0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
93
3
46
47
123
4
48
139
4
0
0
0
1
1
1
5
0
5
17
5
3
1
1
5
1
0
1
1
0
0
0
0
2
0
1
0
6
0
6
54
32
7
16
1
38
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
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
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
47
0
0
0
0
0
1
0
4
0
1
0
1
0
0
2
0
2
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
1
5
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
35
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
282
604
47
0
2
1
1
0
0
1
0
35
0
0
0
0
125
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
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
1
5
0
0
1
3
9
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
6
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
35
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
1
0
0
3
1
5
8
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
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
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
3
1
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
5
0
0
0
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
1
0
0
4
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
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
1
0
0
0
0
0
0
0
0
0
0
46
0
0
0
2
4
11
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
37
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
70
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
125
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
36
0
0
0
0
0
0
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
2
0
8
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
125
0
0
0
0
0
1
2
0
1
1
2
0
2
3
2
0
3
0
1
0
1
1
0
7
1
2
0
0
0
1
0
0
0
0
3
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
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
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
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
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
126
1
0
0
0
0
9
7
1
0
0
1
0
0
4
1
0
0
5
0
8
0
0
125
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
7
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
11
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
2
125
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
125
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
2
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
127
0
0
0
0
0
0
1
1
126
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
7
7
0
8
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
125
1
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
4
0
0
0
2
0
2
4
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
2
0
0
125
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
3
9
0
0
0
4
1
0
46
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
6
19
0
3
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
3
0
5
0
0
0
0
15
4
1
76
186
8
233
18
3
28
4
1
0
13
1
4
0
0
1
1
10
1
3
2
4
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
4
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
11
3
2
0
1
0
0
1
0
1
0
2
5
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
1
0
0
35
0
0
0
0
2
0
0
9
0
0
0
0
0
0
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
7
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
7
6
0
0
0
39
3
0
1
2
1
0
2
0
2
0
1
3
2
0
1
1
0
0
1
0
35
0
1
3
1
0
1
5
3
3
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
5
2
4
0
1
1
0
0
3
2
24
10
34
1
0
4
4
1
1
0
1
0
3
3
1
1
0
0
0
0
2
1
1
1
3
1
1
1
0
0
0
0
3
4
2
6
0
1
1
2
2
2
0
0
0
1
1
0
1
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
3
0
1
2
0
0
0
1
0
1
0
2
0
3
0
0
3
0
1
1
0
0
5
1
1
1
0
0
1
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
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
1
0
2
1
0
0
0
0
1
76
19
25
3
4
0
0
0
0
0
1
0
0
0
0
1
0
35
0
0
0
3
0
1
10
8
8
2
1
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
3
0
11
0
0
0
8
0
0
1
0
125
7
4
0
0
0
3
0
0
1
4
251
36
0
1
0
22
1
0
0
0
0
0
0
3
2
4175
439
9
1
0
2
0
6
1
0
377
1
4
3
0
0
0
3
0
4
0
0
0
0
0
1
3
0
1
3
0
0
0
0
125
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
4
2
0
0
2
1
6
1
0
125
8
3
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
7
5
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
3
3
0
0
5
0
1
2
1
0
0
3
0
0
1
2
0
3
0
0
1
0
0
0
2
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
2
0
2
0
0
0
4
1
1
2
0
0
0
0
0
0
125
0
0
1
0
0
0
1
0
1
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
3
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
125
0
0
2
0
0
0
0
0
0
0
3
7
0
0
1
0
0
0
1
0
3
0
1
35
2
3
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
3
14
0
0
0
2
48
46
0
1
0
1
0
0
0
0
0
0
13
0
0
0
0
0
0
0
1
46
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
50
0
0
0
1
0
0
0
0
0
0
46
0
1
0
1
0
3
0
0
2
3
3
0
2
3
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
6
1
0
2
1
0
0
5
2
1
0
3
4
48
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
2
1
0
0
0
250
0
0
1
0
1
0
0
0
5
4
6
5
1
0
0
0
0
1
0
0
0
4
1
0
1
1
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
125
0
0
1
5
2
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
3
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
125
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
125
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
4
1
0
0
0
1
1
1
1
2
0
6
1
1
0
0
0
4
3
5
1
1
0
0
0
0
0
1
0
0
0
0
0
1
96
0
125
0
0
1
94
46
0
2
1
1
5
3
12
1
0
5
0
2
0
0
2
0
1
0
5
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
6
1
0
0
5
46
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
6
7
1
1
0
1
6
5
1
2
6
1
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
125
0
0
0
1
0
0
0
5
0
3
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
5
0
0
0
0
0
0
0
0
0
1
2
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
35
0
0
0
0
0
1
0
0
0
0
0
2
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
3
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
125
0
0
35
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
2
1
1
0
2
1
4
0
2
0
1
8
0
4
35
0
5
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
2
1
0
0
2
0
1
0
0
0
125
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
2
0
0
0
2
0
0
4
3
2
2
6
1
3
9
2
3
9
12
0
47
0
5
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
8
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
9
0
0
0
1
3
2
20
1
6
0
1
6
0
0
0
0
2
6
0
4
0
2
1
3
0
0
0
2
0
11
5
1
1
0
2
5
2
3
13
1
0
1
1
1
0
0
5
0
4
125
1
6
0
2
1
2
1
0
2
4
1
0
0
2
2
3
1
10
1
1
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
6
31
0
1
0
2
1
1
0
1
0
3
4
0
0
1
1
0
4
127
2
6
2
5
0
1
2
1
2
0
0
0
0
3
0
0
2
0
0
1
1
1
1
0
0
0
0
0
4
1
0
3
2
0
0
0
2
1
1
0
2
0
1
3
0
6
0
2
0
2
4
1
0
0
0
0
0
0
0
5
4
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
7
38
1
4
129
5
0
0
0
0
0
0
0
6
0
0
0
1
0
0
2
3
0
0
0
0
10
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
1
1
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
11
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
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
9
14
11
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
2
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
1
1
1
0
3
1
3
0
0
0
1
0
0
0
1
6
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
3
2
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
12
3
0
0
6
1
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
6
0
1
0
0
0
3
0
1
0
2
1
0
0
4
0
1
0
1
4
0
0
4
0
2
0
1
0
0
0
0
0
3
0
0
0
1
8
4
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
10
1
0
1
1
1
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
2
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
4
0
2
0
3
2
0
0
1
5
0
1
0
2
2
0
2
0
0
0
0
125
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
6
0
2
0
1
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
6
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
35
0
0
46
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
1
1
1
0
2
1
0
0
0
0
46
0
46
46
1
0
1
2
0
1
0
1
1
1
0
46
0
0
0
0
0
0
0
0
1
2
0
1
0
47
2
0
0
1
0
1
0
0
1
1
1
2
48
2
0
0
0
0
0
0
2
1
0
0
0
1
3
0
1
0
0
1
0
1
1
5
2
1
0
15
0
0
0
10
4
1
21
0
0
1
3
0
0
0
3
0
1
3
2
2
0
0
4
3
0
1
8
1
3
1
1
0
2
1
8
7
0
0
0
0
50
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
125
0
0
0
0
0
2
5
0
2
0
0
0
4
46
0
0
0
0
0
0
0
1
0
0
0
1
0
0
49
3
1
0
0
0
0
1
4
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
47
1
0
5
0
2
2
0
0
1
0
0
0
1
47
1
1
2
1
47
5
2
3
0
4
22
11
14
7
6
0
3
3
46
6
8
0
2
0
2
1
0
0
0
0
0
46
0
0
2
0
0
0
0
0
125
250
0
0
0
0
4
47
1
0
0
0
0
0
0
0
1
0
1
1
1
1
46
0
0
0
0
1
0
0
0
0
0
0
1
0
0
46
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
49
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
12
2
0
2
53
1
1
2
0
11
4
0
3
3
0
0
0
3
5
3
0
49
18
7
0
1
6
2
1
2
1
46
0
1
0
3
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
1
0
48
2
2
1
0
0
0
1
0
1
4
2
1
0
0
2
0
47
1
0
10
0
3
0
2
0
0
5
1
0
2
20
1
1
1
2
3
3
0
3
3
2
47
1
2
11
0
3
1
2
5
0
1
0
1
1
1
0
0
0
0
0
0
46
0
3
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
128
18
3
9
3
0
1
0
0
46
0
0
0
3
2
1
0
125
1
0
0
0
0
2
0
1
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
47
0
0
0
125
126
1
1
1
2
0
2
0
4
0
1
0
0
4
2
0
0
0
0
2
8
0
1
2
0
1
1
3
0
0
0
5
0
2
2
1
2
5
6
3
1
2
2
3
0
2
0
2
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
10
3
52
0
0
4
3
0
0
0
1
2
1
2
4
0
52
14
2
1
2
0
0
4
20
3
0
1
8
4
0
2
0
0
3
0
1
2
0
0
0
9
0
0
0
35
0
0
1
0
0
0
0
0
3
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
2
46
3
2
2
0
0
1
0
0
0
3
6
2
0
0
0
0
2
50
2
0
1
0
3
4
2
1
0
1
0
1
3
0
0
2
0
0
0
0
2
4
1
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
46
1
0
0
30
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
47
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
1
5
0
0
4
0
2
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
3
2
0
0
3
0
1
1
0
1
2
1
0
4
0
2
1
1
1
1
1
0
0
0
0
35
0
0
0
1
0
0
3
25
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
1
1
0
3
0
0
46
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
23
46
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
46
1
0
0
0
0
0
0
0
0
0
0
46
0
3
2
6
1
9
1
1
0
1
0
1
0
0
0
125
3
1
2
50
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
134
0
152
1
0
0
1
7
8
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
129
1
0
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
1
2
0
1
7
0
1
2
2
1
0
1
1
1
4
17
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
5
5
0
2
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
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
23
4
7
16
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
46
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
7
0
0
0
0
0
0
0
0
4
5
7
2
1
0
0
0
2
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
7
4
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
0
3
0
1
0
0
0
1
1
6
0
0
0
0
0
0
125
0
0
0
0
1
4
2
70
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
46
0
4
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
93
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
3
0
1
0
1
0
46
2
6
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
35
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
35
0
0
0
0
8
1
0
1
0
0
0
101
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
125
0
0
0
0
36
2
2
1
0
0
1
1
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
2
9
0
0
0
0
3
0
0
4
0
0
18
0
0
0
1
46
2
93
0
0
46
0
0
0
0
125
0
0
250
0
0
1
1
0
0
0
0
0
0
0
3
8
1
125
2
0
4
1
1
1
0
4
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
29
2
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
3
18
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
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
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
3
1
6
0
1
0
0
0
0
0
0
1
0
2
0
0
0
4
10
0
0
0
0
0
0
0
1
0
0
27
0
26
0
0
0
2
2
3
129
9
2
27
2
0
9
48
18
22
37
99
43
63
4
15
81
27
28
36
0
36
3
0
0
0
1
0
0
0
0
9
0
9
0
9
3
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
5
4
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
36
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
125
0
0
0
0
0
0
0
0
250
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
5
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
126
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
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
2
1
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
47
1
0
0
0
47
0
1
1
1
1
0
0
0
0
0
0
0
125
0
0
0
0
0
2
3
3
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
24
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
126
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
125
0
0
0
2
1
2
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
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
1
1
0
0
4
0
0
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
4
1
3
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
125
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
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
2
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
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
2
4
0
1
3
0
1
0
0
1
0
0
46
1
0
0
0
0
0
0
24
2
1
0
0
0
4
1
0
0
0
2
6
0
0
0
0
1
0
0
46
46
48
1
302
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
46
0
1
1
4
0
2
3
0
1
2
3
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
51
1
1
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
4
0
95
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
4
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
46
2
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
13
0
0
0
2
92
1
0
0
1
1
0
0
47
0
1
0
4
1
1
0
4
1
0
0
3
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
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
0
0
0
0
0
2
0
0
10
0
0
0
0
2
6
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
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
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
1
0
0
0
0
1
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
1
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
5
0
5
0
0
0
3
0
1
0
0
0
2
0
2
0
1
5
2
0
1
0
0
2
0
0
0
1
4
0
0
4
7
0
0
0
0
0
0
3
0
0
1
0
0
0
0
6
2
0
1
128
9
6
13
4
3
0
2
7
5
3
0
1
5
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
125
2
14
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
6
2
1
1
0
1
0
1
0
0
7
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
125
2
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
46
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
105
0
0
0
0
0
0
2
0
0
0
1
2
47
0
0
93
47
3
46
0
46
0
1
1
46
1
48
1
0
47
96
52
95
96
126
144
116
0
48
0
0
46
46
1
46
92
1
2
47
0
47
0
0
5
3
48
1
1
2
50
0
0
0
1
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
8
0
1
8
4
3
2
1
0
1
2
1
2
1
1
0
0
0
1
0
0
0
0
4
1
0
1
2
1
0
2
0
1
1
0
0
0
0
2
1
1
8
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
127
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
6
8
3
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
35
4
2
1
0
6
7
3
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
8
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
46
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
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
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
4
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
1
1
0
0
0
3
47
0
140
46
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
6
1
0
0
1
0
0
0
0
0
2
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
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
1
0
2
1
1
2
2
0
0
1
0
4
0
0
7
5
0
0
1
1
2
5
3
5
1
3
1
6
3
0
0
0
2
1
0
2
0
0
3
0
0
2
0
0
250
0
0
0
0
0
0
0
0
0
0
0
4
0
4
4
4
0
0
0
0
0
0
0
0
0
1
39
3
0
0
0
1
1
0
1
0
1
2
3
1
0
2
3
1
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
1
5
1
3
125
2
0
0
1
0
0
0
1
0
2
2
0
0
1
1
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
0
0
1
2
2
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
3
1
0
0
122
8
1
0
1
1
35
0
0
0
2
1
0
13
5
13
4
2
3
1
0
0
0
3
4
14
126
8
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
36
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
250
0
0
1
0
0
0
1
0
1
3
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
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
125
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
0
4
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
3
3
0
0
1
1
0
0
0
0
1
0
2
0
7
10
0
0
2
1
0
0
0
0
0
1
2
4
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
6
0
1
0
0
0
13
3
15
1
5
4
2
0
0
4
2
8
1
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
125
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
35
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
1
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
126
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
21
1
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
5
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
15
3
3
0
7
12
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
1
0
3
1
1
125
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
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
2
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
0
1
0
0
0
0
0
4
0
5
1
0
3
2
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
125
0
0
1
1
0
3
0
0
0
0
1
7
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
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
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
125
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
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
250
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
46
1
4
1
5
16
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
94
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
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
49
0
1
46
0
0
0
0
1
0
0
1
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
46
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
125
0
0
0
4
6
3
0
0
0
5
0
1
0
0
2
1
0
1
0
0
0
2
0
1
2
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
0
0
1
0
0
0
125
0
0
0
0
1
0
0
9
1
0
0
0
0
0
0
0
0
96
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
7
1
0
3
0
0
1
0
1
0
2
0
1
5
1
1
0
2
0
1
0
0
0
0
0
36
0
0
1
11
0
4
0
3
0
6
5
0
0
0
0
2
0
1
0
0
4
0
0
23
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
13
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
49
0
4
4
2
0
0
1
1
0
1
2
2
3
0
0
0
47
0
0
0
0
108
15
0
46
0
0
0
0
0
0
29
1
0
0
5
0
0
0
1
0
4
0
3
0
0
0
3
6
0
3
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
3
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
2
0
0
2
0
0
3
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
250
0
0
0
0
0
2
0
0
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
1
0
1
1
0
1
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
250
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
125
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
125
1
0
3
0
0
0
0
0
0
4
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
7
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
2
2
0
0
0
5
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
125
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
1
0
0
1
163
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
1
2
8
1
0
0
0
3
3
6
9
3
9
3
8
1
2
2
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
2
36
1
1
1
0
3
2
0
0
4
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
1
7
2
2
2
7
2
2
3
2
0
1
8
2
0
8
2
0
3
8
2
1
3
0
1
0
2
1
0
1
0
0
0
2
1
0
3
4
0
0
0
2
0
0
2
0
0
1
0
1
35
3
3
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
3
4
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
5
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
4
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
5
0
4
1
5
3
0
1
3
1
3
3
0
1
2
3
0
1
7
2
0
2
2
1
1
0
1
2
3
0
2
2
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
24
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
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
1
1
0
0
2
6
1
2
1
1
2
6
0
0
0
0
0
0
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
125
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
92
47
0
0
0
0
0
47
1
171
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
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
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
8
0
0
0
3
0
0
4
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
10
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
35
0
3
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
250
125
0
0
0
0
0
0
2
1
2
3
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
4
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
4
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
5
0
9
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
5
0
5
1
0
4
6
1
3
0
1
4
3
3
5
2
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
11
0
2
0
0
1
0
2
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
0
0
0
0
0
0
0
0
125
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
5
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
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
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
8
2
0
0
0
0
0
1
0
0
0
1
0
1
36
1
2
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
128
0
1
1
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
125
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
7
0
0
0
0
0
2
0
0
0
2
0
126
4
0
0
0
0
1
0
0
0
0
0
0
46
0
0
0
1
2
47
46
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
4
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
5
5
2
2
2
0
0
3
1
0
3
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
37
0
0
2
0
2
4
0
0
1
6
3
1
1
1
2
2
3
1
1
0
0
0
250
2
2
1
0
0
0
0
0
0
0
10
15
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
14
14
3
3
9
5
7
0
2
9
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
1
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
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
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
4
1
1
0
0
4
2
0
1
0
0
0
5
1
3
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
1
0
2
2
0
5
18
9
2
0
0
20
20
0
0
0
15
10
0
0
4
7
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
16
30
67
8
4
19
0
3
1
3
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
125
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
9
2
1
0
2
3
0
0
1
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
3
10
2
0
3
1
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
126
0
1
0
0
35
0
0
0
2
0
1
0
40
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
2
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
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
0
1
1
1
2
258
9
0
3
3
15
310
4
129
2
3
6
6
3
0
1
0
1
0
0
0
0
0
1
0
0
5
0
1
6
4
4
5
3
1
0
2
2
1
9
0
2
0
0
0
2
0
2
1
3
14
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
35
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
125
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
35
0
1
0
0
0
0
0
125
0
0
2
0
0
0
4
0
2
0
0
0
35
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
1
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
11
0
1
0
0
0
125
0
0
0
0
3
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
4
2
0
0
3
1
0
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
0
125
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
7
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
2
0
0
0
0
3
0
2
1
4
1
0
0
4
1
1
0
0
0
3
1
4
0
1
0
0
0
0
0
2
0
3
0
0
0
0
24
8
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
4
46
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
4
4
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
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
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
126
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
125
4
0
0
0
0
0
0
0
4
2
71
0
0
0
0
35
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
8
2
27
3
8
3
0
0
6
0
2
1
4
2
12
0
0
0
0
0
1
0
0
8
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
2
2
2
1
127
0
0
0
1
2
1
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
2
5
2
3
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
0
0
0
0
1
0
0
0
0
0
0
0
4
9
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
46
1
46
1
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
3
2
4
3
6
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
48
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
1
127
0
0
0
4
0
4
2
0
6
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
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
125
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
1
3
1
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
4
5
4
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
7
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
46
0
0
0
0
0
0
1
2
99
0
46
5
0
1
1
0
46
0
0
0
0
0
0
46
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
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
126
0
0
0
0
0
1
1
2
0
0
0
0
1
35
1
4
10
0
0
0
0
0
1
0
0
0
0
0
0
0
3
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
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
4
0
0
2
1
0
0
2
2
2
3
0
0
0
4
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
46
0
1
0
47
1
0
0
46
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
1
0
6
0
0
0
0
1
8
0
1
14
1
0
0
3
4
0
5
3
0
3
0
0
1
0
0
5
5
2
0
0
0
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
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
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
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
2
3
0
0
0
0
3
0
0
0
0
0
0
0
35
0
0
0
1
1
0
1
0
0
0
0
0
127
0
0
0
0
6
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
4
0
0
1
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
35
0
0
0
2
0
0
1
0
2
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
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
47
2
0
3
0
1
3
0
0
1
2
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
2
0
0
0
0
8
2
2
0
0
1
0
1
2
4
2
0
0
0
0
0
0
1
0
0
1
3
0
1
0
3
1
0
0
1
0
2
125
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
125
0
0
0
0
1
0
1
1
0
0
125
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
1
1
2
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
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
4
1
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
4
2
2
6
2
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
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
10
1
1
2
0
1
0
1
1
0
0
3
0
2
3
2
0
3
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
3
0
3
0
3
0
0
0
1
2
1
0
0
0
0
3
5
4
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
8
0
2
1
0
1
2
2
6
1
125
0
3
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
3
0
0
0
1
0
0
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
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
1
0
1
3
0
127
3
0
0
8
2
0
2
1
8
0
0
1
0
1
0
7
1
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
3
1
1
2
0
2
0
8
10
0
0
1
1
0
2
0
2
0
4
2
3
2
0
2
1
0
3
6
0
0
0
0
1
1
0
0
6
0
1
2
2
0
0
0
142
1
0
0
3
0
0
3
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
1
3
0
4
5
1
1
1
0
0
2
1
0
1
3
7
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
35
0
1
1
0
2
0
0
0
5
0
2
2
1
0
0
0
0
0
0
125
0
250
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
3
4
0
0
0
0
0
0
0
1
0
0
0
0
0
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
2
0
0
0
2
0
0
0
0
0
0
1
0
48
2
1
0
1
1
0
1
1
1
0
0
0
0
0
2
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
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
93
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
50
0
0
0
0
5
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
1
0
0
0
96
0
47
0
1
0
0
0
46
47
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
375
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
3
0
2
0
3
0
2
1
0
1
0
3
3
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
4
0
0
0
1
0
1
0
0
0
1
1
0
0
6
1
2
0
0
0
0
1
0
2
0
3
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
125
126
0
125
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
6
10
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
139
126
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
46
0
127
1
0
3
0
1
1
0
3
0
0
0
0
0
0
0
586
0
356
0
2
1
1
25
2
0
387
2
1
3
0
0
0
1
0
0
0
11
0
0
0
0
1
0
125
0
126
153
126
0
1
2
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
3
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
2
9
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
3
0
0
2
0
0
4
1
0
0
1
1
0
0
0
1
0
0
0
1
126
0
7
13
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
127
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
35
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
39
1
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
4
0
0
0
0
0
1
8
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
46
1
1
0
0
1
2
574
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
126
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
6
0
0
1
1
0
0
48
1
4
2
0
0
0
0
2
1
3
1
125
0
47
1
0
1
0
0
1
8
11
0
2
0
6
7
133
0
1
1
1
9
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
0
2
0
0
0
250
0
0
0
0
0
1
1
1
7
1
2
1
3
0
2
0
0
1
1
1
0
2
0
0
4
3
3
2
1
4
0
0
0
2
2
0
0
3
0
0
0
0
0
0
5
4
0
0
0
1
1
0
0
0
0
1
1
0
5
2
0
0
0
0
14
5
29
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
105
0
0
0
3
0
1
3
0
2
3
1
0
0
0
0
0
0
0
8
5
0
0
0
0
1
6
0
0
0
0
0
0
0
0
7
0
0
1
2
1
1
0
1
0
0
0
0
2
0
4
0
0
0
1
0
0
4
7
0
0
12
0
0
3
0
4
11
2
2
1
0
0
0
35
0
1
3
1
0
0
1
2
2
5
1
5
0
0
0
3
0
2
2
3
1
0
1
0
0
2
0
0
0
0
3
2
3
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
3
0
0
0
4
3
3
3
0
0
4
1
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
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
47
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
5
1
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
9
12
1
5
4
6
3
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
2
0
1
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
5
0
0
1
0
0
0
2
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
16
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
60
105
0
94
20
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
3
2
2
0
0
3
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
3
2
0
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
7
3
4
0
7
3
0
30
19
9
9
1
2
1
1
6
3
8
4
0
0
0
0
4
1
0
1
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
6
2
0
0
125
1
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
3
0
6
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
6
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
38
0
0
0
0
0
0
2
0
5
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
7
2
1
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
3
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
8
0
0
0
1
1
1
0
47
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
125
1
135
1
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
126
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
38
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
2
6
0
4
2
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
11
1
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
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
2
0
0
0
1
4
5
4
1
0
0
0
4
0
1
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
2
3
0
3
1
4
0
1
0
1
0
2
0
0
1
0
0
2
0
1
49
1
0
3
47
0
46
0
2
0
1
0
1
1
6
4
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
2
1
0
1
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
5
3
0
0
0
9
2
1
0
0
3
0
3
0
2
2
0
3
0
1
0
0
2
2
3
0
0
0
0
0
0
0
3
0
1
1
0
2
2
4
2
2
3
3
6
2
0
9
4
2
0
3
7
4
2
3
5
2
10
2
0
6
1
2
0
7
5
2
2
5
4
0
0
4
5
127
3
1
2
2
4
3
6
4
22
57
33
55
23
8
18
29
523
245
11
15
13
6
8
4
9
130
4
2
0
7
2
13
3
2
1
1
127
9
2
6
3
2
6
4
4
1
0
0
0
1
0
3
2
0
1
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
8
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
6
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
0
4
0
1
4
0
1
0
4
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
4
0
0
1
1
0
0
0
4
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
2
5
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
8
8
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
2
0
1
2
2
0
0
0
1
1
0
3
3
0
5
5
0
1
0
0
0
0
0
1
0
36
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
35
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
5
0
0
0
0
0
0
0
4
1
4
1
1
2
0
0
1
1
1
0
0
2
0
0
5
7
1
1
4
0
2
0
0
0
0
1
1
1
3
0
0
0
126
1
0
1
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
10
1
0
1
1
0
1
2
0
0
1
1
0
0
2
0
1
3
16
4
1
0
0
0
0
6
1
0
0
1
0
0
1
125
1
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
10
125
3
0
1
0
5
0
1
0
0
2
2
1
6
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
35
0
0
0
0
0
35
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
4
1
0
0
0
1
1
0
0
0
0
0
0
47
0
0
0
0
0
0
4
0
0
46
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
0
7
0
2
5
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
47
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
5
0
0
0
0
0
4
0
2
4
2
0
4
0
0
0
1
2
2
0
0
0
4
4
0
1
0
3
0
4
2
2
5
6
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
9
1
22
1
50
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
