0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
4
1
1
0
3
47
47
1
0
0
2
1
0
0
0
0
0
1
1
3
2
0
0
0
0
1
2
46
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
3
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
1
1
2
1
0
6
0
1
1
0
0
1
1
0
9
0
4
0
2
0
4
0
0
1
0
0
46
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
1
1
0
0
0
0
0
0
1
2
2
5
0
3
0
1
0
0
0
0
3
0
0
0
0
127
1
3
4
0
0
0
0
1
0
0
0
1
0
4
35
0
0
8
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
1
12
0
0
0
0
0
0
1
2
0
0
6
0
0
0
0
0
0
2
1
4
1
0
0
1
3
0
0
0
0
4
2
2
4
10
3
0
0
0
1
1
1
0
1
0
0
7
0
0
0
1
0
1
13
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
4
35
0
0
1
0
0
0
0
0
0
0
0
0
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
2
0
0
0
125
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
125
0
0
1
0
0
0
1
0
0
4
1
0
0
0
0
35
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
125
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
125
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
11
2
2
1
4
0
0
1
0
0
0
0
0
0
0
1
0
1
4
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
3
2
0
1
0
3
6
0
0
1
0
2
1
2
0
4
2
1
1
0
0
0
0
0
1
0
0
47
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
6
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
1
3
5
2
6
0
11
8
21
9
4
0
0
3
0
0
2
0
1
2
1
0
0
0
0
4
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
46
0
0
0
46
0
0
47
47
0
234
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
49
140
1
0
4
3
2
0
0
0
1
0
0
0
3
8
1
0
2
0
1
0
125
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
0
0
0
127
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
2
1
2
0
0
1
3
1
2
0
8
3
2
2
0
0
106
0
125
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
3
0
0
3
0
1
0
5
3
0
0
2
1
2
3
0
2
8
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
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
0
0
0
3
2
26
46
22
17
14
15
239
21
18
48
6
18
3
3
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
94
48
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
35
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
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
1
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
10
3
1
3
13
0
2
2
6
0
0
4
14
0
0
0
0
4
2
0
0
1
0
0
0
2
0
0
36
4
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
1
2
3
0
0
5
0
0
1
0
2
0
1
0
0
1
2
0
0
0
47
4
8
3
2
1
2
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
126
64
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
125
0
0
0
0
0
0
0
2
2
0
0
5
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
1
1
1
6
0
0
125
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
1
0
125
0
0
0
7
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
6
2
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
125
0
0
0
1
0
0
1
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
3
0
0
0
46
1
1
6
0
0
0
0
1
0
2
2
2
0
2
3
3
0
0
0
0
0
1
2
11
0
3
1
0
0
0
0
3
2
1
0
57
2
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
1
1
0
0
2
26
189
1
0
0
0
0
1
0
0
46
1
0
1
0
0
37
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
3
0
0
0
10
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
1
0
2
1
3
0
1
2
1
4
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
0
1
1
1
2
4
0
0
0
0
4
1
0
0
0
3
4
36
0
1
0
0
1
0
0
0
126
3
0
4
10
2
0
4
27
1
2
2
0
1
128
134
18
1
1
0
3
5
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
1
1
3
0
1
0
1
0
0
0
0
0
2
2
1
1
1
1
0
125
0
6
9
6
1
10
6
40
2
127
1
3
0
0
0
8
3
4
0
2
1
0
2
2
0
1
7
17
18
7
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
92
46
1
49
0
2
0
46
0
0
1
46
278
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
2
1
2
1
3
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
9
5
2
0
0
1
0
1
0
1
8
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
46
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
3
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
5
2
3
1
8
1
3
20
1
1
1
1
3
4
2
0
1
3
2
0
0
0
0
0
5
1
2
4
0
0
0
0
0
0
0
0
50
0
0
0
1
0
0
0
1
0
0
3
0
94
0
0
1
1
6
3
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
46
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
3
0
1
1
1
0
0
0
35
0
0
0
0
70
3
0
0
36
0
0
0
0
0
0
0
0
3
5
0
2
0
3
2
0
0
0
1
0
1
0
9
0
1
0
0
0
0
0
0
0
9
0
7
1
27
0
4
0
2
0
0
0
0
0
0
53
1
0
1
3
4
0
1
0
0
0
0
0
4
8
12
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
94
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
0
0
0
1
4
1
0
5
1
0
0
0
0
0
2
0
0
2
4
0
1
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
3
2
2
0
0
0
0
0
0
0
0
0
0
2
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
2
0
0
0
0
1
0
0
1
1
46
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
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
3
0
0
0
2
2
0
0
2
1
3
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
46
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
4
4
0
3
1
1
1
0
5
0
11
6
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
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
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
5
4
1
0
4
0
0
0
1
3
1
0
4
3
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
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
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
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
13
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
125
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
2
14
3
1
4
2
4
1
0
0
0
0
2
1
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
17
12
1
0
1
0
125
0
2
1
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
1
2
0
0
8
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
46
1
0
0
0
2
0
2
0
0
2
2
2
0
2
5
5
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
2
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
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
47
47
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
2
1
1
0
1
0
1
2
0
3
0
3
0
1
0
0
0
1
0
2
4
0
2
6
1
3
0
0
0
0
1
0
3
0
2
1
1
4
3
4
1
1
4
13
4
1
4
2
4
0
0
0
0
0
0
1
1
0
1
0
2
138
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
46
94
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
1
0
1
0
0
0
0
0
4
3
1
4
1
3
1
0
3
8
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
8
4
6
5
4
2
0
1
0
7
2
5
4
0
0
1
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
126
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
7
2
4
0
7
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
2
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
1
1
0
1
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
125
0
0
2
0
0
0
2
0
51
46
0
0
0
2
0
2
1
2
4
1
4
0
0
4
2
0
3
4
0
0
2
0
3
10
9
0
0
2
2
7
4
1
2
0
3
5
1
0
3
1
5
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
0
7
0
0
3
0
0
0
93
0
4
1
0
0
1
2
0
0
0
2
0
0
0
2
126
0
2
129
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
4
1
92
0
0
11
2
0
0
125
0
47
1
0
0
2
0
0
0
4
0
12
1
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
4
0
0
125
4
2
6
0
9
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
55
0
20
0
0
0
0
0
1
0
0
1
8
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
11
0
1
0
0
1
12
0
1
0
55
16
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
9
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
5
0
1
4
4
5
5
33
1
3
0
35
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
35
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
125
0
0
125
1
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
1
125
0
0
0
0
0
0
0
125
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
7
1
0
0
0
38
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
3
0
0
3
0
0
0
0
0
0
6
1
2
0
0
3
1
0
0
0
4
0
4
0
0
0
0
0
0
1
0
1
4
0
0
1
3
0
5
2
0
0
1
0
0
0
0
0
0
1
1
1
0
3
0
4
0
6
1
1
2
0
0
3
0
1
3
2
0
1
0
3
2
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
46
46
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
1
1
0
0
48
1
0
0
0
0
0
126
125
28
1
7
2
6
0
4
3
0
0
1
0
0
46
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
10
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
2
1
2
0
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
8
9
0
0
0
4
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
48
0
47
48
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
8
393
15
26
1
0
0
1
0
96
2
0
0
1
1
1
0
0
0
0
0
1
4
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
126
0
0
0
0
0
0
0
0
0
0
2
125
0
2
3
2
0
1
0
1
3
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
1
0
0
0
0
0
2
0
3
6
1
3
4
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
1
0
2
3
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
35
0
0
0
0
0
0
0
0
0
0
1
1
142
138
97
420
46
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
2
1
2
0
2
0
0
0
0
0
0
2
1
2
0
0
3
1
1
0
1
0
0
0
0
0
0
1
0
125
0
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
2
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
8
1
0
0
0
0
1
0
3
5
2
1
0
0
0
0
0
1
1
0
35
0
0
0
0
0
0
0
1
35
0
0
0
0
0
1
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
4
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
0
0
0
0
1
1
3
0
1
3
0
0
4
0
0
3
2
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
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
9
0
2
1
0
0
3
3
2
1
0
1
4
0
0
0
0
0
6
0
0
10
4
0
1
1
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
386
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
19
1
6
0
125
1
1
0
2
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
128
0
0
0
2
3
48
1
0
125
34
0
11
0
3
0
23
2
43
81
4
1
7
0
2
7
11
47
20
1
10
0
0
7
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
5
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
2
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
46
0
47
2
0
0
0
1
0
0
0
0
8
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
47
0
50
50
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
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
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
2
0
0
0
0
0
0
0
0
0
0
1
3
46
0
0
2
1
1
0
0
0
0
0
92
0
1
116
46
0
5
93
50
1
5
7
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
1
6
3
5
1
2
1
0
3
3
4
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
4
3
0
1
0
0
0
2
0
3
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
1
3
0
9
0
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
46
2
0
0
3
0
125
0
0
0
0
92
0
0
46
2
0
0
0
0
2
47
0
0
0
0
0
0
0
46
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
6
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
5
1
0
4
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
6
0
8
5
2
19
9
0
0
4
2
0
4
0
0
0
0
2
1
0
0
0
0
0
8
0
1
0
0
0
0
1
5
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
3
0
0
1
0
2
0
4
0
4
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
9
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
2
0
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
1
125
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
0
0
0
5
4
1
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
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
0
0
2
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
3
1
0
0
1
92
3
6
1
0
3
3
2
0
0
0
2
0
0
0
2
8
9
14
21
15
0
0
0
1
4
5
21
0
0
2
1
2
0
2
2
0
0
15
2
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
3
2
1
0
1
3
4
1
0
2
4
0
0
0
2
0
3
2
2
5
4
4
1
2
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
3
0
25
14
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
47
2
0
0
1
4
2
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
5
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
3
0
0
0
3
1
3
1
2
2
3
0
9
128
18
0
67
5
0
12
0
19
13
18
15
0
0
0
36
0
1
0
0
0
0
0
0
0
0
0
1
1
0
36
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
125
1
0
1
0
1
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
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
4
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
3
3
6
1
5
0
1
0
1
0
13
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
7
16
10
0
0
0
0
0
1
1
0
0
0
1
2
3
2
0
11
0
0
0
0
10
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
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
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
125
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
35
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
35
0
0
1
0
0
0
0
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
1
2
0
1
0
0
0
0
0
0
0
1
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
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
0
1
2
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
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
4
7
1
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
1
0
0
0
0
0
0
0
35
1
4
0
0
0
0
0
0
0
0
0
1
0
0
35
0
0
2
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
1
0
0
35
0
0
0
6
0
0
127
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
2
0
0
0
0
0
0
0
0
2
2
3
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
126
2
0
0
0
12
129
0
0
0
4
1
0
1
4
6
0
3
128
1
0
2
0
0
1
1
0
0
3
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
1
0
1
0
3
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
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
125
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
5
1
3
3
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
14
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
6
0
0
4
4
1
0
0
1
0
0
1
0
3
9
2
1
1
0
4
36
1
3
1
47
0
0
46
0
0
10
0
0
1
2
0
1
1
0
1
0
9
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
125
0
0
0
0
0
2
0
0
0
125
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
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
1
0
1
3
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
8
0
0
2
1
2
0
0
1
17
15
3
3
0
2
1
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
131
2
1
0
2
2
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
1
0
1
24
8
0
1
0
0
0
0
1
2
0
0
1
1
2
2
3
4
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
8
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
1
1
9
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
4
0
0
0
0
0
0
0
0
0
0
0
0
126
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
1
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
9
1
0
3
0
2
0
0
3
0
5
131
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
3
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
125
0
0
0
1
0
1
0
0
0
129
0
0
0
0
0
0
4
9
2
0
0
11
1
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
1
1
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
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
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
1
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
9
0
0
0
0
0
0
0
0
0
2
0
4
1
1
4
4
0
3
0
0
2
0
4
2
9
2
1
1
1
0
1
2
1
3
0
5
1
0
0
4
3
9
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
2
0
0
0
125
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
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
7
0
1
38
4
0
0
0
0
1
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
7
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
2
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
125
0
0
125
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
1
0
0
0
0
0
0
0
0
1
0
0
0
4
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
0
0
2
1
0
3
1
0
0
0
0
1
0
0
2
0
1
0
1
6
0
0
2
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
35
1
0
0
0
46
0
1
0
47
0
0
47
0
1
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
105
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
2
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
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
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
2
0
12
5
9
1
0
0
0
0
93
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
125
0
0
0
125
1
0
1
0
0
0
0
0
1
3
1
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
1
0
0
0
0
0
2
0
845
228
0
3
0
0
0
0
5
1
0
0
1
1
0
0
0
0
2
0
5
0
7
49
2
0
3
13
0
0
0
0
0
2
19
0
0
0
1
0
1
3
13
92
0
4
1
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
35
0
0
1
16
2
4
51
0
0
7
0
0
0
0
2
0
3
9
1
0
2
1
2
0
0
0
0
0
2
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
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
2
0
0
0
0
0
0
0
0
0
0
36
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
6
0
0
0
47
0
0
0
0
1
1
0
0
0
0
0
125
125
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
105
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
2
7
1
0
2
3
5
0
1
1
0
0
125
126
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
4
0
55
13
11
0
2
3
4
0
2
1
3
1
0
1
8
21
2
16
0
21
7
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
125
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
9
0
0
0
0
0
0
36
0
0
0
0
0
0
2
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
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
14
9
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
4
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
750
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
46
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
46
93
0
47
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
51
1
3
0
0
0
0
0
0
1
0
46
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
3
0
3
0
1
0
0
2
125
0
2
0
2
0
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
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
35
1
1
6
10
14
2
9
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
2
3
0
1
5
16
3
5
7
22
1
2
16
1
4
2
0
1
2
4
1
0
2
7
1
0
0
1
0
0
0
3
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
20
0
2
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
270
3
0
0
1
0
0
1
0
1
92
46
0
46
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
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
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
13
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
48
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
46
0
1
0
0
1
0
0
0
0
46
0
9
9
17
36
2
1
0
0
0
0
46
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
2
1
0
1
2
0
2
2
4
0
3
0
2
1
1
3
2
3
184
24
1
0
0
1
0
2
0
1
0
2
4
94
4
0
4
2
0
6
9
46
6
4
6
3
4
0
0
0
0
3
46
51
0
3
0
3
101
1
0
3
0
0
0
4
2
0
5
1
0
5
0
0
0
4
1
0
3
56
25
0
7
0
1
3
3
0
3
47
1
2
0
0
1
3
3
1
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
4
0
6
0
0
24
0
6
18
1
9
4
4
21
0
2
0
1
1
0
0
0
3
0
3
0
0
0
0
4
5
1
0
2
0
1
0
0
1
16
1
1
0
0
0
0
1
2
0
4
9
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
6
1
0
0
37
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
46
0
47
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
46
0
0
0
0
0
0
0
0
0
1
0
0
3
12
0
1
0
0
0
0
0
0
6
5
0
2
9
0
0
4
1
2
1
0
1
1
0
0
2
4
2
51
0
46
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
1
2
1
1
0
0
2
1
0
0
2
0
0
46
51
1
0
0
0
1
0
125
3
5
1
139
1
117
371
1
0
0
0
0
0
0
3
0
1
0
4
47
4
0
4
3
0
0
0
93
0
46
1
2
0
0
0
0
0
0
1
72
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
6
20
6
0
10
58
2
5
1
1
3
36
1
1
2
21
3
26
12
26
3
11
0
2
0
0
0
0
4
4
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
5
0
0
0
0
1
4
0
0
1
1
0
1
0
2
0
6
0
1
0
0
0
0
0
5
0
1
0
1
2
0
0
1
46
2
0
0
1
2
6
2
0
1
0
1
0
1
4
0
0
1
0
1
3
0
3
6
0
1
4
255
2
1
2
2
0
4
0
0
1
0
7
10
1
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
3
1
0
1
0
9
3
0
0
1
1
2
0
0
0
0
0
0
46
1
0
47
46
0
0
0
0
0
1
0
0
46
2
1
1
0
0
0
1
0
0
0
1
1
0
0
2
93
92
1
6
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
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
0
0
1
0
0
0
0
47
93
46
0
0
0
0
1
47
0
0
117
47
0
0
1
0
0
0
46
1
0
46
1
186
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
36
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
8
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
125
0
0
0
0
0
0
0
1
3
0
82
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
4
258
2
4
0
2
0
0
2
0
0
7
1
5
0
2
4
1
0
0
0
0
0
0
8
4
0
2
0
3
35
0
0
0
4
4
0
48
0
48
1
47
0
0
0
0
0
0
25
1
1
99
2
4
46
1
0
1
0
0
46
0
46
0
125
1
0
0
0
1
0
0
0
2
8
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
9
3
2
46
0
46
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
2
5
3
1
0
0
47
1
0
1
47
162
0
0
0
185
0
0
0
0
1
0
0
47
0
47
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
1
0
0
0
1
4
0
2
5
0
7
7
6
0
0
0
0
0
8
1
1
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
7
50
179
6
5
190
56
14
2
1
0
47
2
47
1
1
3
0
1
193
106
0
64
5
11
4
4
1
0
8
0
0
0
0
0
0
0
1
0
0
4
0
0
0
6
0
1
0
0
1
10
0
0
0
0
0
1
0
0
2
1
0
0
35
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
4
2
0
1
0
0
1
0
0
0
0
0
3
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
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
1
1
0
1
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
3
0
0
1
0
0
0
4
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
5
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
1
5
0
2
0
0
1
0
125
0
0
2
125
250
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
9
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
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
1
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
0
0
0
0
0
3
4
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
2
2
0
2
25
21
19
22
0
0
0
9
1
2
0
93
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
46
46
46
2
0
0
0
0
0
0
0
1
0
0
0
0
0
46
0
218
46
0
0
46
1
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
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
138
0
0
0
0
0
0
0
0
0
2
66
280
141
54
293
50
1
12
0
233
280
2
0
1
0
0
0
0
2
141
0
1
0
0
0
50
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
4
18
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
4
0
0
0
46
0
2
0
0
0
6
5
1
0
2
2
0
0
3
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
4
3
6
10
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
1
2
0
17
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
4
125
0
0
1
1
3
1
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
0
2
3
5
3
2
6
1
1
0
0
1
1
0
0
1
11
10
16
3
0
1
0
0
49
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
7
0
1
125
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
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
47
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
1
0
0
0
0
0
0
0
0
1
7
3
2
4
1
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
6
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
4
3
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
3
1
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
251
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
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
3
0
1
0
0
0
0
0
6
0
5
3
0
2
1
0
0
0
0
0
0
1
2
1
0
2
2
0
2
0
0
0
0
0
0
0
6
3
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
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
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
7
2
2
1
0
0
0
0
2
3
11
2
8
41
8
5
4
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
46
0
0
1
0
0
0
0
0
0
0
0
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
35
1
0
4
2
46
0
0
0
0
0
0
0
0
1
46
0
0
0
0
0
0
3
0
0
5
0
1
1
1
0
1
0
0
0
47
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
4
0
4
1
0
0
0
0
0
1
126
0
0
0
0
1
0
0
0
1
0
7
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
46
93
0
0
0
95
0
0
0
0
1
0
0
0
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
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
14
0
0
0
1
4
2
1
1
0
1
7
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
8
0
0
1
0
0
5
0
0
0
3
0
1
0
0
0
9
0
0
0
2
4
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
1
0
7
0
0
4
3
0
0
0
0
0
0
125
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
0
0
0
0
1
2
10
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
46
0
1
0
2
2
0
0
0
0
1
0
0
0
2
100
46
1
1
1
0
0
0
0
0
0
35
1
3
0
0
0
1
0
0
35
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
11
4
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
0
0
0
0
0
2
6
2
47
0
3
2
1
1
2
3
1
35
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
35
3
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
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
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
2
0
0
0
1
0
1
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
35
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
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
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
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
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
1
0
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
1
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
9
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
126
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
46
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
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
2
0
0
0
0
125
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
92
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
48
1
4
2
2
71
8
743
1523
730
101
193
517
52
92
0
0
0
0
93
0
0
46
1063
97
25
600
1
920
0
784
3
1
4
3
1
50
1
94
416
0
0
0
0
25
46
0
0
0
1
0
1
0
2
5
0
5
3
48
2
0
0
0
0
2
0
2
1
1
2
0
4
3
47
2
5
4
6
1
0
3
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
20
2
1
0
3
10
0
0
1
3
2
2
6
1
1
0
2
1
0
0
3
0
8
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
1
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
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
8
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
125
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
15
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
125
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
5
0
35
2
0
0
0
0
0
0
0
3
2
1
0
1
0
6
3
10
0
1
0
2
4
5
12
5
1
1
0
0
0
0
4
49
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
1
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
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
388
138
95
48
277
48
0
0
0
2
1
0
0
1
0
0
0
1
47
2
0
1
0
36
0
0
0
0
0
46
1
92
0
0
2
4
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
5
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
54
5
2
0
0
125
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
3
2
0
1
0
0
0
1
7
2
0
3
1
0
5
16
6
0
50
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
46
0
0
1
0
0
0
0
0
0
0
0
0
139
0
4
0
92
0
0
48
94
48
25
46
0
4
0
0
4
2
0
3
2
0
1
1
40
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
7
5
1
3
5
4
0
0
5
5
2
1
3
1
3
5
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
125
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
125
1
95
0
0
2
2
0
0
0
0
0
4
6
3
1
1
0
186
48
0
48
0
0
0
0
0
0
0
0
0
1
46
1
1
0
46
0
0
1
2
0
0
46
1
0
0
0
1
0
0
0
0
0
13
0
125
0
2
0
5
0
0
0
0
1
5
0
0
3
3
2
0
0
0
0
1
0
2
0
0
0
9
0
36
0
0
0
5
0
0
0
1
9
2
4
5
1
0
0
2
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
1
3
1
1
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
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
2
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
0
0
0
0
0
0
0
0
0
2
0
0
4
3
2
0
0
4
3
1
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
1
1
3
0
1
0
0
3
0
0
2
0
0
1
1
0
0
1
7
1
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
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
0
1
4
0
2
0
0
0
0
46
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
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
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
27
0
12
1
0
0
2
0
0
0
0
0
0
0
0
0
4
4
1
0
125
1
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
1
1
6
2
1
0
0
0
2
0
0
0
0
0
0
7
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
2
0
1
1
0
0
1
0
0
3
16
6
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
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
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
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
3
0
3
0
0
1
1
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
1
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
1
0
0
0
0
4
2
2
0
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
2
0
0
0
0
0
0
1
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
2
0
0
2
0
1
17
1
8
0
1
6
4
13
22
10
22
19
6
9
4
27
39
24
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
4
0
1
0
0
1
0
0
0
1
3
1
5
1
1
0
0
3
2
0
0
2
0
1
0
2
1
0
1
0
0
0
1
0
3
0
4
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
4
8
4
12
12
0
2
2
1
4
0
8
5
1
12
1
1
2
3
0
0
0
0
0
1
0
0
1
3
1
0
7
1
0
0
6
3
0
0
0
2
0
1
3
0
0
0
7
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
7
0
0
0
2
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
28
1
1
7
0
1
2
2
8
2
0
0
0
0
37
0
0
0
0
0
0
0
2
5
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
3
1
0
0
0
0
0
0
0
0
0
16
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
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
1
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
47
0
0
0
0
0
48
2
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
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
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
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
36
0
1
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
125
1
2
0
0
0
0
0
1
0
0
0
0
6
1
1
0
0
2
0
2
0
1
1
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
4
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
6
0
1
0
0
125
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
3
2
4
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
4
0
0
3
0
0
0
0
1
6
1
1
0
1
1
2
2
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
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
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
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
46
5
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
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
4
0
46
0
10
1
340
74
0
0
0
0
1
0
0
1
0
0
46
2
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
1
0
0
0
2
0
0
0
1
0
0
0
0
78
3
2
46
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
126
0
0
0
0
0
0
0
0
126
1
0
0
0
0
0
1
0
1
35
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
1
0
0
125
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
125
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
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
125
0
0
4
1
0
1
2
0
0
0
0
1
0
1
0
126
0
0
0
0
7
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
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
127
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
125
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
1
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
0
125
0
0
0
0
0
125
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
0
0
0
0
2
10
4
3
0
0
0
0
1
0
1
0
4
21
3
6
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
49
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
93
1
0
0
0
126
1
2
1
0
0
6
0
2
0
0
3
47
46
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
125
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
35
35
0
0
0
0
0
0
0
0
0
1
0
0
0
125
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
1
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
125
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
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
379
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
35
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
13
6
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
35
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
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
125
0
0
1
0
0
0
0
125
0
0
0
0
0
0
1
10
0
0
0
35
0
4
0
0
0
1
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
126
0
0
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
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
35
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
125
0
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
4
15
0
1
4
5
11
3
127
131
1
0
5
0
0
0
0
0
0
0
128
0
0
2
4
12
0
2
1
0
0
1
0
2
0
0
0
1
0
2
4
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
3
0
1
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
1
0
0
1
35
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
3
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
127
1
0
0
0
2
0
0
4
4
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
1
0
0
0
0
0
0
0
1
2
0
0
125
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
125
0
0
0
0
0
0
0
2
0
1
1
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
71
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
1
0
0
0
0
0
0
0
0
125
125
0
0
375
0
0
2
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
1
0
1
0
0
0
0
0
0
4
52
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
172
64
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
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
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
