OI-codes/LibreOJ/10114/data/stars7.out

4
9
11
16
3
10
7
8
8
8
2
7
3
10
5
2
9
8
6
6
9
5
3
4
6
4
7
5
10
7
8
6
6
7
4
6
11
8
4
4
6
4
2
12
12
4
2
1
4
5
5
9
4
8
3
5
3
5
4
5
3
4
8
6
4
5
8
4
5
5
2
7
5
3
5
5
6
2
5
10
7
3
3
6
5
4
7
9
4
11
7
5
3
6
1
5
6
4
5
4
4
6
2
5
7
3
9
3
1
4
3
11
5
6
2
5
5
7
1
3
7
2
4
6
9
4
3
6
3
6
6
5
7
5
5
5
10
3
1
3
9
3
10
6
6
5
5
4
8
8
9
5
3
2
6
3
5
2
3
9
1
3
3
4
6
4
2
8
3
3
4
2
5
2
7
6
5
4
3
6
6
6
4
4
4
4
4
5
5
1
7
5
2
3
6
3
7
4
10
6
4
7
7
3
2
7
5
5
4
4
3
3
3
4
6
4
3
9
8
5
8
7
4
8
4
2
1
10
5
5
8
4
6
3
4
3
3
3
2
9
10
1
4
6
6
4
2
4
3
10
1
1
4
3
5
7
4
8
7
1
3
6
5
1
8
4
5
0
5
3
3
3
0
4
3
5
4
5
5
6
4
4
4
3
3
6
2
2
1
5
5
2
10
6
6
3
1
4
3
5
5
10
5
4
3
8
4
2
7
7
6
4
5
7
4
5
3
9
4
4
8
7
2
4
5
3
2
1
4
3
3
6
6
3
4
2
4
2
4
3
1
2
2
2
5
3
3
6
3
2
4
7
7
5
4
4
2
6
0
3
1
4
1
3
1
2
3
4
4
4
4
4
4
2
2
4
6
2
5
3
5
5
2
3
7
4
6
2
7
1
5
6
4
5
6
2
3
4
4
5
4
4
2
4
0
4
4
3
2
4
2
4
2
5
3
6
3
6
3
5
3
3
0
3
3
1
4
4
6
7
2
1
4
2
6
1
1
6
4
3
2
1
3
2
3
1
2
1
3
1
4
2
6
3
1
4
5
7
5
4
6
5
5
6
6
4
2
2
4
2
3
4
6
3
1
2
3
2
3
8
3
7
3
2
0
3
1
4
1
5
4
2
3
4
1
3
3
3
5
2
5
4
3
2
6
5
0
7
6
2
1
2
4
7
6
4
4
2
3
3
0
4
3
3
4
6
6
7
2
5
1
4
4
1
2
6
7
3
4
3
4
4
4
5
2
5
5
3
2
2
5
6
6
5
1
1
4
1
1
3
5
5
4
2
3
2
2
0
3
2
4
5
4
2
1
5
5
3
5
3
2
3
1
2
5
4
4
7
2
2
5
1
2
4
2
0
2
3
2
3
4
3
3
3
5
3
1
3
1
7
4
1
4
3
0
3
3
4
0
1
4
0
3
4
1
4
4
4
3
2
1
2
4
3
1
2
3
2
2
4
5
4
3
2
3
3
3
2
4
5
2
7
2
4
1
5
2
6
2
1
2
5
5
2
2
4
6
3
1
0
3
2
7
1
3
3
3
6
3
2
4
3
4
1
3
0
4
4
9
5
0
1
2
4
6
3
4
3
4
3
8
3
2
5
6
3
2
2
2
4
3
1
3
2
9
0
4
2
3
3
2
2
6
3
3
0
1
6
6
3
1
2
6
4
2
6
6
4
3
1
3
1
2
4
3
6
5
1
2
3
0
0
3
1
1
1
1
0
1
2
3
2
0
6
3
6
1
1
2
5
2
3
2
5
2
1
5
1
6
2
2
3
4
2
3
4
6
3
5
1
2
0
1
3
2
3
2
1
2
1
7
2
2
5
3
3
3
0
4
2
4
0
3
3
5
5
2
2
4
7
2
8
4
2
0
2
3
3
2
2
4
3
1
1
4
2
4
4
1
6
6
3
0
1
2
4
3
3
2
1
6
1
6
2
3
2
1
2
4
1
5
2
6
5
2
0
4
4
3
3
4
3
2
8
1
2
6
3
3
2
2
1
5
4
0
2
3
4
3
2
4
3
3
5
3
2
3
1
1
2
2
0
3
2
2
3
4
5
4
4
1
4
4
2
1
3
6
3
5
2
1
2
4
0
2
5
4
2
3
1
3
2
1
1
3
1
3
4
2
5
5
4
1
0
3
3
2
4
2
4
4
2
3
2
3
5
0
5
3
4
6
3
1
2
3
2
4
1
2
1
3
2
2
3
2
1
3
0
3
6
4
0
3
0
1
1
1
7
3
3
1
4
2
3
2
4
4
1
0
3
4
4
4
1
8
4
4
3
2
5
0
2
3
2
1
4
1
3
1
4
2
2
4
1
2
3
3
1
1
2
2
2
4
3
0
2
2
6
1
3
2
4
2
1
2
3
2
0
4
3
1
3
3
5
1
3
0
2
6
5
4
4
0
1
2
3
2
2
3
4
2
1
3
2
3
6
3
2
1
2
2
2
3
0
2
4
5
3
6
0
2
1
4
1
3
2
4
2
3
3
3
2
1
5
1
2
3
4
4
3
1
2
4
1
4
2
2
7
5
3
6
6
0
2
5
3
0
3
3
4
1
1
4
1
3
5
4
4
7
4
1
5
3
2
2
5
1
3
2
0
3
1
4
3
3
1
4
2
2
1
4
3
1
2
2
2
3
2
2
3
6
5
1
2
3
0
4
2
1
3
4
2
5
3
1
1
0
1
2
3
1
3
0
2
0
1
7
2
3
4
2
2
2
0
1
0
4
0
3
3
1
3
4
3
2
3
2
1
5
4
2
3
1
5
4
0
2
4
4
6
2
0
1
3
3
1
2
1
2
5
4
3
2
1
0
2
2
0
0
2
2
1
1
2
1
0
0
4
2
4
5
2
3
3
2
3
2
4
4
1
2
4
3
3
3
2
5
3
1
3
3
3
3
0
2
2
3
4
2
3
1
3
3
2
1
3
4
2
3
0
3
4
3
3
4
2
2
3
2
6
3
4
2
4
1
2
3
1
3
3
3
2
5
2
2
2
3
2
2
1
2
2
4
2
2
5
3
1
2
3
3
1
1
5
5
2
2
5
3
0
2
3
3
4
2
4
1
0
2
3
2
2
2
4
8
5
5
2
2
2
2
1
1
3
6
2
3
3
2
2
1
3
2
1
1
0
0
2
0
1
4
4
1
3
2
4
1
1
1
2
2
1
0
4
6
0
3
0
2
3
3
4
2
5
1
2
4
2
0
1
5
0
1
2
2
1
4
7
4
2
1
1
3
4
4
2
4
2
2
3
5
2
2
1
3
1
2
3
2
3
4
0
3
3
1
0
0
1
0
1
3
2
3
3
4
2
4
2
3
2
6
4
0
3
3
2
6
4
4
1
2
0
2
4
5
3
2
5
0
3
2
2
2
3
7
5
4
3
3
0
1
1
2
2
5
4
2
1
1
1
3
1
0
2
1
0
2
1
1
2
1
3
4
1
1
1
0
2
3
4
1
6
1
3
1
1
1
1
3
5
2
1
4
3
2
1
1
2
0
1
2
1
3
2
2
3
2
1
4
0
1
2
2
1
4
3
5
0
3
2
2
4
3
3
0
5
3
2
3
2
0
1
0
4
1
3
6
5
1
2
1
1
1
2
0
0
1
1
2
1
3
1
2
2
1
2
4
5
1
1
2
3
5
3
4
5
2
3
1
3
1
3
1
4
2
2
2
0
3
2
1
1
2
4
0
1
4
1
2
0
3
4
1
0
2
6
3
5
1
3
1
1
2
2
3
4
5
3
2
1
5
2
3
5
7
5
1
3
0
2
4
2
3
1
2
1
4
1
2
0
3
1
3
3
2
4
2
0
1
1
3
2
3
5
0
2
0
2
3
0
1
1
5
1
5
3
4
1
2
1
2
3
1
2
2
2
3
2
2
5
2
1
0
3
0
1
3
2
1
3
2
4
4
1
4
0
4
4
1
3
2
0
3
2
1
0
2
0
4
1
5
7
2
0
3
3
2
6
2
2
4
5
2
2
0
3
1
4
2
1
3
2
2
2
0
1
3
1
2
2
1
0
2
3
6
4
4
3
2
1
3
2
0
4
2
1
2
1
2
3
2
1
3
3
3
2
2
2
2
0
3
3
2
3
2
1
0
2
3
0
3
5
3
1
1
3
2
2
1
0
3
1
3
2
2
1
6
10
4
2
3
3
0
1
2
0
0
2
1
2
1
1
2
1
5
1
0
2
0
1
3
0
4
1
1
1
5
0
2
3
2
2
0
2
2
4
2
2
1
3
3
1
1
1
2
3
2
1
1
6
1
4
3
1
2
3
2
3
3
0
0
1
3
0
1
1
3
3
2
0
3
2
0
1
0
1
3
3
3
4
1
0
0
1
3
4
0
2
0
2
2
1
2
1
1
7
1
1
5
2
2
1
5
1
3
3
2
1
5
1
1
1
4
4
2
3
0
3
2
3
2
4
1
3
2
6
1
0
0
2
3
2
4
3
1
3
4
5
4
2
1
1
1
2
1
0
2
2
2
2
2
2
2
1
1
1
2
3
4
1
3
1
0
3
0
1
1
1
1
0
1
3
3
3
3
2
1
3
1
1
1
0
3
4
1
2
0
1
5
6
1
3
3
0
1
0
0
0
1
3
3
4
3
2
1
3
1
3
0
3
3
1
3
1
1
1
3
3
2
3
1
1
1
1
0
1
6
2
1
1
1
0
0
3
2
0
1
2
0
2
2
3
3
0
1
1
2
3
4
1
1
1
2
1
1
2
1
1
2
1
2
3
0
2
4
4
4
2
1
4
0
2
1
1
2
4
0
3
4
1
4
0
0
0
0
3
1
1
1
2
2
2
1
2
1
2
0
2
1
1
3
2
0
0
2
2
2
2
1
1
2
4
1
2
2
0
1
3
2
1
0
6
1
2
3
1
2
2
2
5
1
1
1
2
3
4
1
1
1
3
3
4
2
5
0
2
3
3
1
1
2
2
4
3
1
1
1
2
3
3
0
2
2
2
1
3
4
3
2
0
0
1
3
4
2
1
0
1
0
0
2
2
1
1
2
1
1
2
1
2
1
1
1
4
1
3
1
1
1
1
2
1
7
0
1
1
1
4
5
1
1
2
2
2
1
4
2
3
2
4
2
3
1
1
2
2
1
2
3
1
1
2
2
0
2
2
2
2
0
1
1
3
3
3
1
1
0
2
0
1
5
2
0
3
2
2
0
3
1
0
2
2
5
3
1
3
3
6
1
3
0
0
1
2
1
3
2
3
5
1
0
0
3
1
0
4
3
1
0
4
7
1
3
2
1
5
1
1
4
1
4
2
2
3
1
2
1
0
2
2
2
1
2
1
2
2
0
2
2
2
1
1
1
3
2
3
3
1
1
4
1
2
1
2
2
4
2
3
1
5
1
2
1
2
0
3
0
1
2
1
2
5
2
1
3
4
0
0
3
2
3
1
2
0
4
1
2
1
0
3
1
1
0
1
1
1
1
5
0
2
0
3
2
5
0
3
3
2
2
4
2
8
6
5
3
0
3
0
2
0
0
0
0
0
1
4
2
0
2
2
2
0
1
1
1
2
2
1
1
2
0
1
0
1
2
2
3
2
2
2
4
3
2
1
1
2
1
0
3
1
1
2
2
0
3
1
1
1
1
0
1
1
2
0
2
2
0
2
0
1
2
0
2
0
1
3
1
0
1
1
1
2
2
4
0
1
1
3
1
1
3
2
0
1
2
0
2
1
5
2
0
0
1
0
3
2
3
1
0
4
0
1
2
2
2
0
1
2
1
0
3
2
3
2
1
1
3
0
1
3
2
0
2
1
1
2
3
2
3
1
0
2
2
0
1
2
0
2
1
1
1
2
4
1
2
6
1
1
2
3
4
1
4
3
0
4
1
2
0
0
2
4
1
4
2
1
4
1
1
2
1
0
2
2
0
5
5
1
4
2
2
2
3
1
3
1
0
2
0
2
0
0
2
0
1
2
0
2
1
6
3
1
5
5
0
1
1
1
1
2
1
3
3
4
1
3
1
3
1
2
5
1
2
1
3
2
3
0
0
1
1
2
3
4
1
0
0
2
0
3
2
2
0
1
3
3
1
1
2
3
3
2
2
3
1
1
1
2
2
2
2
4
0
1
0
3
0
2
0
3
1
6
3
0
2
2
2
1
0
4
1
0
1
2
2
1
3
2
3
2
2
1
3
4
1
3
0
2
1
1
2
1
2
1
3
1
3
6
3
1
6
3
3
0
0
2
0
4
1
4
0
0
2
3
0
1
2
1
0
1
4
0
2
3
4
1
1
1
2
3
0
1
1
1
2
1
4
2
1
4
1
3
0
1
0
1
1
0
2
0
2
4
2
3
2
0
0
0
4
2
2
0
1
4
3
4
1
0
1
4
2
1
1
0
2
1
1
3
0
5
3
4
2
1
3
3
2
3
3
1
0
3
0
0
3
0
1
0
0
2
1
0
0
1
2
3
2
1
0
2
2
0
3
1
1
1
0
0
3
2
2
1
4
5
3
0
2
3
2
1
2
2
2
2
1
1
3
2
1
0
4
4
0
1
3
1
2
1
4
0
2
3
0
0
0
2
2
1
0
2
1
3
4
3
1
1
2
0
3
1
3
2
1
0
2
1
4
0
3
4
1
2
4
3
0
0
1
0
1
2
2
0
3
3
1
0
1
2
2
1
1
4
2
1
2
2
2
1
1
3
1
4
3
4
1
0
3
1
0
2
3
4
0
5
2
0
2
1
1
1
1
2
5
2
1
0
1
0
0
1
2
5
4
2
1
3
0
1
1
1
3
1
2
0
0
2
1
1
3
4
1
1
3
1
1
1
1
3
0
1
0
0
2
1
1
2
1
2
1
0
1
0
0
1
0
4
4
4
0
6
0
1
1
2
5
1
3
0
4
3
2
2
3
4
1
1
1
3
2
0
2
1
2
1
0
3
2
1
2
2
0
3
1
1
2
2
1
2
3
1
2
0
2
2
2
1
1
2
1
1
4
0
1
0
2
0
1
1
1
2
2
0
2
1
2
2
1
0
2
4
2
0
1
0
2
2
1
2
2
1
2
1
1
2
3
2
3
0
1
0
3
2
1
2
0
0
1
3
1
3
2
1
2
1
2
1
1
3
1
3
0
1
2
0
3
2
0
2
2
0
1
6
1
2
1
2
2
4
2
0
1
0
3
0
1
1
3
1
3
0
2
1
3
1
2
1
2
0
0
0
1
0
1
0
5
4
0
2
0
0
2
0
3
1
2
2
2
0
2
1
1
2
4
1
2
3
3
0
2
1
2
0
4
2
1
0
0
4
1
1
2
4
2
0
1
1
2
0
3
2
0
0
1
0
1
2
1
1
0
2
3
4
2
0
0
1
1
0
1
0
2
0
2
1
2
0
3
2
0
2
0
1
0
1
1
1
0
3
3
1
1
0
2
0
2
2
2
1
2
1
0
4
1
0
1
1
0
3
1
2
1
3
1
0
0
1
1
0
3
4
2
2
2
2
1
0
1
1
0
1
2
0
2
1
0
1
5
2
3
2
0
2
2
0
1
1
0
1
2
3
1
1
1
0
2
0
2
0
0
1
0
3
3
0
1
0
1
3
3
3
3
2
3
3
3
1
2
0
3
2
2
0
0
0
0
1
2
5
1
2
1
4
2
4
0
1
4
2
1
1
2
3
1
0
3
2
0
2
0
1
2
1
0
3
1
1
1
1
4
2
3
0
1
2
1
2
2
3
2
2
2
1
1
0
0
1
2
3
1
1
3
3
2
2
2
1
1
1
2
2
1
0
2
3
1
1
3
1
1
1
3
1
1
3
0
1
4
2
0
2
3
5
1
1
0
3
1
4
1
0
1
1
2
0
1
4
0
1
3
3
1
0
0
1
4
1
1
2
2
1
1
2
2
3
1
3
0
5
3
4
1
2
4
0
1
1
0
2
1
1
1
1
1
0
3
2
2
5
0
1
1
1
4
3
1
1
2
1
3
1
3
2
3
1
2
1
1
0
0
1
2
2
1
0
1
0
3
1
2
0
0
1
2
2
2
2
1
2
1
3
1
1
2
1
0
1
3
3
3
1
2
1
1
0
2
1
1
1
1
3
0
3
2
2
0
4
2
1
0
3
2
2
0
3
0
1
2
2
1
2
4
0
1
1
1
3
1
0
0
0
1
2
1
5
0
0
3
1
3
3
1
3
4
2
2
2
1
2
1
0
3
0
1
2
1
2
2
1
0
3
1
1
1
2
5
2
3
1
1
0
0
1
1
0
0
2
1
1
3
2
2
0
2
2
2
4
0
1
1
0
1
1
3
2
3
0
3
3
0
0
1
4
2
0
2
3
1
0
0
0
4
3
1
3
0
2
0
3
1
1
0
0
2
0
0
0
1
0
1
2
2
2
3
0
0
1
0
0
1
0
1
4
1
1
3
1
0
2
1
3
2
2
2
2
1
2
2
2
2
0
2
2
3
2
1
0
4
0
1
1
2
1
0
3
4
1
0
1
4
0
2
1
1
1
0
1
1
0
2
1
0
0
1
4
6
1
1
0
2
2
1
2
0
1
1
0
2
0
2
3
2
1
2
1
0
3
2
3
0
2
0
1
1
1
1
2
3
0
2
3
0
1
2
3
2
1
1
0
0
0
2
0
0
4
2
0
0
3
0
2
0
4
3
1
3
1
4
1
0
0
1
3
0
2
3
1
1
1
1
0
2
0
0
1
2
1
1
3
0
1
4
0
0
2
0
3
0
0
1
1
1
1
2
1
1
3
3
4
1
2
0
0
5
1
3
0
1
2
0
2
1
0
0
1
2
0
0
0
3
1
3
0
0
2
0
0
1
0
1
4
0
2
2
4
0
3
0
0
4
1
3
2
0
1
2
2
0
1
0
1
1
0
2
1
2
1
0
0
1
2
0
1
2
1
1
0
1
0
0
3
0
2
0
1
1
1
0
2
0
1
2
1
0
1
1
3
2
2
1
1
1
2
1
1
0
1
3
2
1
1
2
2
1
1
4
1
0
2
1
2
2
1
3
2
2
1
0
1
0
1
1
2
1
3
1
2
1
1
0
0
5
1
1
2
0
0
0
4
2
3
0
1
2
0
2
1
2
1
3
0
2
0
1
2
1
0
1
2
2
2
1
0
0
1
1
3
1
0
2
0
2
1
1
2
3
2
0
0
0
2
0
0
2
2
1
1
0
1
2
1
3
0
4
2
0
0
0
1
1
2
1
2
0
3
1
0
2
0
2
4
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
1
1
1
0
1
1
3
0
1
0
0
0
3
0
1
1
2
1
0
2
2
0
0
1
1
2
1
3
2
1
2
0
0
1
0
0
1
3
1
1
0
3
0
1
1
3
1
0
0
1
0
2
1
2
1
2
1
1
1
2
0
0
1
2
3
1
1
2
0
0
1
1
1
2
2
1
0
1
2
5
2
1
0
1
1
1
1
1
1
0
3
1
1
0
3
1
2
0
3
0
0
1
0
2
0
3
3
1
0
3
0
2
0
0
3
2
0
4
0
2
2
1
2
0
3
1
1
1
1
2
0
1
0
1
2
0
2
1
0
1
1
3
1
2
2
1
0
1
1
0
3
4
4
0
0
3
1
3
0
1
1
2
0
1
2
1
0
3
2
1
3
2
2
3
3
0
2
1
0
0
3
2
2
3
1
1
3
0
1
0
1
1
0
2
1
1
0
1
1
2
1
2
3
3
0
0
0
0
1
2
0
2
3
0
0
1
1
2
2
3
1
2
1
1
1
0
1
1
2
1
2
0
0
1
1
1
2
0
0
1
3
0
0
0
0
1
1
0
0
2
3
0
2
2
2
2
1
0
1
2
1
1
0
1
2
2
1
0
3
1
2
2
1
1
3
1
3
1
0
3
0
1
1
1
2
5
2
4
4
2
3
1
1
1
1
0
2
1
1
0
1
1
1
2
0
6
1
1
1
2
1
1
2
1
1
1
0
1
2
3
4
0
1
0
1
0
2
3
1
1
2
1
3
1
2
2
3
1
1
1
1
0
3
0
5
1
0
0
0
1
2
2
1
2
2
4
0
1
1
0
1
1
2
0
2
0
2
1
1
2
1
2
3
0
0
1
2
1
1
0
0
2
0
2
0
0
3
3
0
0
2
0
0
3
0
1
3
3
0
0
0
0
1
1
1
1
1
1
0
2
1
2
0
2
2
1
1
2
2
3
1
1
1
0
1
1
2
1
0
0
3
1
0
1
2
2
2
0
2
0
0
1
1
1
2
2
0
2
2
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
4
0
0
0
1
3
1
2
0
1
1
0
4
2
2
2
3
4
0
0
1
2
0
1
0
1
2
3
1
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
3
0
1
1
2
0
1
0
0
0
1
0
3
1
0
3
1
2
0
0
1
1
3
2
1
0
3
2
1
0
2
0
2
1
0
2
2
1
0
0
1
1
2
0
1
1
3
1
0
0
2
2
0
0
3
2
2
0
0
0
0
2
1
2
0
2
3
0
2
1
0
3
1
2
1
0
1
1
0
1
0
1
0
0
2
0
1
2
0
1
2
3
0
0
2
1
1
2
1
3
2
2
0
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
4
0
0
2
0
1
3
0
0
0
0
1
1
2
0
0
1
1
0
3
3
1
3
0
1
0
0
0
0
0
1
2
0
2
1
0
1
2
0
4
1
4
1
1
1
0
4
0
3
0
1
2
0
1
0
3
1
3
1
2
2
0
1
5
3
3
2
2
0
0
1
0
0
1
2
2
2
0
3
3
1
2
1
4
2
1
1
1
0
1
1
2
2
0
4
0
0
2
4
1
1
0
2
0
4
2
0
1
0
0
2
1
0
2
2
0
1
3
0
2
1
0
0
0
2
1
0
2
0
0
2
1
0
0
1
2
0
2
1
2
1
2
1
2
0
1
1
2
1
0
1
0
0
3
2
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
2
2
0
2
0
3
0
1
0
2
3
0
1
1
0
0
0
2
1
2
2
0
1
2
0
2
3
0
0
2
2
3
3
2
0
3
3
2
1
1
0
1
3
0
3
1
1
0
0
0
2
1
1
2
1
2
2
4
0
0
0
1
1
2
2
2
0
0
3
1
1
2
0
0
1
1
2
0
1
1
4
0
0
0
0
1
3
2
1
0
0
0
0
1
1
0
1
2
0
1
2
1
1
0
0
0
0
0
2
0
2
0
1
1
1
3
1
2
1
1
2
3
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
2
0
2
0
3
1
3
1
1
1
2
4
2
0
0
2
3
1
3
2
2
2
1
0
0
1
0
1
0
1
1
0
3
2
1
1
1
1
0
1
0
3
1
0
1
1
1
1
1
4
2
1
0
1
2
0
0
1
1
0
5
1
2
0
0
1
1
5
1
0
1
1
0
0
1
2
2
2
0
2
1
2
1
0
2
0
1
0
2
0
1
3
4
1
3
0
2
0
2
0
2
0
1
2
0
0
0
1
1
1
0
3
1
3
1
2
1
2
3
0
0
2
0
1
1
2
0
1
1
0
0
1
2
4
1
0
2
1
0
2
1
0
2
1
1
1
1
1
2
3
2
1
1
0
2
3
1
1
1
1
0
0
0
1
0
1
2
1
2
2
3
0
2
0
3
1
1
0
3
0
0
1
1
1
2
0
2
1
0
1
2
0
3
0
1
0
1
2
0
1
2
1
0
2
1
1
0
2
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
1
0
3
1
0
1
2
2
1
2
3
0
2
1
0
1
1
1
0
2
1
4
1
0
3
0
2
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
3
1
2
0
2
1
0
1
2
1
0
0
0
0
2
1
0
1
2
3
0
0
2
1
0
1
2
1
4
0
1
2
1
3
2
0
1
1
0
3
1
2
1
0
3
1
1
0
2
0
0
0
1
1
1
1
0
2
0
3
2
0
2
1
1
1
1
1
1
1
3
3
0
0
1
1
0
2
0
2
1
1
3
3
2
2
0
0
2
1
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
4
1
2
0
2
1
0
0
2
0
1
0
1
1
3
1
1
0
2
1
1
1
0
1
4
1
2
0
1
2
1
1
1
0
2
0
1
2
1
2
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
1
1
1
0
2
1
0
2
0
2
2
1
0
1
0
0
0
2
2
0
1
0
1
0
1
1
1
2
0
3
1
0
0
1
2
0
2
0
0
1
0
2
1
2
3
0
1
0
1
0
2
1
0
0
1
0
0
0
3
0
0
1
0
1
1
0
1
1
2
2
3
1
0
1
2
0
3
4
0
2
2
0
0
0
0
1
2
1
2
0
0
1
1
3
2
2
0
0
0
3
2
1
0
1
1
1
1
0
0
0
0
0
2
3
0
0
3
2
0
2
2
4
1
0
0
1
0
3
1
1
2
3
0
3
1
0
2
0
0
1
1
0
0
2
0
1
1
1
3
1
1
3
2
0
2
1
0
2
1
1
2
3
2
0
0
2
1
1
0
3
1
1
1
1
2
2
2
0
1
2
0
1
0
1
0
0
2
2
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
2
1
2
3
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
4
1
2
3
1
0
1
0
0
1
2
1
1
2
2
3
0
2
0
0
0
1
2
2
0
0
1
0
3
3
0
2
0
1
1
1
1
1
2
0
1
0
0
0
1
0
0
2
2
1
1
1
0
1
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
4
1
0
1
1
3
1
1
0
1
2
2
3
0
2
3
1
0
4
2
0
1
1
0
2
1
1
0
3
2
0
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
1
1
1
3
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
2
0
1
2
2
1
1
1
2
1
1
0
2
1
0
0
0
2
3
0
2
2
0
0
0
2
0
1
1
1
1
2
1
0
0
0
1
3
1
2
3
2
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
1
1
2
1
1
1
2
0
1
0
3
2
0
1
0
0
1
2
0
1
0
1
1
2
2
0
1
2
1
2
0
0
4
0
4
0
2
0
0
1
0
1
3
2
1
0
1
0
2
0
1
0
2
0
2
0
1
3
1
2
5
0
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
1
1
1
0
0
2
0
0
1
1
1
2
0
3
1
0
1
1
3
2
2
0
1
0
1
1
0
0
0
5
1
0
0
0
1
3
0
1
2
2
1
0
0
1
1
1
1
1
2
1
0
1
0
3
0
1
1
1
0
1
0
3
0
2
0
0
1
1
1
1
1
0
0
0
2
2
0
0
1
1
1
0
1
1
1
1
0
2
0
0
3
1
1
0
4
2
1
2
1
0
1
1
2
0
0
0
0
0
0
1
4
0
2
1
0
0
1
1
1
0
0
0
0
0
3
0
2
1
0
1
0
1
3
2
1
0
1
1
0
0
1
3
0
1
0
0
0
3
0
1
0
3
2
1
0
0
1
1
2
1
0
1
0
1
1
2
1
0
1
0
1
1
1
1
3
2
1
1
0
0
1
3
1
1
1
2
2
1
1
0
1
1
1
1
2
0
0
4
2
0
0
0
1
1
1
2
2
0
4
0
1
1
1
1
1
2
2
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
2
2
1
0
1
1
1
2
2
4
0
2
1
0
0
1
0
0
0
0
0
2
3
0
2
1
0
0
2
1
1
3
1
1
0
0
0
2
0
0
2
0
1
1
1
0
4
2
1
3
1
0
1
0
0
0
2
3
0
3
1
0
0
0
0
0
1
1
1
1
1
2
0
0
4
1
1
1
0
1
1
1
2
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
0
1
1
1
1
1
2
2
1
2
0
1
3
1
1
1
2
0
1
1
2
1
0
1
0
0
1
0
2
0
1
0
4
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
1
0
1
0
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
2
0
2
1
0
0
1
2
3
2
1
0
3
0
1
1
1
2
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
3
1
0
0
0
3
1
1
1
0
0
0
3
2
1
0
1
1
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
2
1
2
0
2
1
1
1
0
0
3
0
1
1
2
1
1
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
1
3
1
3
2
1
1
2
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
2
1
2
0
1
0
3
1
0
1
1
0
0
3
0
1
1
1
0
1
1
0
2
1
1
0
0
3
1
0
1
0
4
3
1
0
1
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
1
1
1
3
3
1
1
0
1
1
0
1
1
2
0
2
1
0
0
0
1
2
2
2
0
0
0
1
0
1
2
0
0
4
0
0
0
1
1
0
1
0
2
0
1
0
0
1
3
1
0
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
0
1
0
0
1
3
1
1
0
0
1
1
2
1
1
0
1
0
2
0
0
1
1
0
2
2
1
1
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
2
1
2
0
0
1
1
1
2
2
1
4
2
1
0
2
1
0
1
0
0
1
1
2
1
0
1
0
0
0
1
0
2
0
2
0
1
1
0
2
1
0
0
2
0
0
0
1
1
1
0
2
0
1
1
2
0
1
0
0
0
1
0
1
1
2
2
1
2
0
0
0
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
3
2
1
1
0
3
0
2
2
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
1
0
0
2
1
2
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
2
1
1
2
0
1
0
2
0
0
2
1
0
3
0
3
0
1
1
2
0
1
0
0
0
0
0
1
1
2
1
1
2
0
1
1
5
1
0
1
2
0
1
1
0
0
1
3
3
1
0
4
0
0
0
0
1
2
1
1
1
1
0
2
1
0
1
0
1
3
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
1
0
3
1
1
1
1
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
1
0
1
2
3
0
0
2
0
0
2
1
2
1
1
1
0
1
2
3
0
0
1
0
0
1
0
0
0
1
1
1
0
1
3
0
1
0
0
2
1
3
0
1
0
0
0
0
1
2
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
3
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
3
3
0
0
1
1
1
0
0
1
0
2
0
1
1
0
2
1
0
1
2
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
1
0
1
0
1
2
2
2
2
0
2
1
0
0
0
5
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
3
1
0
4
1
0
2
0
2
0
1
0
1
0
1
1
2
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
2
1
1
3
4
0
0
1
0
0
0
1
1
0
0
0
1
1
2
2
0
0
1
0
1
1
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
5
2
0
1
0
0
2
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
2
1
1
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
3
2
1
2
1
1
1
1
0
1
0
3
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
0
1
1
0
1
2
1
0
0
1
0
0
2
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
2
2
1
1
0
0
0
3
0
0
0
0
1
1
1
0
1
2
0
1
2
1
0
2
0
0
2
0
0
1
0
2
1
1
1
0
0
1
1
0
3
0
1
0
1
3
0
1
1
0
0
0
0
0
0
1
4
1
0
0
1
2
0
1
1
1
1
1
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
1
1
1
1
3
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
2
1
0
0
2
1
0
2
2
0
1
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
3
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
3
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
0
1
0
3
1
0
0
0
1
0
1
1
1
0
1
2
0
3
1
0
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
2
2
1
3
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
4
1
2
0
0
1
0
0
1
3
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
3
0
2
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
3
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
2
1
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
2
1
0
0
4
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
2
1
2
1
0
1
1
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
0
2
1
0
1
2
0
0
3
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
1
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
2
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
3
1
0
1
1
0
0
1
0
0
2
2
0
3
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
2
0
0
1
2
1
1
1
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
2
3
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
0
2
0
2
0
0
1
0
2
0
0
0
1
1
0
2
2
1
0
0
1
1
0
0
2
1
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
3
1
0
2
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
3
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
1
1
0
1
1
0
1
0
1
0
1
1
3
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
1
0
0
3
0
0
3
0
0
1
1
1
1
3
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
1
0
0
2
0
0
2
1
0
0
0
1
0
0
1
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
1
3
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
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
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
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
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
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
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
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
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
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0