0
1
1
0
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1
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0
0
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2
0
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0
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0
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0
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0
2
0
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0
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0
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1
0
1
1
0
1
0
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1
0
1
0
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0
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0
1
0
0
2
1
0
1
0
1
2
0
1
0
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0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
3
1
2
1
1
0
0
0
3
2
0
1
3
3
1
1
0
0
1
3
0
2
1
0
0
0
0
0
0
1
3
1
0
1
0
1
0
1
2
0
0
0
3
2
5
1
0
2
3
2
3
1
2
2
1
3
2
1
3
2
4
3
1
2
1
2
3
4
4
5
4
2
3
3
4
7
3
3
6
5
7
5
10
12
5
6
10
11
14
17
11
15
18
15
14
20
19
19
17
27
20
15
19
23
26
30
27
19
29
27
31
26
33
31
29
30
43
36
38
38
30
39
32
36
28
40
34
34
41
36
50
26
31
33
43
33
36
44
37
52
38
49
42
53
42
38
42
48
43
38
33
48
35
32
33
18
24
30
26
25
14
23
25
14
14
15
31
18
8
14
7
10
13
10
6
7
6
6
9
0
5
5
7
5
1
0
3
2
1
1
0
1
3
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
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0
0
0
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1
0
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0
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1
0
0
0
0
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0
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1
0
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0
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1
0
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1
0
0
0
0
0
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0
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0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
4
1
0
1
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
1
3
1
0
1
1
1
1
0
0
3
2
2
2
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
2
2
2
0
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
2
3
2
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
1
2
3
1
4
1
0
1
0
1
0
1
2
0
1
0
1
2
1
0
1
0
0
1
2
0
0
2
2
0
0
3
1
3
2
1
2
0
1
0
4
1
4
1
2
3
1
4
5
4
3
5
4
3
2
2
3
2
2
6
1
2
3
3
1
0
3
2
2
2
4
3
7
3
4
5
1
4
5
3
5
3
5
6
1
2
3
7
2
4
4
3
5
3
3
2
1
3
1
0
3
4
0
0
2
3
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
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
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
1
2
0
0
0
0
1
0
0
2
3
1
1
1
1
2
0
0
0
1
1
1
2
2
1
1
2
2
4
0
1
0
2
0
5
0
1
0
2
1
1
1
0
0
1
1
2
4
3
1
1
2
1
1
2
1
0
2
1
2
1
2
1
3
2
2
6
1
1
2
6
2
2
0
0
1
2
2
3
4
3
2
2
1
3
1
3
3
5
3
5
5
7
4
6
1
1
4
2
2
4
6
2
4
2
2
6
5
5
2
7
2
1
5
8
2
8
4
3
3
10
4
6
3
9
7
3
6
6
1
5
7
4
4
5
4
8
11
6
6
8
6
11
10
7
6
5
11
11
11
10
8
9
4
9
4
11
9
9
9
12
21
8
10
13
10
10
15
11
9
15
15
13
11
11
11
13
14
19
16
15
8
14
18
18
17
14
21
20
13
17
20
19
26
27
20
19
19
22
22
17
18
24
15
19
22
32
31
32
21
31
32
29
27
28
34
41
45
57
40
56
52
51
36
72
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