5
6
8
9
4
8
11
4
3
5
9
4
8
7
6
5
6
7
7
5
3
11
9
6
12
13
3
12
14
7
10
2
9
7
8
6
6
5
3
4
9
5
3
9
6
13
7
6
2
4
5
5
8
12
6
10
6
12
16
15
9
6
8
9
8
15
4
2
11
9
11
8
8
5
18
7
5
9
6
8
4
2
10
7
6
4
9
8
8
9
8
3
3
5
6
17
7
8
5
3
16
4
14
10
22
6
19
5
11
4
4
13
6
9
6
5
7
6
8
2
10
4
10
9
4
5
7
11
7
2
16
18
4
11
9
3
4
3
3
8
20
13
6
6
6
6
6
4
12
6
6
4
6
5
5
5
7
4
11
4
7
4
2
9
9
4
6
21
4
5
6
3
9
4
7
7
23
5
2
2
7
3
17
7
11
7
3
7
12
11
5
7
6
6
4
3
12
3
8
10
3
6
5
6
13
0
5
4
4
7
5
5
8
9
9
8
8
4
3
6
6
15
6
7
4
6
7
8
4
7
2
7
4
7
3
8
3
5
7
7
6
2
6
14
4
13
7
1
3
6
11
5
5
4
2
6
4
12
6
5
5
5
7
7
23
7
3
7
3
8
11
6
13
6
7
6
8
13
6
6
3
6
3
10
8
9
6
5
13
1
11
4
11
5
8
11
12
5
10
5
4
3
6
5
16
5
7
3
10
5
4
10
6
6
4
5
2
8
6
4
5
9
9
4
2
13
7
1
8
9
2
1
3
6
6
8
11
7
2
5
5
6
9
7
6
6
4
3
3
5
1
8
2
4
8
3
3
9
5
1
8
6
4
2
3
10
5
5
7
5
11
10
4
3
3
7
12
9
4
3
6
9
3
3
6
6
4
2
9
3
5
2
6
12
7
2
10
7
5
6
9
10
7
13
6
4
7
4
6
3
12
5
4
9
8
3
3
6
11
8
2
9
5
3
7
1
3
3
9
7
5
6
3
4
7
4
8
11
8
5
8
2
9
17
6
6
10
1
13
5
7
3
11
3
2
5
10
6
9
3
6
2
2
4
3
2
9
7
6
6
1
10
7
6
7
9
1
6
13
7
5
1
1
6
5
2
2
17
4
2
3
4
8
6
4
6
7
3
17
4
2
5
5
6
4
6
5
5
6
7
6
2
3
19
5
9
6
1
2
3
12
2
4
5
7
6
9
4
20
3
1
2
1
5
5
6
8
4
8
13
13
4
7
6
3
5
6
7
9
4
3
5
5
3
5
3
4
8
6
7
5
9
6
4
4
5
5
4
5
4
3
7
10
7
2
5
1
8
6
6
5
3
3
3
7
11
16
4
8
4
5
10
3
10
1
3
4
5
3
7
7
4
12
6
4
7
3
4
7
3
9
4
5
6
13
10
7
18
10
12
3
5
4
4
15
4
7
4
4
10
8
5
4
1
13
13
8
3
2
6
8
4
6
1
6
5
14
6
10
6
9
13
1
7
1
2
4
10
6
10
5
13
7
3
3
1
3
4
4
11
5
6
13
8
8
3
8
19
3
2
4
1
2
3
0
1
7
5
9
4
3
4
1
3
8
5
4
3
7
2
14
9
3
5
4
6
4
5
4
3
4
6
1
2
3
3
5
4
3
2
3
4
4
9
3
8
8
7
6
2
14
7
12
6
5
2
2
6
7
5
4
7
6
6
4
6
1
3
4
8
11
4
7
4
3
10
4
4
5
3
4
2
7
8
3
4
2
9
6
1
4
1
6
6
1
15
1
2
12
7
4
5
7
5
7
3
3
6
5
6
7
2
3
5
13
14
9
9
7
6
4
3
8
7
8
3
3
6
5
14
4
5
11
4
3
4
2
6
3
11
7
5
4
9
13
5
1
4
4
7
1
11
25
11
7
5
11
2
4
4
3
3
23
5
9
7
4
7
5
6
15
4
6
6
4
6
9
6
9
4
10
6
3
8
4
4
7
10
3
5
2
4
1
3
2
1
6
11
5
2
4
3
1
5
6
5
2
0
6
5
10
4
0
6
15
2
3
3
3
7
7
6
5
8
6
2
8
7
5
5
9
4
9
6
8
4
3
13
4
5
5
4
11
3
6
3
0
7
7
4
7
9
5
6
9
3
2
8
3
3
9
8
4
4
3
8
4
1
9
6
5
7
2
4
4
5
6
7
5
5
5
6
4
24
2
11
12
4
4
4
3
4
4
3
4
11
6
7
0
13
2
7
6
11
3
8
11
7
6
2
22
10
3
6
6
4
5
4
1
2
5
6
10
6
10
11
5
4
7
2
8
5
3
3
3
2
4
8
1
2
3
3
3
3
8
15
6
1
2
9
6
11
1
4
9
16
8
4
7
7
6
5
3
6
14
7
2
2
2
2
4
2
6
7
10
4
2
7
2
2
2
7
2
4
6
0
2
8
19
4
9
2
7
2
11
6
5
6
8
2
2
4
5
4
6
2
4
7
4
2
8
16
8
5
10
2
4
6
17
6
2
6
7
4
6
7
8
12
2
2
2
6
4
4
3
3
2
5
3
6
6
8
7
2
4
6
5
6
3
10
7
5
4
8
6
5
1
6
3
3
2
8
4
4
7
4
7
5
4
11
10
9
4
8
4
4
10
2
6
4
3
5
6
5
8
2
3
10
1
6
13
2
3
8
3
2
2
7
4
3
1
9
5
2
1
2
5
5
7
5
3
0
3
9
6
5
4
4
3
7
2
7
1
7
7
4
4
6
0
7
2
8
4
4
1
7
2
6
4
5
7
8
4
1
2
5
4
7
1
6
13
7
6
11
6
3
5
10
3
2
2
7
10
5
4
9
4
2
4
10
6
7
5
3
10
4
1
2
12
5
6
6
8
8
3
10
8
6
6
3
5
15
2
9
3
2
9
2
6
4
5
14
5
4
1
5
7
3
3
1
4
2
14
1
6
4
9
11
7
4
3
7
1
3
4
2
4
5
15
6
6
9
8
4
5
4
2
5
4
4
11
4
4
3
7
4
7
5
7
5
4
2
4
3
4
2
4
10
12
4
4
3
9
7
7
6
3
2
1
2
3
5
3
8
3
4
2
10
2
3
3
6
15
2
3
3
13
7
1
4
3
2
2
5
7
3
4
7
7
4
2
3
6
7
7
3
0
5
1
6
2
1
2
17
5
6
2
3
3
1
3
3
3
5
6
6
4
6
3
9
5
5
2
5
6
7
5
14
6
3
6
2
9
5
4
5
3
4
1
2
2
4
4
5
10
3
3
5
4
3
4
9
4
3
7
3
0
0
5
4
6
2
1
5
5
4
1
5
5
8
6
1
2
4
7
0
1
8
6
3
8
3
4
4
3
2
0
4
4
0
3
8
0
1
3
0
10
4
7
6
6
1
2
3
8
2
2
4
3
5
11
6
4
3
4
1
11
9
4
3
10
2
4
1
3
2
2
5
2
4
7
3
3
4
10
3
6
1
4
8
2
4
4
8
9
4
5
6
4
4
0
1
3
8
3
1
3
4
3
1
2
6
4
3
2
7
13
3
7
3
2
2
4
3
1
4
4
4
2
7
7
5
2
12
4
4
3
5
3
3
10
19
6
3
0
2
1
9
4
3
11
6
1
4
1
5
4
6
9
7
6
3
3
7
11
4
2
4
5
6
4
2
4
3
6
5
3
5
3
2
7
6
6
2
11
3
5
2
3
7
2
5
7
4
2
4
2
10
2
4
7
3
1
5
8
1
19
6
5
5
3
4
3
5
3
6
2
4
7
10
2
4
0
6
3
4
3
4
5
2
5
1
3
6
2
2
2
7
1
3
5
7
6
2
2
3
6
3
5
4
2
4
4
5
2
6
3
5
4
10
2
6
1
10
3
5
6
8
1
9
1
6
11
3
3
6
2
4
11
15
3
5
4
3
7
4
4
3
7
2
1
1
2
1
2
6
5
7
13
3
1
0
3
3
1
10
2
5
3
1
2
3
5
4
5
2
4
6
1
1
10
3
12
3
6
1
14
1
1
4
2
4
1
4
5
4
1
5
3
3
6
8
3
2
6
11
3
4
4
6
9
3
0
8
4
5
4
1
2
8
2
4
6
7
2
3
2
5
4
4
4
4
1
2
0
3
4
2
4
0
8
5
8
7
6
6
3
2
6
2
5
4
4
3
6
1
3
7
1
4
7
0
5
3
4
1
3
2
7
2
3
2
3
0
4
7
4
2
3
6
6
5
6
3
3
1
5
2
14
4
3
13
4
10
27
2
2
3
2
3
9
12
4
6
4
7
6
2
7
1
4
15
1
13
5
5
3
14
3
3
7
3
3
7
13
1
0
1
5
6
7
9
2
5
3
1
3
3
2
6
3
2
4
20
0
2
5
1
0
16
8
1
2
7
4
4
8
3
4
1
1
6
1
1
6
4
4
7
0
5
4
6
2
3
2
2
2
7
4
10
7
5
0
4
2
2
1
3
3
2
3
3
6
3
2
3
11
6
9
2
8
3
10
2
15
1
6
4
3
5
3
3
11
2
1
5
6
2
3
2
0
8
3
3
7
2
4
3
5
5
1
3
4
1
3
3
2
5
3
14
10
2
5
5
1
0
3
3
1
6
6
10
5
1
0
1
21
4
4
3
3
6
8
6
5
4
4
2
3
4
3
8
2
2
3
7
4
17
5
15
3
3
1
4
5
14
4
10
6
12
6
2
2
4
2
0
2
5
4
2
5
4
5
3
3
6
15
0
3
5
4
2
6
4
2
10
5
2
3
5
2
3
15
3
4
3
10
2
1
0
3
2
3
4
2
8
4
1
1
4
5
1
2
7
2
5
3
16
2
3
2
1
2
3
9
4
4
5
1
5
5
4
4
3
6
0
5
14
9
3
2
6
2
2
0
5
2
5
6
1
10
3
8
3
2
6
5
6
2
6
7
5
2
2
3
1
3
6
2
14
3
1
3
5
6
2
12
4
6
4
1
6
12
3
1
2
3
6
4
1
4
3
4
2
1
14
2
2
2
3
2
2
4
7
0
4
2
2
4
4
0
7
4
3
1
4
3
2
1
9
4
1
6
11
2
4
5
4
1
3
7
5
4
0
3
4
5
3
5
2
2
10
2
6
3
5
1
2
7
1
8
3
1
4
5
2
18
6
4
9
3
2
1
1
2
5
3
0
4
5
10
7
0
17
10
1
0
6
3
4
10
1
3
10
4
1
6
3
5
3
5
2
0
4
6
4
12
3
3
2
8
5
3
5
1
5
11
1
8
1
4
2
10
5
5
4
9
3
4
2
5
2
3
2
3
4
13
0
7
2
8
5
2
4
4
2
3
1
6
11
1
4
5
4
3
0
1
12
10
4
4
1
7
2
3
6
14
2
5
8
2
1
4
4
0
3
0
1
0
3
3
6
2
2
2
2
4
3
3
4
4
2
4
1
3
2
4
5
1
2
4
5
3
3
7
6
3
4
4
4
4
5
0
8
2
2
2
3
6
3
3
3
3
4
8
3
4
3
6
2
2
3
8
2
7
4
5
1
1
3
5
4
7
1
3
7
2
1
3
3
4
3
3
15
11
8
2
6
4
5
3
4
4
3
10
3
4
7
5
2
5
1
4
3
7
3
1
3
4
1
11
3
3
1
7
1
5
4
1
2
6
2
2
4
1
10
6
8
2
2
3
2
3
2
4
8
11
8
3
3
2
3
5
3
3
4
6
3
14
3
3
6
2
5
3
5
3
12
5
4
3
6
4
5
2
5
8
5
6
2
22
6
2
2
1
5
8
1
8
10
1
3
6
6
10
7
7
1
5
1
3
1
3
6
2
2
5
2
8
1
1
2
2
2
6
7
0
2
4
1
3
4
3
2
1
3
4
17
3
4
1
0
3
3
9
3
4
0
0
4
2
1
3
8
2
10
4
0
8
6
3
6
2
6
4
2
13
4
10
2
9
3
8
3
2
6
4
0
6
3
3
1
1
0
6
7
5
1
5
1
12
6
5
4
10
5
9
1
2
1
1
2
3
4
4
4
2
5
4
7
3
4
1
1
3
9
3
2
6
4
7
6
3
4
0
1
8
2
2
4
1
13
4
4
2
5
5
0
2
6
2
2
3
3
4
6
0
0
0
5
4
8
6
1
4
2
5
1
6
2
2
4
5
2
1
2
5
4
2
2
4
1
2
1
6
4
3
0
4
7
4
3
18
10
1
5
5
3
4
3
4
3
7
3
4
3
0
5
3
3
4
4
2
5
2
1
2
1
4
1
4
2
1
0
6
2
3
1
2
5
7
5
3
1
11
1
6
5
2
1
6
1
14
6
1
5
3
1
2
1
2
9
3
1
3
2
3
7
3
9
4
8
5
4
7
2
4
3
0
1
0
4
3
4
22
1
20
6
5
7
3
5
8
4
1
2
6
1
1
3
1
11
3
4
7
2
2
2
15
5
1
7
3
4
4
4
2
6
5
4
3
3
1
2
4
2
19
3
7
2
1
0
5
3
5
1
1
1
1
4
9
4
4
2
1
2
5
2
6
2
5
6
5
5
18
1
2
4
2
4
3
1
2
3
3
3
1
9
7
1
5
3
10
4
13
4
19
11
5
6
2
7
3
1
0
2
2
4
4
9
5
0
13
3
1
7
2
5
3
6
2
4
5
0
5
1
2
2
2
0
26
3
3
4
17
1
6
2
1
1
14
6
6
1
3
2
0
4
2
3
1
4
2
0
1
0
3
2
2
6
13
0
4
5
3
5
1
9
3
6
4
3
2
3
3
2
2
0
5
3
4
2
5
3
2
0
3
0
1
3
4
2
3
4
3
1
2
2
2
7
3
2
1
1
3
2
1
3
2
2
5
5
6
2
3
0
1
2
3
3
3
3
1
2
3
4
1
2
4
1
3
2
2
1
3
6
1
8
3
2
2
1
3
2
1
3
3
4
2
1
3
5
13
3
6
6
2
2
2
5
2
4
3
0
0
3
3
2
3
1
2
2
7
2
2
6
1
2
8
3
3
2
2
1
3
5
5
2
2
4
3
2
3
2
2
1
3
11
2
5
1
3
2
7
5
1
3
2
1
2
4
14
3
4
2
2
4
6
1
7
1
19
3
4
3
4
2
2
6
5
2
3
1
3
2
2
3
3
4
3
6
3
2
5
7
1
7
1
2
4
12
4
3
1
10
2
2
1
4
3
1
8
2
2
1
2
6
1
2
5
7
6
5
0
9
2
2
1
4
4
0
0
4
3
1
1
2
2
1
4
2
1
1
5
5
5
0
3
2
3
6
5
5
1
4
2
2
4
3
3
2
2
5
0
13
7
5
17
4
2
2
4
4
4
5
0
2
10
2
6
6
4
5
1
3
6
4
0
5
3
8
3
2
0
3
5
1
2
1
0
4
1
1
7
2
3
1
3
2
3
2
9
3
1
3
7
3
3
1
2
13
3
4
7
2
1
3
1
3
2
11
0
3
6
11
5
2
7
5
11
5
2
2
3
1
0
2
2
2
4
4
4
3
1
4
6
2
0
3
4
4
6
4
5
0
3
2
2
4
2
3
11
13
4
2
0
3
3
1
3
4
3
5
6
11
1
2
3
3
8
1
4
4
3
3
7
2
1
2
3
2
2
2
1
8
1
1
5
3
4
6
6
4
5
2
8
4
3
2
11
6
4
0
1
3
3
7
0
4
5
3
4
3
5
2
3
1
2
9
6
4
3
4
2
2
9
3
2
1
6
1
2
5
4
1
3
3
3
2
2
4
2
4
2
8
3
2
2
2
5
8
2
1
1
2
1
10
1
5
2
4
0
3
2
3
4
3
6
1
1
2
9
0
2
1
17
1
2
4
5
3
5
1
1
0
1
3
2
3
1
6
3
1
2
1
5
0
2
2
2
3
8
4
2
2
6
1
5
0
5
3
0
1
1
4
2
2
2
4
5
2
3
7
1
4
2
2
4
4
2
2
4
4
4
2
2
1
2
2
3
2
3
2
8
2
8
2
1
2
5
3
7
1
2
2
3
4
1
2
7
2
6
0
1
1
3
6
3
0
2
0
4
2
0
2
4
14
4
5
4
0
4
2
9
4
8
6
8
3
5
1
2
15
1
4
1
3
1
1
3
2
1
4
6
4
1
3
7
3
2
3
8
3
1
5
1
4
2
3
6
2
6
5
1
2
1
5
0
2
2
1
3
3
5
1
2
3
2
2
4
4
2
3
2
2
4
1
6
1
0
5
7
5
6
2
4
4
3
4
2
4
0
6
4
2
4
4
1
3
3
3
4
2
1
4
2
2
10
5
3
6
5
2
2
4
2
1
0
2
3
3
3
2
1
3
2
1
2
5
1
5
1
1
3
3
3
1
8
2
2
0
6
0
2
2
7
3
2
4
2
1
2
2
1
3
0
1
4
3
3
1
0
1
5
1
4
3
4
5
7
2
3
1
0
2
1
0
1
3
1
2
2
0
3
4
1
3
4
5
1
2
9
1
6
12
2
2
1
0
1
17
4
2
1
5
3
2
3
14
4
4
4
3
0
5
1
3
6
3
1
2
1
4
4
13
3
3
0
1
3
2
2
2
3
4
6
2
2
3
4
2
4
5
1
2
2
6
3
9
1
0
0
4
3
3
3
0
7
2
3
2
4
3
2
3
4
4
4
4
1
1
2
1
5
1
1
4
4
4
3
5
6
3
3
1
8
0
3
2
1
3
4
5
4
3
0
0
0
1
3
3
4
1
2
5
7
7
4
4
3
2
3
2
4
2
3
5
4
7
2
3
17
3
4
2
1
2
1
3
1
10
1
4
2
2
2
4
7
0
2
1
5
2
6
1
1
14
0
5
1
4
3
3
3
2
3
4
3
3
1
0
2
2
6
23
3
1
5
2
5
0
2
16
3
2
0
2
0
10
4
1
1
8
3
1
2
6
4
1
1
0
0
0
2
2
1
4
2
2
4
2
11
12
3
1
5
1
3
2
2
7
1
1
4
2
2
2
3
3
1
4
0
2
2
0
3
1
3
6
7
6
3
2
8
1
0
3
2
3
0
2
3
3
3
7
3
3
1
3
1
5
3
4
3
1
2
0
22
2
2
2
1
3
3
3
0
2
3
1
3
3
8
2
8
3
9
1
4
1
2
6
3
1
1
1
1
2
6
1
0
0
6
1
6
0
6
4
2
1
1
1
3
6
0
1
2
2
5
22
2
1
0
3
3
1
7
2
3
3
2
14
1
5
6
3
4
5
3
0
3
4
1
2
1
6
2
0
2
2
3
3
2
16
1
5
1
4
1
0
3
3
2
0
9
5
4
3
3
3
3
2
5
2
2
6
4
3
0
2
6
5
0
3
2
2
3
4
3
1
3
1
8
5
3
2
4
2
6
3
3
3
14
0
1
1
1
0
6
2
3
3
12
2
2
2
2
0
15
4
3
1
1
2
5
8
5
4
5
1
1
0
4
2
4
3
5
0
2
1
2
3
2
2
1
3
6
4
3
4
2
7
2
4
2
1
11
2
2
1
3
4
3
2
2
3
1
10
3
4
3
3
3
2
0
6
1
2
2
2
7
2
1
1
2
2
1
5
6
2
2
5
5
0
1
3
0
3
4
0
3
3
4
4
2
10
1
0
8
6
4
3
1
4
2
3
1
4
2
2
2
3
1
8
0
1
2
1
4
2
4
2
2
4
5
2
2
0
2
0
3
2
2
10
16
2
0
4
1
4
2
5
3
2
1
1
1
9
2
0
5
2
3
1
2
2
1
6
2
3
1
2
4
1
3
0
3
1
4
2
2
0
2
2
1
4
3
3
2
2
3
1
1
1
1
0
14
3
6
3
0
3
1
4
2
1
6
2
3
3
1
3
3
3
2
6
3
2
3
6
6
2
1
3
0
2
1
1
7
0
2
2
1
1
2
3
3
3
0
6
1
3
1
1
1
3
2
2
1
3
7
2
0
2
1
2
3
2
1
3
9
3
1
2
1
2
10
1
3
0
3
7
11
3
1
2
2
3
4
3
3
2
2
3
2
4
2
7
2
4
0
1
5
1
3
3
2
13
0
3
1
2
1
2
0
0
3
3
1
5
2
8
3
2
1
6
5
1
1
3
3
5
2
0
4
5
2
4
2
0
3
4
2
2
2
1
1
0
2
1
2
1
3
1
5
0
1
1
4
2
3
0
1
2
2
1
1
2
3
4
3
13
9
0
2
2
1
4
3
1
3
3
1
6
3
3
1
2
3
0
2
2
1
1
2
2
1
2
6
0
1
2
0
9
9
4
1
10
1
0
0
5
4
9
0
3
4
3
2
2
4
1
2
2
3
2
3
3
7
0
1
4
1
6
6
2
1
0
7
6
11
3
7
1
6
2
1
6
2
2
2
1
1
7
1
1
0
0
1
0
1
1
2
2
1
3
0
0
3
3
0
4
3
3
0
8
0
0
2
4
4
3
2
1
2
6
2
2
6
3
2
1
0
0
3
7
1
7
0
1
4
2
2
8
1
6
3
3
2
0
5
3
3
3
2
2
1
2
4
7
2
1
2
0
0
3
1
2
4
1
4
2
1
2
0
1
1
3
4
0
13
4
4
1
2
1
1
2
2
2
4
3
2
7
2
5
0
2
1
4
3
2
0
4
0
1
1
1
4
2
1
3
0
1
1
3
3
3
0
2
3
1
3
1
3
2
1
3
7
2
3
2
5
2
2
6
6
2
7
10
5
2
0
3
1
8
2
9
3
3
0
3
1
0
2
1
2
2
1
1
1
3
2
13
3
1
4
1
3
2
3
4
0
0
0
15
1
2
0
0
1
4
2
3
2
2
0
0
3
4
1
2
1
0
1
1
1
2
2
2
1
6
0
4
3
5
4
6
3
1
1
7
4
1
2
0
2
1
5
3
1
2
3
3
2
1
9
0
1
2
3
4
6
4
1
5
3
1
1
2
6
1
2
3
2
3
4
9
1
2
2
2
4
2
5
4
0
4
1
2
4
4
0
1
1
2
3
2
2
0
3
2
4
2
4
1
0
3
2
2
3
4
3
3
1
2
1
3
2
1
3
4
1
3
3
2
3
0
4
3
3
2
2
2
1
4
4
1
2
2
4
1
2
4
0
1
2
2
0
2
2
1
2
2
4
0
3
1
1
2
2
0
3
3
1
2
3
2
1
2
1
1
0
2
0
1
2
0
1
3
2
1
2
1
7
2
6
1
3
4
3
0
4
4
5
2
4
0
2
2
5
0
4
5
1
1
4
1
2
1
5
2
3
2
2
1
3
2
3
1
5
2
6
3
3
3
1
3
7
1
1
1
6
1
1
3
5
6
1
8
0
4
3
1
5
0
4
1
4
3
5
0
1
6
5
3
1
3
4
3
2
2
2
1
1
1
1
1
2
2
1
1
4
2
9
3
11
1
0
1
0
12
2
3
5
1
1
3
2
2
0
1
3
1
1
7
1
0
3
4
1
9
1
2
4
8
1
2
5
1
1
2
5
3
5
2
3
3
2
1
0
6
3
1
2
2
2
3
4
4
2
3
4
2
2
6
1
0
1
1
3
5
6
5
2
5
1
0
2
3
2
1
3
1
0
2
1
2
3
3
0
0
2
3
5
1
2
1
0
11
1
1
2
1
7
4
7
0
0
1
9
2
0
3
2
1
5
1
4
2
0
7
6
0
2
2
4
1
19
0
2
4
0
3
1
1
11
0
2
0
4
0
3
2
3
0
0
0
1
2
4
4
5
1
4
0
3
3
8
5
3
3
4
2
1
2
1
2
0
1
2
3
3
8
4
2
2
6
2
5
5
1
2
1
0
1
0
3
1
2
5
1
2
4
2
2
1
2
0
6
5
2
1
3
0
1
5
1
2
1
2
5
4
0
2
5
4
2
4
4
5
2
0
4
7
1
0
1
4
0
2
5
5
4
1
1
3
1
5
1
3
4
3
0
3
2
1
0
1
3
2
0
4
1
1
4
2
1
2
2
2
1
1
6
2
0
1
5
3
1
2
3
5
0
1
3
1
9
3
1
4
1
0
0
2
0
2
1
3
2
9
0
3
3
0
0
1
1
3
2
2
4
0
6
1
4
1
0
1
2
4
2
5
5
7
2
8
0
1
0
2
4
2
2
0
2
0
5
2
3
3
0
1
1
1
3
7
5
1
2
4
4
0
3
4
1
7
1
0
3
2
1
1
3
5
2
1
1
1
1
0
1
1
2
4
1
5
2
16
3
4
0
2
1
2
1
2
2
1
2
0
2
0
1
0
2
2
1
1
1
2
3
6
1
1
0
3
2
2
4
4
1
1
1
2
2
6
1
1
2
2
2
0
2
2
3
5
1
4
3
1
2
2
1
2
6
2
1
0
3
1
1
0
3
3
1
3
0
2
2
8
0
4
2
4
2
1
1
1
5
3
3
4
2
1
0
4
3
1
0
5
4
2
4
2
1
0
1
5
3
0
3
4
7
1
3
2
1
11
2
0
2
1
0
0
1
2
1
0
1
3
13
4
2
3
5
5
2
2
1
4
3
3
1
6
1
4
7
2
3
2
0
4
1
4
2
2
7
5
0
0
1
3
1
2
0
4
0
4
3
3
2
4
0
1
1
0
1
0
2
2
0
4
0
0
2
0
1
2
1
2
2
1
0
4
1
1
3
2
1
2
1
2
5
0
12
1
1
1
0
5
0
2
17
1
1
1
2
1
1
0
6
3
1
2
1
1
2
1
1
0
4
1
7
1
3
1
1
5
4
3
3
2
1
1
5
2
0
2
7
0
2
1
1
0
2
7
1
1
11
2
1
9
2
0
4
2
8
4
0
0
1
1
2
3
1
6
1
5
2
3
1
3
1
3
5
1
4
5
1
3
5
0
5
2
1
2
2
1
5
3
4
1
1
1
5
1
1
2
3
2
1
1
3
0
1
2
4
3
3
2
1
0
1
3
0
0
0
0
5
2
2
1
25
1
1
1
7
2
1
5
1
1
5
2
1
3
2
1
1
1
4
0
2
1
1
4
3
3
2
2
5
2
10
6
2
4
3
3
0
2
2
0
1
18
0
2
1
1
3
0
3
2
2
1
1
2
3
2
7
2
1
6
3
2
3
0
4
2
4
2
1
1
1
1
7
2
9
1
6
5
1
2
1
2
0
1
0
3
3
0
4
1
2
1
3
2
2
2
3
0
1
2
1
4
5
1
4
5
0
1
13
2
0
0
5
2
3
2
2
2
1
1
2
2
2
2
1
13
4
2
2
2
1
1
8
9
6
3
1
2
3
5
2
1
1
4
3
3
9
3
0
4
2
3
4
4
2
8
2
3
3
1
4
0
2
3
0
0
3
1
3
0
1
2
1
0
5
0
2
1
2
5
1
3
16
3
2
5
2
2
3
0
4
4
1
2
1
5
1
1
1
2
3
2
3
1
1
5
0
0
0
0
3
1
3
3
4
1
2
3
2
1
4
6
1
2
4
2
2
1
2
1
2
2
1
0
1
5
0
3
1
2
3
4
3
0
2
4
2
2
2
2
0
2
2
2
2
2
1
0
0
2
0
2
2
1
1
0
4
3
1
2
4
4
3
3
1
0
2
4
4
3
4
1
10
3
0
3
1
1
0
2
2
4
2
6
1
3
2
1
1
2
1
9
5
8
1
0
2
2
2
1
0
1
2
2
19
1
3
4
2
1
1
0
4
1
0
1
0
1
2
0
2
1
2
0
0
6
1
2
1
1
6
3
0
0
2
2
0
8
2
2
2
3
0
3
3
2
3
4
5
1
0
2
2
2
1
2
2
3
2
3
0
1
2
0
2
0
1
0
2
1
1
2
1
1
0
1
1
3
0
1
2
1
12
1
3
3
3
0
2
5
1
1
1
0
2
1
4
4
4
1
5
12
3
0
1
2
7
0
3
2
1
1
1
7
3
2
2
2
2
8
1
2
0
2
3
2
1
1
2
8
2
2
2
3
1
0
17
5
6
2
1
1
0
2
1
1
0
2
2
1
0
6
5
2
3
9
3
2
1
1
0
4
1
0
1
1
4
2
2
1
4
0
0
2
0
1
2
2
3
4
1
0
1
0
3
1
2
1
2
5
0
0
0
1
0
3
1
1
3
3
5
0
5
1
1
1
1
0
0
2
2
1
0
2
1
0
0
2
2
3
1
0
5
6
5
1
3
4
2
4
9
2
2
0
5
1
4
3
2
2
4
1
2
2
4
0
2
4
3
3
2
2
1
1
3
0
17
1
1
1
2
3
1
13
1
7
1
2
1
2
2
2
1
0
3
1
12
5
1
2
2
3
4
1
2
1
1
2
1
2
2
1
1
1
8
6
4
1
1
2
0
3
0
2
1
1
0
3
1
1
2
9
3
3
2
2
1
6
1
1
1
2
2
1
4
0
1
1
2
5
1
3
2
2
3
0
1
3
2
1
5
3
0
1
2
1
0
2
0
1
2
2
0
1
1
2
0
13
1
2
2
1
0
7
4
1
6
10
3
4
2
4
0
1
1
2
0
1
1
2
4
1
0
2
0
0
9
1
5
5
0
1
1
0
2
1
1
6
0
0
2
2
1
3
3
1
1
4
1
0
0
0
1
2
1
2
2
4
1
0
3
7
2
0
1
9
3
2
0
3
1
0
3
1
1
8
2
4
1
2
7
2
4
1
2
1
2
4
0
1
2
1
0
0
1
1
3
0
0
2
0
4
1
0
2
3
2
2
3
3
1
1
0
8
2
3
1
6
0
3
0
3
2
1
1
2
3
0
0
1
4
2
1
5
2
2
1
3
3
2
2
1
3
2
7
2
2
1
1
2
2
2
3
2
1
2
3
5
3
1
0
1
0
2
3
2
3
2
2
1
2
1
4
3
3
1
0
0
2
0
0
1
0
3
1
1
1
3
0
2
1
0
3
6
2
1
29
2
1
0
3
3
1
2
3
1
1
1
2
1
2
3
0
6
0
3
3
2
1
1
1
0
0
0
1
2
0
0
8
10
3
3
2
0
2
3
8
1
1
2
1
3
1
1
2
1
0
0
1
3
2
2
2
0
1
3
2
3
1
2
2
1
0
8
1
2
2
1
3
2
5
0
3
2
1
1
1
2
2
5
13
1
2
0
1
0
1
1
1
1
2
1
0
2
4
2
0
0
2
2
0
1
1
2
0
1
1
1
1
3
1
1
4
0
4
5
5
1
1
0
2
3
1
3
3
1
2
0
3
9
6
1
2
2
3
3
1
0
2
0
7
2
2
3
0
1
0
0
1
0
0
5
0
2
2
3
4
1
0
3
2
4
1
1
2
3
6
3
1
0
1
3
0
0
0
0
1
1
2
4
1
1
1
3
0
1
2
0
2
2
0
1
0
2
1
2
1
3
3
3
1
0
1
0
1
3
2
2
1
0
1
0
2
6
0
0
0
0
3
1
3
0
5
2
3
2
0
1
1
9
1
2
3
6
3
0
4
2
10
1
3
0
2
1
2
1
1
12
3
1
8
2
2
1
3
4
1
2
1
2
3
7
0
2
1
4
1
3
3
1
3
0
1
2
1
2
1
0
0
2
1
0
0
0
1
2
1
0
5
3
2
4
3
8
2
4
0
5
2
2
3
1
2
2
2
0
0
0
3
3
4
10
12
4
3
1
2
2
1
4
3
2
2
1
1
0
0
0
0
1
0
3
2
3
2
0
2
2
17
3
0
4
2
2
1
1
0
1
1
1
1
1
6
6
1
10
1
0
0
1
1
3
1
1
2
2
2
0
1
1
1
1
5
1
2
1
0
3
2
0
1
1
4
6
3
0
3
2
2
1
2
3
2
1
1
1
1
2
1
0
1
0
1
2
3
1
3
1
1
1
1
0
1
5
1
6
0
2
1
0
2
2
1
0
2
14
1
0
1
2
0
1
1
3
0
0
3
3
1
3
6
0
5
2
2
1
1
2
3
0
1
0
1
5
3
0
0
2
1
4
0
3
1
2
0
1
3
3
5
1
1
1
2
2
1
1
0
2
1
2
2
1
2
2
3
9
0
2
3
0
2
0
0
5
1
1
3
5
0
1
1
0
1
5
0
2
4
2
2
2
0
2
3
3
1
2
0
1
3
2
0
5
2
1
1
1
4
1
3
1
2
0
13
2
0
1
1
2
0
2
2
7
1
2
3
1
4
0
3
2
1
0
0
2
2
3
0
2
1
0
0
3
2
1
1
1
0
1
0
0
0
2
2
0
1
1
1
0
0
3
1
7
0
3
3
2
3
2
4
1
0
1
0
2
2
4
2
1
1
2
2
0
1
6
5
0
1
2
1
6
1
3
0
0
1
2
3
1
1
2
1
0
2
3
0
2
1
0
4
1
1
1
1
0
1
2
1
2
3
0
13
6
7
0
2
2
0
3
1
1
5
2
0
0
1
2
2
3
1
1
1
4
1
0
2
3
2
1
2
3
1
1
0
2
1
2
1
1
1
9
1
2
4
1
1
3
3
1
2
0
4
0
2
1
1
1
4
0
4
1
2
0
3
3
3
11
1
1
1
7
3
0
1
2
0
1
0
0
1
1
5
1
0
3
0
4
3
2
11
4
0
2
9
2
1
1
1
3
3
7
4
2
2
0
1
1
2
0
4
1
9
0
1
2
2
0
8
3
7
2
0
0
2
2
0
1
1
2
4
2
1
0
1
2
3
1
3
2
1
1
1
2
1
0
1
0
2
2
2
3
7
1
0
2
2
5
1
1
5
1
3
3
1
2
1
1
0
1
6
0
1
0
4
0
0
1
5
5
2
0
0
4
0
1
2
1
4
5
3
2
2
2
3
2
3
1
3
0
2
1
1
1
2
0
1
9
1
0
1
1
0
0
2
0
1
3
2
1
3
1
1
1
2
1
1
1
0
0
3
1
2
0
2
2
1
3
6
11
2
10
4
0
1
0
3
3
0
1
0
0
1
7
1
1
1
2
0
0
3
1
1
0
1
2
3
1
0
1
2
1
3
0
0
4
2
0
0
1
1
1
1
1
2
3
2
4
1
0
1
1
0
1
0
2
0
0
2
1
1
2
11
1
2
4
0
2
1
0
1
2
1
0
1
3
0
3
1
2
0
0
1
0
3
1
5
2
0
0
1
0
5
3
2
1
0
2
0
1
0
2
2
2
1
3
3
0
0
1
4
2
0
1
1
1
0
1
0
1
3
1
0
1
1
0
1
1
1
0
2
5
0
3
0
1
2
3
2
2
0
0
1
0
1
1
1
1
1
0
1
0
1
2
3
1
2
1
0
3
2
0
2
2
1
0
2
2
1
2
1
0
3
2
2
0
2
2
1
3
4
2
2
1
2
2
2
1
1
0
9
2
0
1
3
13
0
0
0
2
2
0
1
0
1
2
0
2
2
7
0
1
1
0
1
2
3
2
2
2
0
2
1
3
4
3
8
0
0
2
3
1
2
0
0
1
3
3
0
1
3
2
1
4
1
3
1
2
3
6
3
1
1
2
2
1
3
0
1
2
2
2
1
1
2
0
2
1
3
3
0
4
2
5
1
4
2
1
1
1
2
1
1
2
1
1
3
2
2
1
2
1
3
1
0
1
1
5
0
3
0
2
1
0
1
0
0
0
1
0
1
0
1
1
3
6
0
0
4
0
9
2
1
2
2
6
2
0
3
0
3
6
3
1
2
2
7
1
1
1
1
2
1
2
1
0
1
1
2
0
2
4
1
1
5
0
1
0
1
0
1
1
6
4
1
1
1
5
5
1
3
0
3
0
2
1
1
2
1
2
2
6
3
3
1
1
2
0
0
0
1
14
1
1
2
1
1
2
1
0
0
2
2
1
1
1
4
3
0
1
2
2
5
0
2
0
1
1
1
1
2
3
0
0
3
1
1
8
1
1
1
3
2
1
0
1
7
3
0
0
4
2
1
5
3
1
1
1
0
0
8
0
2
0
1
4
0
0
2
2
2
1
3
2
2
2
3
1
0
2
3
1
4
1
1
0
1
3
0
1
1
1
1
0
2
1
2
10
3
1
1
0
1
0
1
1
6
1
2
0
0
1
5
1
2
1
0
0
1
0
1
0
0
2
0
1
6
1
3
0
1
1
1
1
0
7
0
1
0
2
2
1
6
1
1
0
2
2
2
1
2
7
0
2
4
2
0
2
3
12
2
1
0
2
1
2
1
1
1
5
1
0
4
1
2
1
2
0
1
0
1
2
1
1
3
4
4
1
4
2
1
1
2
1
1
0
1
0
0
3
1
2
1
1
0
3
9
2
0
1
2
0
0
4
5
1
1
0
1
1
2
2
2
0
1
2
2
2
0
2
3
0
5
6
6
2
2
1
2
2
3
2
2
1
2
0
1
14
1
6
1
0
2
2
1
1
2
0
5
1
1
2
0
2
0
0
1
1
0
1
0
8
3
1
1
2
1
0
1
1
0
1
3
6
1
1
3
0
2
1
8
1
3
2
2
0
2
2
1
1
2
2
2
1
0
0
0
0
0
2
1
0
2
1
1
1
4
2
1
0
0
0
0
1
0
6
4
1
14
2
1
2
1
6
2
4
0
1
1
1
1
0
0
3
1
2
0
7
0
2
2
1
2
1
0
2
0
4
3
0
0
1
1
0
3
0
2
0
3
2
0
0
2
2
1
0
0
3
0
5
4
1
1
4
2
1
2
1
6
1
0
1
3
2
3
2
1
1
1
0
1
3
1
1
2
2
3
4
1
1
5
2
0
2
2
0
3
1
0
1
1
0
11
1
1
1
3
2
7
1
9
1
2
4
1
1
2
0
5
2
0
3
0
1
2
2
1
1
2
0
3
0
2
3
0
1
2
0
5
2
0
0
1
0
2
2
0
1
5
3
1
2
1
5
2
2
0
2
1
3
6
0
0
2
3
5
0
2
6
1
1
0
2
5
2
1
0
0
1
2
2
2
1
2
0
1
1
0
1
1
1
2
1
0
1
2
0
0
1
1
1
0
1
0
2
1
1
0
2
1
2
2
1
2
0
14
4
0
0
0
3
1
0
3
1
0
1
2
1
1
2
0
2
0
2
3
1
0
2
1
1
0
3
0
3
1
3
1
0
2
6
2
3
1
2
0
0
4
0
0
1
1
4
1
4
1
0
1
3
0
2
1
2
0
0
1
0
5
1
0
0
4
5
0
1
1
2
5
0
0
3
3
2
2
1
0
1
1
2
1
0
4
1
1
2
3
2
3
0
1
2
3
2
1
2
1
9
2
1
0
0
2
1
0
1
0
2
1
2
1
2
0
1
6
0
0
1
1
3
0
0
1
0
1
2
2
1
1
0
0
1
0
1
1
0
1
2
0
2
0
2
1
0
1
2
4
4
1
2
1
0
8
0
3
3
1
1
2
1
0
3
1
0
2
0
0
2
4
0
1
0
3
0
1
1
2
2
2
1
1
0
1
1
0
0
2
6
1
0
0
0
1
3
2
1
1
3
2
0
1
0
1
0
1
0
2
2
0
1
1
7
1
0
1
4
4
0
0
1
1
1
2
1
2
4
0
1
0
0
12
2
3
2
1
2
3
0
0
1
2
1
0
0
1
2
2
5
3
3
3
2
2
0
1
0
2
1
1
0
1
2
1
2
1
1
3
1
1
3
5
1
1
2
1
1
1
0
1
3
1
0
3
4
1
0
4
3
1
3
2
2
0
2
0
1
1
0
10
1
4
2
0
2
1
1
1
0
1
0
1
2
6
9
1
3
1
1
2
3
0
1
0
2
1
0
4
0
0
1
0
3
5
1
0
1
1
1
0
1
0
1
3
2
1
2
3
0
3
3
1
0
1
1
2
2
2
2
0
3
1
1
0
1
0
0
0
2
6
1
1
0
1
0
1
2
13
3
2
0
0
2
0
0
2
1
0
1
1
0
2
0
3
2
1
5
1
0
0
1
0
1
3
1
2
0
0
0
1
0
2
2
2
0
1
2
2
2
0
1
0
2
0
2
2
2
0
0
1
2
4
3
2
0
4
0
1
1
0
2
1
1
3
3
4
3
1
0
7
8
1
0
1
1
1
0
2
1
1
1
0
1
1
0
0
1
13
0
5
2
2
0
0
0
1
2
1
3
4
0
1
2
0
1
1
0
3
2
3
0
3
2
2
0
1
0
0
1
2
0
1
0
1
1
1
1
1
0
4
1
2
2
1
0
2
2
10
4
1
1
1
0
2
3
1
2
1
0
7
4
1
1
0
4
1
2
5
0
19
1
1
0
2
1
2
3
2
0
0
0
2
0
2
0
3
0
2
8
1
1
1
1
1
2
1
0
0
0
1
1
0
2
0
4
4
1
0
2
1
0
3
0
2
0
0
0
4
7
1
1
3
2
0
0
3
1
0
2
0
4
1
0
3
1
2
0
5
1
1
1
4
1
2
7
0
0
0
1
2
0
0
3
0
0
0
1
2
2
0
2
0
1
3
1
0
1
1
2
0
1
0
3
2
0
3
0
1
2
0
1
2
0
1
4
0
2
0
1
1
1
2
0
0
1
2
2
0
0
0
1
2
0
0
8
1
0
2
1
2
2
1
0
2
1
2
1
1
1
1
2
0
1
0
0
1
0
0
1
1
1
3
0
2
1
0
2
2
3
2
0
3
3
1
1
1
0
0
0
4
1
0
0
1
0
2
0
2
1
1
3
2
1
5
1
2
4
1
0
1
0
1
1
3
1
1
8
0
0
2
1
1
4
4
1
0
2
5
3
1
2
0
2
2
2
1
2
2
1
0
2
1
2
0
6
2
4
0
2
4
0
1
1
2
0
1
5
1
1
2
1
1
2
0
1
1
2
1
0
3
0
1
1
0
2
0
3
3
2
1
2
3
1
0
2
7
1
2
0
1
0
0
2
3
5
0
0
4
1
1
0
0
0
5
1
0
1
3
1
2
4
0
1
0
1
1
4
2
0
7
2
4
0
0
1
20
1
4
1
5
2
3
0
1
7
2
2
1
1
15
1
8
2
1
3
2
1
0
3
0
1
1
1
3
1
0
2
1
0
0
0
2
2
3
6
3
2
1
0
1
0
0
2
14
0
1
1
0
1
0
1
1
0
3
1
1
1
1
0
1
0
3
1
0
1
0
1
3
2
10
1
1
0
2
0
2
0
0
0
1
1
3
8
2
2
1
1
0
2
1
0
1
0
1
2
2
1
4
0
1
3
0
0
3
0
3
2
0
0
0
2
1
3
0
1
8
1
0
3
0
6
1
11
0
2
8
3
2
0
3
4
2
0
1
2
1
0
2
0
2
0
1
0
0
1
1
7
0
1
1
0
0
3
1
1
0
2
2
1
4
3
1
0
1
1
1
0
1
4
1
0
2
0
4
2
0
3
1
0
5
0
1
2
1
0
1
1
2
9
1
1
0
0
3
4
1
3
1
2
0
1
1
1
0
1
1
1
4
0
2
0
0
0
4
2
0
1
1
0
2
1
1
4
1
0
1
4
3
6
1
3
3
1
0
1
1
0
0
1
3
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
4
2
1
4
3
0
1
1
0
2
1
1
0
0
2
0
0
1
1
0
3
3
0
1
0
0
1
0
2
0
3
1
4
0
0
2
11
2
1
1
3
1
1
1
0
1
1
4
0
3
1
2
1
0
0
0
2
1
4
0
1
3
3
0
0
0
0
1
3
1
0
1
0
6
0
3
0
1
0
0
1
1
1
0
2
2
1
3
6
0
3
0
0
1
0
5
0
5
2
0
4
0
1
1
0
0
3
0
2
4
1
1
5
1
0
4
1
0
0
4
0
2
3
0
0
0
0
8
2
5
1
0
1
4
1
1
1
0
1
1
5
1
2
3
2
3
1
0
0
1
4
1
1
2
0
1
4
1
1
1
2
8
1
2
1
0
0
1
4
1
8
1
1
3
1
1
1
0
0
4
2
0
2
0
2
1
0
1
4
1
3
0
1
0
0
0
1
3
0
1
1
5
0
2
1
1
0
0
2
2
1
0
0
1
1
2
1
3
4
1
1
1
1
1
0
1
1
4
1
1
0
1
1
2
2
1
2
1
0
3
1
6
0
3
2
0
0
1
0
0
2
1
1
2
1
1
1
3
0
2
0
1
0
1
4
2
2
2
1
0
1
0
0
2
2
3
3
1
0
2
3
1
0
0
0
8
3
1
1
0
4
1
1
2
3
0
1
1
0
1
1
1
3
1
0
12
1
0
1
3
0
1
3
4
1
1
0
0
2
1
0
3
1
0
1
0
0
0
2
2
1
0
0
1
1
2
0
5
0
0
2
0
1
1
9
1
1
3
0
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
0
8
1
0
0
2
0
1
2
2
1
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
3
2
3
1
1
1
3
2
5
10
2
1
1
0
1
3
2
0
2
2
3
0
1
0
1
1
1
0
1
0
1
1
2
4
0
0
2
1
0
0
1
1
2
2
0
1
0
3
0
3
0
0
3
2
8
1
1
0
1
2
1
0
2
2
1
1
3
0
0
0
1
1
0
0
1
1
2
0
1
1
2
0
3
1
0
0
2
5
0
1
0
2
0
3
1
1
8
1
0
1
2
1
1
3
0
0
2
0
2
0
1
1
0
0
0
1
0
1
1
2
2
1
2
0
5
1
2
0
5
4
3
0
2
0
0
3
2
0
1
4
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
3
3
2
2
4
0
1
2
8
1
0
0
0
3
0
0
2
2
1
2
1
0
1
0
3
0
1
1
1
0
1
0
14
0
1
0
1
0
2
1
0
7
0
0
0
1
0
2
1
1
1
0
1
0
4
0
1
2
2
2
2
1
2
3
0
0
0
0
1
2
0
0
1
0
0
3
1
1
2
1
0
1
1
2
0
2
3
1
1
1
1
1
3
1
1
3
0
1
2
1
0
0
1
1
0
2
2
1
3
0
0
3
1
3
1
1
5
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
1
2
0
12
1
5
2
1
2
1
0
3
2
1
0
0
1
1
0
2
0
0
0
2
2
1
0
1
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
1
1
0
0
0
1
1
1
1
2
2
0
2
4
2
1
1
2
1
2
5
4
1
6
1
1
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
1
0
0
10
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
6
0
0
0
1
0
2
0
2
0
2
3
1
2
0
0
1
3
1
0
1
1
2
1
3
4
2
1
4
3
1
1
1
3
2
0
0
1
2
1
1
1
1
0
1
1
1
2
13
1
0
2
0
0
1
1
3
1
1
0
2
1
0
0
0
2
0
0
0
2
2
3
0
1
0
2
2
1
2
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
3
0
1
0
13
0
1
1
3
1
1
3
0
0
0
1
7
1
1
2
1
1
0
2
3
0
1
0
1
0
2
0
2
1
3
0
6
1
1
0
0
0
2
0
2
3
3
1
1
0
3
1
1
1
5
0
1
0
1
2
5
2
1
0
1
0
0
1
1
1
4
1
0
1
1
0
1
1
7
0
2
1
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
3
2
1
1
1
2
2
0
2
1
2
0
0
2
0
3
1
0
2
3
2
4
4
0
1
7
1
4
1
2
0
2
2
1
1
1
1
0
0
2
2
3
2
2
3
2
1
4
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
8
1
2
0
1
2
0
4
1
3
0
1
0
3
2
1
0
2
2
2
1
4
1
1
1
2
0
0
2
2
0
0
0
3
2
2
1
0
2
0
0
2
5
0
0
2
3
2
0
0
1
1
0
2
0
2
3
0
0
1
2
0
2
0
1
0
1
1
3
2
2
1
0
0
0
0
0
1
0
1
2
2
1
0
0
0
7
3
0
2
0
0
1
1
3
0
2
0
1
0
2
0
0
0
1
3
2
1
4
1
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
1
0
4
0
1
0
0
5
1
1
1
1
1
1
0
1
0
1
1
5
2
0
0
2
0
1
2
1
2
2
0
0
0
1
3
0
0
3
1
1
3
1
1
1
1
1
0
2
2
1
1
0
1
2
0
0
4
0
0
2
1
0
1
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
4
2
3
2
0
3
1
0
1
0
0
5
6
0
2
2
0
2
0
1
0
1
1
1
1
2
0
0
0
0
3
1
2
0
3
1
1
0
1
1
0
5
0
0
2
1
0
0
0
1
4
2
1
0
0
1
2
2
1
1
4
2
1
1
1
2
0
1
0
3
1
2
2
2
0
0
1
4
0
9
0
2
0
3
0
2
0
1
1
0
0
1
0
1
1
0
1
1
0
2
0
0
0
1
0
5
1
0
0
0
1
2
0
2
0
0
12
1
0
0
0
4
0
1
2
0
1
0
0
1
1
2
3
1
2
0
1
1
2
0
2
0
6
1
0
1
1
1
0
0
10
0
0
3
9
1
3
0
1
2
3
0
1
1
1
1
2
1
1
0
3
1
2
2
0
1
1
1
0
0
1
1
1
3
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
2
0
2
0
4
2
1
0
0
1
1
0
2
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
3
1
2
1
2
1
3
0
1
1
1
1
1
8
0
0
3
0
1
2
1
1
3
1
3
1
1
0
0
4
2
6
9
0
1
1
1
1
2
5
2
0
1
1
0
1
0
1
0
0
0
1
3
0
0
1
0
2
0
0
1
0
1
0
0
1
0
7
1
4
0
2
0
8
0
2
1
1
1
1
0
9
0
0
1
0
1
1
1
0
0
1
0
5
1
1
3
0
0
2
0
0
0
1
2
1
0
2
0
0
5
1
0
0
0
0
2
1
3
2
0
2
0
0
0
0
3
0
1
16
2
4
2
0
0
1
2
2
1
0
0
1
0
1
0
1
0
1
1
3
2
0
3
1
0
1
2
2
0
3
0
1
0
1
1
1
2
2
2
1
0
2
1
1
1
2
0
2
1
2
1
1
0
1
3
2
3
3
2
0
2
0
0
1
0
1
5
1
2
2
3
2
2
1
1
0
0
2
2
0
0
0
2
1
1
0
0
1
1
1
0
3
0
2
2
1
3
0
1
1
1
2
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
6
1
1
0
1
1
2
1
0
0
1
1
0
1
3
2
2
2
0
2
3
2
1
1
1
0
0
0
0
2
0
1
3
0
3
0
0
4
1
1
1
4
1
1
2
1
1
0
0
1
3
1
2
14
2
1
2
1
0
2
5
2
1
1
0
2
1
2
1
0
2
0
0
1
0
0
0
2
1
1
1
5
1
0
0
1
1
0
5
1
2
1
0
3
0
0
0
9
3
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
2
3
1
3
2
2
0
3
0
0
2
0
2
1
0
3
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
0
0
2
1
1
0
3
0
2
0
1
0
0
1
1
0
0
2
0
3
0
1
4
3
0
2
2
0
1
1
2
1
0
2
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
1
1
0
14
1
1
2
1
2
0
9
1
1
1
0
1
0
7
0
0
1
1
0
0
1
0
2
2
2
1
1
2
2
11
2
1
1
1
0
0
0
0
3
2
2
1
1
0
1
0
0
2
2
1
1
0
0
3
2
0
1
1
0
2
1
1
0
0
2
0
2
0
1
0
0
1
3
2
0
2
1
1
0
1
0
1
0
2
2
2
2
1
0
0
0
4
4
2
1
1
0
4
3
0
1
5
2
0
14
0
0
6
1
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
0
2
2
1
1
0
0
2
0
3
2
0
3
0
0
2
1
1
3
0
0
2
0
2
2
2
1
0
1
1
1
1
1
0
1
2
2
0
0
0
1
1
1
3
0
0
1
2
3
2
1
1
2
0
0
0
1
2
1
1
0
3
2
1
0
0
2
0
4
2
0
2
2
2
1
0
0
2
1
1
0
0
1
1
0
0
3
2
0
2
1
0
2
2
1
4
2
0
1
1
2
7
4
1
1
2
2
3
0
0
1
0
2
2
0
0
0
1
0
0
1
1
2
2
0
3
4
0
1
2
2
1
2
0
2
0
1
0
0
0
1
3
0
1
1
1
2
1
0
2
0
0
1
0
0
2
3
0
2
0
1
2
0
0
1
0
2
1
1
1
2
0
3
2
2
1
0
0
3
1
1
2
1
0
1
1
1
0
3
0
5
2
2
2
1
2
1
0
0
2
1
2
0
0
2
4
3
0
1
2
0
2
0
0
1
1
1
1
1
1
0
3
7
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
1
1
6
1
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
2
0
1
1
1
3
1
2
0
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
0
1
0
2
0
0
0
5
1
1
0
1
0
0
0
2
2
3
1
1
1
3
2
0
1
1
0
3
0
3
0
1
3
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
1
1
0
4
0
2
1
0
0
1
0
2
1
2
2
2
1
0
0
1
3
0
0
0
1
0
1
0
1
1
2
0
2
0
1
4
1
2
0
0
2
2
0
0
1
0
1
1
1
0
0
0
1
3
1
0
0
1
3
1
2
0
0
0
0
2
0
2
1
1
0
1
2
1
0
1
7
1
3
0
1
0
0
1
0
1
0
1
0
0
2
4
1
0
2
0
0
2
1
1
0
2
2
0
1
0
1
3
2
2
1
0
2
5
2
1
0
2
0
1
0
1
12
1
0
0
0
1
1
2
0
2
1
0
0
1
5
1
0
2
1
0
0
1
0
3
4
0
0
0
2
0
2
0
6
0
1
3
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
1
10
0
1
0
0
1
1
6
1
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
4
0
1
0
1
0
0
3
1
1
0
2
14
0
1
0
0
1
0
1
3
0
0
0
0
5
2
1
0
0
1
0
0
1
3
1
2
0
0
0
1
0
1
0
2
0
4
1
2
0
0
3
0
1
0
0
0
3
1
1
0
0
2
0
0
1
0
1
0
3
2
2
5
1
0
0
2
1
1
1
0
0
0
0
0
1
1
0
2
2
0
1
1
3
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
1
0
2
1
2
1
3
5
2
0
0
2
0
0
0
0
2
2
0
7
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
3
0
1
1
0
0
3
3
0
1
1
1
0
0
0
1
0
1
4
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
5
0
3
1
2
0
0
1
1
0
1
0
7
1
1
1
1
0
0
0
1
1
3
4
2
3
0
1
2
1
1
0
1
4
0
1
0
1
0
0
2
0
1
1
0
1
1
2
6
0
1
1
4
1
2
1
0
5
0
0
0
3
0
2
0
1
0
0
0
2
2
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
3
0
1
0
3
0
0
0
0
1
2
0
0
0
1
1
2
1
1
1
1
0
0
3
1
0
1
3
1
0
0
0
0
1
3
0
0
2
1
0
1
0
0
8
1
0
0
1
0
2
1
0
0
4
2
1
2
1
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
1
0
2
0
2
0
2
0
7
0
0
0
0
15
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
0
3
0
0
2
2
1
0
1
2
1
1
1
2
0
0
1
0
0
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
7
0
2
0
0
0
2
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
4
2
2
0
0
3
0
2
0
0
2
1
1
2
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
1
3
1
2
1
3
0
3
0
0
0
0
0
1
1
2
2
0
1
1
2
0
1
1
0
3
1
0
1
1
1
0
0
0
1
1
0
1
4
0
5
2
1
0
0
3
0
1
0
0
0
1
1
1
1
2
2
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
2
3
0
1
2
1
0
0
0
1
1
2
1
0
0
0
2
1
1
1
1
0
2
0
1
2
1
1
1
0
0
1
0
2
1
1
1
3
11
2
4
2
2
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
1
1
1
3
0
2
0
0
0
1
0
11
0
1
0
1
1
2
0
0
3
0
2
0
5
1
0
1
0
6
1
1
0
0
0
3
0
1
2
1
0
5
1
1
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
2
0
2
7
1
4
2
3
0
0
1
1
0
1
0
1
2
2
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
3
1
4
12
0
0
13
0
3
1
0
2
0
0
0
1
0
4
0
1
1
0
2
2
2
0
2
0
0
1
7
1
3
0
0
1
0
2
0
2
0
2
8
0
0
1
0
0
1
0
0
1
1
1
4
1
0
0
2
0
1
0
12
1
1
2
1
0
0
0
2
1
0
0
1
2
1
0
0
0
3
1
1
0
7
2
1
1
0
1
3
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
1
3
0
0
1
1
1
9
2
1
4
0
2
1
0
1
0
1
1
0
0
1
1
1
13
1
0
3
4
0
0
1
3
2
2
1
1
1
1
1
0
2
1
1
2
2
2
0
1
1
1
7
4
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
1
2
1
0
0
3
0
1
0
0
1
0
0
4
1
1
1
1
3
0
2
0
0
2
1
0
0
2
3
0
0
1
1
5
1
0
0
1
1
2
3
1
1
1
0
2
0
0
0
0
0
10
0
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
2
2
2
0
1
0
1
2
0
0
0
1
2
0
2
1
3
1
0
1
1
0
0
1
1
2
1
2
2
1
1
1
2
0
3
7
2
7
2
0
1
1
1
0
3
0
2
2
2
2
3
0
0
3
12
1
0
5
1
1
1
1
0
2
1
1
1
0
2
1
1
1
3
1
2
1
0
0
0
3
1
1
3
4
0
3
0
2
2
0
0
0
0
1
0
2
1
0
1
1
4
1
2
1
1
4
5
0
0
10
1
0
6
0
3
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
1
0
8
1
5
1
2
1
3
2
0
3
1
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
3
3
1
0
1
2
2
0
1
1
1
0
1
0
1
2
2
1
0
1
1
1
0
1
0
1
2
0
1
1
0
0
0
1
0
3
0
1
0
0
1
2
0
0
0
5
1
1
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
3
3
0
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
1
0
1
0
4
2
0
2
1
0
0
0
1
0
2
2
10
1
1
1
6
0
1
0
0
0
2
1
0
0
0
2
1
1
1
0
3
1
0
3
2
0
1
0
2
1
0
1
0
0
1
0
3
0
0
0
8
1
0
1
0
0
0
0
0
0
0
10
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
1
1
0
3
1
1
2
10
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
1
0
1
0
3
0
2
1
2
0
1
0
0
2
1
0
1
1
2
0
0
1
0
1
1
0
0
1
1
2
1
0
1
0
2
0
2
0
1
1
1
0
5
1
2
0
1
1
0
0
3
0
1
0
2
0
0
0
0
1
2
1
4
2
1
1
0
2
2
1
1
0
0
1
2
0
0
2
3
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
1
0
1
2
0
1
0
1
2
3
0
0
0
1
1
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
2
1
0
1
1
2
2
0
2
2
1
0
1
1
1
0
0
1
1
3
2
4
0
0
1
2
1
0
2
2
7
1
0
1
1
1
0
0
1
1
1
1
1
0
1
12
0
0
1
1
3
1
0
1
1
1
1
0
1
0
0
0
0
0
1
3
4
2
0
0
0
1
0
1
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
12
7
3
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
1
3
0
4
6
1
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
1
0
3
1
1
1
0
1
1
1
0
8
1
0
0
1
0
0
2
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
0
0
0
1
2
0
4
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
2
1
2
2
0
4
1
0
0
2
1
0
8
1
3
1
1
7
3
2
0
0
0
1
4
0
1
0
1
3
2
0
1
0
0
2
1
0
1
0
1
0
0
0
11
0
2
1
0
0
1
0
0
0
0
0
0
0
0
4
1
3
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
2
0
1
1
0
1
0
1
0
1
0
1
2
1
0
1
1
1
3
5
0
0
0
2
2
2
1
0
1
2
0
1
0
0
1
2
0
1
0
0
2
1
1
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
1
1
0
0
1
0
1
1
1
2
2
5
0
2
5
2
1
0
0
1
1
0
2
5
2
0
2
1
1
0
0
0
1
2
0
0
2
5
1
1
1
2
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
3
0
2
2
2
1
0
8
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
9
1
0
1
1
0
2
1
0
10
0
1
1
1
0
1
3
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
1
0
1
2
0
1
0
1
1
2
0
1
0
0
0
1
2
2
1
0
1
0
0
1
0
0
1
1
0
0
0
3
1
0
2
1
0
0
0
0
0
0
4
2
3
0
1
0
1
0
2
2
0
2
1
0
0
2
2
1
1
3
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
1
1
0
2
4
1
0
1
1
1
2
0
1
6
2
1
0
0
1
1
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
7
1
0
0
0
1
1
0
1
1
0
2
0
2
1
0
2
0
0
2
1
1
1
0
0
0
1
0
0
0
4
1
1
0
1
1
2
0
2
1
2
0
3
0
0
1
7
0
2
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
2
2
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
2
4
0
1
1
0
0
1
1
0
0
0
3
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
3
1
0
0
2
2
0
0
1
2
0
0
1
1
0
1
0
0
3
2
1
2
1
1
1
0
0
0
5
0
1
1
3
1
0
1
2
2
0
1
1
0
0
0
0
2
3
2
1
0
1
0
1
2
1
3
0
1
0
2
12
0
1
1
1
0
1
1
8
0
0
1
0
1
1
11
0
3
1
0
4
0
0
0
2
0
5
0
1
0
1
0
4
1
0
0
2
3
0
0
1
2
0
0
2
0
0
0
3
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
3
1
0
0
1
1
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
1
3
1
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
1
2
0
0
2
11
1
1
1
0
1
0
1
1
2
1
0
1
2
5
1
1
0
0
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
2
0
1
0
0
3
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
1
1
1
2
0
0
1
0
0
2
5
1
1
2
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
4
2
4
1
1
7
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
6
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
3
0
0
2
0
1
1
0
1
1
1
1
0
1
0
1
0
2
1
0
2
0
1
1
0
3
0
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
1
0
0
3
1
0
0
3
0
1
0
0
1
0
1
1
3
7
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
2
1
0
1
2
1
0
2
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
4
1
1
0
0
2
1
0
1
2
0
0
0
1
2
2
1
0
1
3
1
1
0
0
1
2
0
2
0
0
1
1
0
1
1
2
0
2
8
1
1
0
3
0
0
1
0
4
0
1
1
1
1
2
1
3
0
3
1
2
0
0
1
0
0
0
1
0
1
0
2
0
1
0
3
10
0
1
1
0
1
0
1
0
0
1
0
4
0
7
1
1
1
1
1
0
0
0
0
2
0
5
0
1
0
0
0
6
1
3
2
10
1
1
2
1
2
0
1
1
1
2
2
0
0
1
0
1
2
0
0
0
1
1
1
6
2
1
0
0
0
1
1
0
0
0
0
1
0
8
1
3
1
0
0
0
0
3
0
0
0
1
0
8
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
1
1
0
2
1
2
0
1
0
0
2
1
2
3
0
1
1
2
2
1
2
0
1
1
0
2
0
0
2
0
1
0
6
1
1
2
1
1
2
1
0
9
0
1
0
0
0
0
3
1
2
1
1
0
1
2
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
4
0
0
0
0
0
0
1
8
2
0
2
1
0
7
2
0
1
4
1
2
0
0
3
0
2
1
1
1
0
1
0
0
1
1
1
0
2
0
4
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
6
1
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
1
0
0
2
0
0
1
0
1
1
0
1
2
2
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
1
0
0
2
0
0
1
1
0
1
0
0
1
2
2
1
1
0
0
3
1
0
0
1
5
0
0
0
1
2
1
1
0
0
1
1
2
2
0
2
0
1
0
1
2
1
1
0
0
0
1
0
0
0
2
1
1
0
4
0
0
0
1
0
0
3
0
1
1
0
1
5
1
0
0
5
1
1
0
0
2
1
0
1
1
1
1
1
1
3
0
0
0
1
1
2
0
0
0
3
1
0
0
2
0
1
0
2
0
0
0
0
2
0
6
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
1
1
0
0
2
1
0
0
0
3
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
3
1
3
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
1
0
1
1
3
1
3
0
2
1
0
4
1
0
0
1
0
0
0
2
1
0
0
0
1
1
1
1
1
0
0
5
0
2
3
1
0
1
1
0
0
0
0
1
1
0
1
0
2
1
1
1
2
0
0
0
0
2
1
1
1
0
0
1
1
2
0
1
1
0
2
0
0
4
2
0
7
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
6
0
0
1
1
0
2
2
0
0
1
0
1
0
0
3
0
1
0
2
2
1
8
0
1
0
0
0
3
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
4
0
0
1
3
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
2
3
2
1
1
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
3
1
2
0
0
0
2
0
2
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
3
1
4
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
1
1
1
1
2
1
0
1
0
1
2
0
1
1
0
1
1
1
0
0
0
0
1
0
2
1
3
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
0
1
3
2
1
3
0
0
1
3
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
2
0
2
2
2
0
0
0
1
0
1
2
2
0
0
6
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
1
2
0
1
0
0
1
0
1
2
0
1
1
2
2
1
1
1
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
6
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
1
3
0
0
2
0
1
0
0
1
2
0
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
1
1
1
1
2
0
1
0
2
1
2
0
1
0
1
0
1
2
0
2
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
2
1
0
1
0
2
0
1
1
1
1
0
2
0
0
0
2
0
2
0
0
20
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
0
3
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
7
2
3
3
1
0
1
0
0
0
2
5
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
6
0
0
0
0
1
1
2
1
0
1
1
0
0
4
0
0
1
0
1
1
6
1
1
1
8
1
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
0
1
0
1
3
1
0
1
1
0
2
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
1
2
1
0
1
0
0
0
3
0
1
2
2
0
0
0
0
0
1
1
0
0
0
9
9
2
1
1
0
2
1
0
6
0
4
0
1
1
0
0
1
1
1
1
0
2
1
0
1
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
6
1
1
1
1
0
0
2
0
1
0
1
3
0
0
1
1
0
0
0
8
0
0
0
1
0
0
2
0
0
1
0
0
0
4
1
1
1
0
0
2
0
2
1
6
2
0
1
2
0
0
0
0
1
0
14
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
2
1
14
1
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
3
3
1
2
0
1
0
0
1
1
0
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
3
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
2
2
1
2
0
1
2
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
2
0
4
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
2
2
5
0
1
1
0
2
1
0
2
1
1
2
0
0
1
2
0
3
4
0
1
1
0
0
1
0
0
0
3
0
1
2
0
0
0
1
1
0
1
1
1
1
0
0
14
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
4
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
7
0
1
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
5
2
1
1
2
0
3
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
5
0
1
0
0
1
1
1
0
3
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
1
0
6
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
0
1
1
1
0
2
0
2
1
0
0
2
0
0
0
3
1
1
1
0
0
0
2
0
0
0
1
3
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
3
1
0
0
4
0
1
1
0
0
0
2
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
1
10
2
0
1
0
0
0
1
0
1
2
1
0
3
1
2
1
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
2
2
1
1
0
1
0
1
0
0
2
0
0
1
1
1
2
1
0
1
1
0
0
5
0
1
0
1
1
1
0
6
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
1
9
1
0
0
0
0
2
0
0
0
1
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
2
0
1
3
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
8
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
2
1
0
0
1
2
0
1
0
0
0
3
1
0
2
1
0
0
1
1
0
0
1
1
0
1
0
0
0
3
0
1
0
0
0
8
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
4
0
0
0
1
4
1
1
1
0
1
0
0
0
1
0
7
1
0
0
0
0
0
0
2
0
1
2
0
2
0
2
1
0
0
8
2
1
1
0
1
0
2
0
2
3
2
0
0
1
2
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
3
0
1
1
1
6
2
0
4
0
0
1
0
0
0
0
1
1
0
5
3
2
1
1
1
0
0
1
1
1
3
0
0
1
0
1
0
19
0
1
1
2
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
7
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
12
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
1
0
0
0
0
0
3
2
2
1
1
1
1
2
0
0
3
0
7
2
0
1
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
1
2
5
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
7
0
1
0
0
4
2
0
0
1
2
0
9
0
0
1
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
1
1
0
1
0
0
1
0
0
7
0
0
0
4
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
5
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
5
1
0
1
0
0
1
0
0
0
1
3
0
5
0
1
1
0
0
0
1
0
0
1
1
1
2
0
0
0
1
6
0
1
0
1
1
2
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
2
1
8
1
0
0
0
0
0
0
0
0
0
11
1
0
0
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
5
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
1
0
0
1
0
0
0
0
0
3
0
4
1
0
0
0
1
5
1
0
9
0
0
0
0
0
0
5
1
0
1
1
0
1
3
2
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
10
1
1
1
2
0
2
1
1
0
0
0
1
0
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
1
2
0
1
0
1
2
0
1
1
1
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
9
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
0
1
0
1
1
0
2
0
1
0
1
1
1
0
0
0
0
1
0
1
0
2
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
5
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
3
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
16
0
1
0
0
1
0
0
0
0
1
0
0
1
15
0
0
0
0
0
2
1
1
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
8
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
13
0
1
0
0
0
0
1
2
0
0
0
2
1
0
10
1
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
1
2
3
0
0
18
0
1
3
0
0
1
0
0
0
3
0
1
0
1
0
2
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
8
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
1
0
0
4
0
0
0
1
2
0
0
0
9
1
0
1
0
0
0
1
2
0
7
0
0
1
0
1
0
2
0
1
1
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
0
1
4
1
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
3
0
0
3
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
4
0
1
0
0
2
1
1
2
1
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
3
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
4
0
0
0
1
1
0
0
3
1
1
0
5
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
1
0
5
1
0
0
2
1
5
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
4
0
0
1
0
4
2
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
3
1
0
0
0
1
0
0
1
0
1
0
4
0
0
1
1
5
0
0
0
1
13
0
0
3
0
0
0
0
2
1
2
0
1
1
0
0
1
2
0
0
0
2
0
1
7
0
1
0
1
1
0
0
0
0
2
1
1
1
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
6
1
0
0
0
0
0
0
1
1
0
2
0
3
6
0
0
0
0
2
0
1
0
1
1
0
0
4
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
0
1
1
2
0
1
0
1
0
1
11
0
0
0
0
0
2
0
3
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
9
0
1
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
6
1
1
0
0
0
1
1
1
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
4
1
0
0
0
1
1
3
7
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
10
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
5
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
5
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
3
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
3
0
1
0
2
0
1
0
0
3
1
1
2
1
2
0
0
0
0
0
0
2
0
0
1
1
1
2
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
1
0
0
9
0
0
2
0
0
1
0
2
0
0
0
2
1
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
9
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
5
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
2
0
1
1
7
0
0
2
1
1
0
3
3
2
1
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
2
0
5
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
1
1
2
4
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
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
1
2
1
1
3
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
6
0
0
1
0
3
1
0
1
1
18
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
1
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
10
1
2
1
1
1
0
1
1
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
2
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
3
0
0
0
1
0
0
0
0
1
0
3
3
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
6
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
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
6
0
1
0
1
0
1
3
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
1
1
1
0
1
2
0
0
0
0
1
0
0
1
3
0
0
1
0
3
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
6
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
3
1
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
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
4
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
3
0
1
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
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
9
0
0
0
0
0
5
0
0
0
1
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
12
0
1
0
1
0
0
1
0
1
0
11
0
0
0
0
0
0
0
0
1
2
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
2
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
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
2
0
1
1
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
1
0
5
0
2
1
0
2
0
1
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
1
0
1
0
2
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
2
0
0
3
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
0
2
1
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
10
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
4
8
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
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
1
1
0
0
0
0
0
3
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
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
1
0
1
1
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
1
2
1
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
6
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
16
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
4
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
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
8
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
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
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
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
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
5
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
1
0
0
0
12
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
8
2
0
1
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
2
0
0
4
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
1
3
0
0
1
0
3
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
8
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
1
0
1
0
0
0
5
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
2
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
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
6
1
0
0
0
0
11
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
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
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
5
2
0
1
1
0
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
3
2
0
0
0
1
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
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
13
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
6
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
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
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
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
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
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
6
0
0
0
0
0
1
0
2
0
3
0
1
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
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
4
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
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
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
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
1
0
1
5
0
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
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
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
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
7
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
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
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
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
9
1
2
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
1
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
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
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
0
0
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
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
1
0
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
10
0
0
1
0
5
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
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
4
1
0
0
0
0
1
1
0
6
0
0
1
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
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
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
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
5
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
10
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
4
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
1
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
10
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
8
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
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
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
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
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
1
1
0
1
0
0
3
0
0
0
0
4
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
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
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
7
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
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
9
0
0
1
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
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
4
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
10
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
3
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
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
3
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
2
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
4
1
0
0
0
0
0
1
0
0
0
0
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
0
0
1
0
0
0
1
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
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
3
1
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
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
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
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
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
9
0
0
1
0
0
0
0
1
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
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
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
0
0
2
1
0
1
2
0
0
1
0
0
10
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
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
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
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
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
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
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
1
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
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
6
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
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
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
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
9
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
12
1
0
0
1
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
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
25
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
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
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
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
8
0
0
0
0
0
0
1
1
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
2
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
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
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
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
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
2
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
1
0
0
0
0
4
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
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
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
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
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
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
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
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
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
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
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
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
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
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
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
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
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
14
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
5
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
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
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
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
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
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
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
1
0
1
0
0
0
0
1
0
0
0
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
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
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
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
1
0
2
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
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
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
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
1
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
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
1
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
1
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
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
1
1
0
0
0
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
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
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
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
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
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
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
1
0
0
0
0
0
4
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
12
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
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
2
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
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
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
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
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
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
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
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
1
0
1
0
0
1
0
0
0
4
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
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
1
0
3
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
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
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
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
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
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
1
1
0
0
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
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
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
0
0
0
0
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
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
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
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
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
1
0
0
0
0
0
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
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
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
3
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
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
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
3
0
0
0
0
1
0
1
0
0
1
25
2
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
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
1
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
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
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
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
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
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
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
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
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
0
0
0
0
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
1
0
0
0
1
0
11
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
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
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
1
0
0
0
0
0
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
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
1
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
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
2
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
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
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
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
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
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
1
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
2
4
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
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
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
0
0
0
1
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
1
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
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
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
2
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
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
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
1
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
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0