0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-11-09 01:38:48 +00:00
OI-codes/LibreOJ/2130/data/manager8.out

100001 lines
196 KiB (Stored with Git LFS)
Plaintext

8
12
12
4
17
8
9
9
10
8
6
6
7
4
11
8
5
11
6
8
10
6
6
4
11
11
5
6
5
4
10
6
7
6
9
5
5
11
8
7
10
7
6
3
0
2
2
2
7
4
6
6
5
0
9
8
12
5
5
8
8
0
0
5
3
4
7
8
0
2
7
7
6
7
8
13
6
8
11
2
0
7
5
7
8
8
12
6
5
5
13
1
4
5
6
9
2
7
0
6
9
6
5
4
8
5
7
12
5
3
4
5
14
4
9
8
3
2
5
6
10
7
3
5
8
6
8
5
5
11
3
8
9
0
7
0
3
10
6
4
1
6
5
5
1
11
4
7
6
5
2
5
4
8
4
8
7
3
4
3
8
2
2
0
0
4
7
4
4
12
4
8
5
2
8
5
8
3
2
1
5
1
4
7
3
5
5
4
6
6
8
3
4
3
3
6
4
9
5
6
3
3
6
6
6
4
4
5
0
5
9
5
6
1
6
2
7
6
6
4
0
5
11
7
7
5
0
2
5
11
3
3
7
3
3
9
3
3
6
6
6
7
4
6
5
4
6
10
2
5
3
5
9
5
9
8
8
7
2
13
6
7
5
7
7
6
7
7
7
3
0
11
5
1
4
3
6
2
5
9
5
5
2
11
11
6
6
6
4
0
3
7
4
6
5
2
7
3
8
4
7
4
3
6
3
3
3
6
4
4
3
3
7
6
7
3
6
4
3
4
6
6
6
3
4
4
4
7
2
5
3
1
5
7
7
4
4
9
8
7
0
7
3
0
4
5
0
3
4
1
6
4
7
7
4
3
0
6
9
2
5
6
5
3
4
2
0
0
9
3
7
1
4
1
8
8
2
5
4
1
5
5
4
7
1
4
5
11
9
7
1
5
11
8
4
2
0
4
7
9
6
3
6
2
0
2
2
1
9
4
2
5
5
1
0
4
8
6
4
7
3
5
4
2
1
6
0
3
3
4
5
1
3
6
5
4
5
4
4
0
7
1
4
3
5
3
9
3
6
9
2
6
4
2
3
6
7
7
7
3
6
3
4
5
0
4
5
4
2
6
5
7
11
0
5
5
1
4
4
5
7
3
1
2
3
2
5
5
5
0
9
6
3
6
8
5
0
10
5
6
2
4
3
8
2
0
0
9
10
5
6
4
2
3
8
6
5
2
8
8
7
8
4
5
1
0
4
4
4
3
0
5
4
3
6
2
7
6
1
10
3
4
4
8
4
2
2
8
7
3
5
4
2
4
4
3
3
2
2
3
2
3
2
4
5
3
4
3
0
6
2
8
4
3
4
2
6
2
2
3
1
8
4
5
4
5
2
4
11
4
0
6
6
2
2
6
5
3
5
6
4
6
4
7
1
4
4
3
3
8
5
1
7
3
3
3
2
8
1
5
2
4
5
2
7
4
7
1
4
4
4
3
5
3
3
4
7
6
4
5
7
4
8
11
7
6
1
2
3
8
0
0
0
2
8
1
6
1
1
6
2
1
7
5
5
2
0
4
5
3
6
4
6
5
5
9
4
2
3
0
7
1
4
0
1
6
4
2
6
4
0
4
3
10
4
4
3
4
6
2
4
6
3
5
3
4
0
0
5
7
7
0
4
4
20
4
5
5
3
2
3
4
5
2
6
1
4
6
2
5
3
0
5
2
5
3
7
6
5
3
2
2
6
4
3
2
2
2
5
7
2
3
4
0
4
3
5
3
5
2
2
2
4
5
6
6
5
2
0
6
2
5
6
4
7
6
5
2
7
6
5
5
4
3
3
4
5
5
5
0
7
3
3
1
5
3
4
7
4
8
5
2
2
0
0
5
1
4
2
7
7
2
2
4
4
4
5
4
6
3
2
4
3
4
3
2
5
2
1
3
8
4
1
4
1
1
6
5
2
2
2
0
2
7
4
4
1
4
2
3
6
1
2
3
4
5
4
3
0
4
5
3
5
7
6
6
7
6
3
3
2
4
6
4
4
6
1
1
1
4
2
4
4
1
5
4
4
0
2
4
8
3
6
4
3
4
0
7
4
3
3
1
4
1
4
1
3
4
2
4
4
5
8
0
2
1
5
6
3
3
3
6
2
4
6
4
5
2
1
4
4
2
3
2
3
2
0
5
2
6
5
4
3
2
2
4
4
3
5
4
11
0
4
5
6
2
3
3
2
2
1
2
7
3
10
0
4
2
4
6
5
3
3
1
0
1
6
1
1
3
4
2
2
2
2
9
7
6
2
1
4
2
6
5
3
8
3
3
4
5
2
3
0
5
5
5
8
2
4
2
4
0
5
5
0
3
5
0
5
6
7
4
7
0
4
2
0
3
2
2
3
0
0
7
4
5
2
3
1
11
4
3
0
6
5
2
4
3
4
4
2
4
3
1
8
1
0
1
5
7
6
2
8
6
5
4
2
5
4
4
7
3
8
3
1
3
2
2
4
5
5
6
6
1
7
4
3
6
2
1
3
6
3
0
2
5
2
4
2
6
4
3
9
3
4
4
2
3
4
5
10
8
1
2
2
1
8
0
2
3
2
5
5
2
3
2
5
4
11
2
3
6
3
2
7
3
8
4
3
0
4
0
6
12
6
1
1
4
4
1
0
1
8
5
5
2
6
3
4
0
1
3
6
0
7
0
6
6
1
2
7
0
7
5
3
1
3
3
7
1
0
2
5
4
5
1
2
4
5
4
8
0
0
0
3
2
7
0
2
6
3
4
3
4
4
0
3
4
9
0
4
1
0
3
4
6
2
9
4
0
4
3
2
4
7
5
8
3
4
4
3
6
5
3
2
1
2
8
3
1
2
3
4
4
3
7
3
6
3
3
4
3
3
3
5
10
6
4
3
6
3
0
6
4
4
0
2
3
4
4
8
3
5
4
0
0
1
7
1
2
2
8
6
3
6
3
6
0
1
3
3
1
0
9
2
1
4
2
5
1
3
3
0
0
2
2
6
3
0
4
3
5
2
4
5
1
0
3
0
2
1
6
3
6
2
5
2
3
3
5
0
2
5
9
4
0
0
4
3
4
0
2
1
2
6
8
2
3
4
2
6
2
2
1
5
2
0
6
3
7
1
4
2
3
3
0
6
0
5
3
7
3
2
3
4
6
1
0
3
3
6
1
4
7
4
0
1
3
4
3
2
2
0
5
6
1
3
4
5
7
4
1
0
6
4
1
3
4
4
5
4
3
4
6
5
5
3
4
2
3
4
6
5
0
3
2
1
4
3
7
2
2
1
3
4
3
7
0
1
4
4
2
0
1
5
1
1
2
1
3
3
3
4
10
1
5
1
1
7
3
1
6
0
2
8
0
1
2
4
5
5
1
4
2
2
3
3
4
1
2
6
6
6
4
6
3
5
8
5
3
3
3
0
6
3
4
0
2
5
2
7
3
3
2
0
2
2
2
2
8
6
3
2
2
3
3
6
6
4
6
0
5
3
5
1
1
2
5
2
4
6
5
3
2
2
0
7
6
6
5
3
7
5
7
4
3
2
2
4
3
0
0
6
3
3
2
3
0
2
4
4
2
5
2
3
4
1
5
3
6
0
1
1
4
6
6
3
4
5
0
1
3
8
1
4
4
8
1
3
3
4
4
2
5
0
1
9
7
4
4
0
1
4
5
2
5
3
5
2
1
2
2
4
7
4
4
0
5
3
1
2
3
4
3
4
1
2
1
4
4
0
2
1
2
3
1
3
3
0
1
4
7
0
4
5
4
1
1
0
0
0
5
2
5
3
0
1
0
2
4
4
2
3
0
7
2
0
1
4
6
6
2
4
4
6
1
5
4
2
6
3
3
5
2
5
4
6
6
5
5
4
3
4
0
3
1
4
5
0
4
2
4
6
3
2
4
2
4
3
3
4
2
4
1
2
3
7
4
3
4
2
7
5
5
3
2
5
0
3
0
3
0
1
7
1
1
2
8
2
2
2
6
3
6
6
2
4
7
7
0
3
4
3
4
2
1
5
0
0
0
5
3
3
3
4
3
0
2
6
0
5
3
0
4
4
6
4
2
6
3
7
3
7
3
4
0
9
3
2
7
3
4
5
3
5
1
1
5
2
1
2
3
4
2
5
7
2
4
6
6
2
5
5
2
5
1
1
3
2
5
2
4
4
4
6
2
2
2
1
4
2
3
3
1
4
5
0
6
10
3
3
2
0
4
2
5
5
1
2
0
3
5
5
5
2
2
1
2
0
4
1
3
4
3
5
4
0
4
2
6
2
5
4
4
0
9
0
1
0
3
3
3
5
6
1
5
2
2
5
3
3
2
4
4
6
2
1
1
5
0
4
0
0
1
2
2
3
2
4
0
0
3
2
5
8
3
2
0
2
0
4
7
5
0
2
3
2
3
5
2
2
0
3
6
1
1
1
5
4
6
3
7
3
3
3
3
7
4
4
1
6
0
1
4
3
1
4
3
2
5
2
1
4
5
4
3
1
4
4
2
0
9
1
5
7
1
1
2
2
3
3
1
4
3
3
1
3
2
4
4
1
1
6
3
1
2
4
0
5
2
4
4
5
2
6
4
4
0
4
0
3
2
4
2
8
2
2
2
4
4
0
3
2
3
3
4
2
3
3
4
3
3
27
2
1
3
5
6
4
5
3
7
4
3
3
7
0
3
6
1
3
4
1
2
1
6
8
5
2
0
4
3
1
4
3
3
3
0
5
6
4
1
1
2
4
5
4
4
3
5
9
0
3
2
1
1
1
3
2
4
4
3
0
3
3
2
0
6
3
0
5
1
3
5
4
1
3
3
2
0
4
2
3
5
1
1
1
3
3
0
4
0
3
4
6
3
0
3
6
2
0
3
0
7
2
2
6
8
4
3
3
8
2
2
2
2
4
0
7
3
3
5
2
0
4
4
4
1
4
3
1
6
3
3
2
7
1
1
3
6
1
2
3
1
2
3
4
3
4
3
4
2
2
3
6
1
3
3
4
2
1
1
8
2
0
2
4
5
3
5
2
0
0
5
3
2
4
4
4
0
0
3
1
3
5
1
0
2
1
0
4
3
1
3
3
5
4
2
2
4
3
4
2
7
2
3
1
5
4
3
0
1
0
2
4
2
5
4
7
1
5
2
8
1
1
6
6
3
8
4
5
2
2
2
7
1
1
7
4
3
4
2
4
0
3
2
3
2
3
4
4
2
5
0
0
3
4
4
0
5
2
4
0
2
4
6
4
5
6
6
1
5
2
1
5
4
9
5
4
1
3
1
6
2
1
5
5
6
0
4
1
2
6
4
2
3
4
2
0
4
5
5
3
4
3
4
3
2
3
2
3
6
0
3
4
4
2
0
5
1
7
0
2
4
6
1
3
3
2
4
5
4
0
6
5
3
4
3
6
5
7
2
5
3
3
3
4
2
3
5
0
2
6
4
1
2
0
4
0
3
1
0
5
1
3
1
0
2
1
6
6
3
1
3
1
1
5
1
3
2
1
5
0
0
3
7
4
0
4
4
4
2
1
3
2
3
3
3
4
1
3
3
3
3
2
0
2
0
4
8
0
6
2
7
1
5
5
5
2
0
2
1
6
0
1
6
4
0
3
1
3
1
1
4
1
3
6
0
0
3
2
0
5
2
0
1
2
5
5
1
2
2
0
3
5
1
3
3
2
1
7
0
4
2
7
4
1
5
3
1
0
5
2
3
0
3
2
0
3
3
0
5
1
2
3
0
3
2
2
4
2
7
0
4
3
1
3
0
3
1
2
3
2
7
3
4
6
3
2
0
3
1
5
1
5
4
2
1
3
3
0
2
1
0
3
2
4
1
4
0
7
0
5
2
1
4
1
4
1
3
3
0
5
1
2
3
2
1
1
2
0
4
6
0
0
3
2
1
3
1
0
5
1
2
5
5
1
5
2
1
0
1
5
2
0
1
1
2
0
7
0
4
3
4
4
3
1
6
1
3
7
2
2
0
4
0
3
3
0
4
4
0
6
2
4
2
0
4
4
2
1
1
3
5
1
1
4
2
0
0
2
1
7
3
3
2
3
2
2
2
2
4
5
3
0
0
5
3
6
3
3
4
2
5
2
0
4
0
1
2
3
5
3
2
2
2
5
2
0
8
0
0
4
0
6
8
3
4
5
1
1
1
0
2
0
6
3
3
3
2
3
7
3
3
8
4
6
2
4
1
1
1
0
2
4
6
2
4
0
1
0
3
1
1
3
3
2
3
2
3
4
4
2
2
2
1
3
0
4
4
2
1
1
3
2
1
2
3
4
6
3
1
0
6
1
3
3
4
1
2
4
1
7
3
1
4
3
2
1
2
7
5
5
3
4
2
3
2
2
8
1
3
0
3
0
5
2
3
3
0
0
3
2
5
1
5
2
2
4
8
2
2
4
4
0
1
3
7
6
4
3
3
3
5
0
5
2
3
2
4
3
6
6
6
1
2
2
5
1
3
2
3
3
0
0
0
4
2
4
3
0
2
0
4
3
2
1
3
1
2
1
3
2
0
4
0
1
1
4
2
3
3
0
0
3
2
1
0
1
7
3
3
4
0
5
0
2
7
1
3
9
2
3
3
1
4
2
4
4
3
4
1
4
3
1
3
2
2
2
3
0
8
0
0
3
4
3
1
3
8
5
1
5
4
2
2
3
4
3
0
7
6
3
3
0
3
2
4
2
4
0
2
2
0
0
5
0
3
4
3
3
5
4
4
2
2
2
2
1
0
3
1
2
0
1
0
3
2
0
5
3
3
3
5
0
1
1
6
2
3
5
0
4
1
2
3
3
2
2
4
0
0
1
1
1
0
3
1
1
4
1
2
0
5
1
3
2
4
4
3
0
1
5
1
2
3
0
0
5
1
3
2
6
4
1
3
2
2
1
4
3
2
3
1
1
1
4
2
0
2
2
1
3
1
1
4
2
3
2
5
1
4
2
2
2
2
0
2
3
2
6
2
1
5
1
1
0
4
1
4
4
2
5
6
0
7
2
0
1
2
6
2
6
1
2
1
1
3
5
2
3
1
9
1
2
6
6
4
3
5
3
2
1
4
1
3
4
2
2
1
0
3
1
4
0
1
3
1
1
1
1
2
4
5
4
2
7
5
3
2
5
0
5
1
1
6
5
6
4
0
1
2
0
1
5
5
3
2
3
1
2
7
1
3
0
3
2
6
0
5
3
3
2
2
2
7
1
7
1
0
2
1
0
1
0
2
0
3
2
2
5
6
2
6
0
2
4
1
0
0
3
3
2
5
2
5
4
5
3
6
4
4
1
3
1
2
3
0
2
3
0
5
2
2
3
7
3
2
4
2
4
0
3
2
2
3
4
2
0
4
2
2
4
0
4
7
2
3
3
1
0
3
2
2
1
4
3
2
3
2
3
1
0
6
4
3
1
1
7
2
5
3
2
1
3
5
2
0
4
3
3
1
4
2
0
1
3
4
0
2
7
0
3
4
2
6
0
5
4
1
3
3
0
0
1
1
3
1
1
4
0
0
0
1
5
0
6
6
2
1
1
5
3
3
0
3
0
2
0
3
3
4
0
2
2
2
2
3
0
6
3
4
5
5
2
2
2
0
0
2
2
5
2
0
1
5
2
4
0
0
5
6
4
0
3
0
2
4
4
4
0
3
2
1
3
3
0
4
1
6
1
5
4
4
2
2
0
3
4
5
3
0
2
2
5
3
1
2
4
3
1
2
3
3
0
2
3
4
2
4
4
0
4
1
5
2
1
2
2
4
3
1
2
0
3
0
4
3
5
2
4
8
2
4
0
5
3
1
4
2
2
3
2
2
2
2
3
5
2
1
3
2
6
4
6
1
0
1
4
3
3
2
2
0
1
0
6
0
3
8
2
0
4
4
4
1
1
6
0
2
3
3
4
4
2
4
3
0
5
3
3
1
1
2
4
2
1
1
2
2
1
3
0
4
1
2
5
2
7
5
2
0
2
0
2
4
5
3
4
1
3
4
4
1
0
1
4
5
5
0
3
3
3
2
3
2
1
0
0
4
2
0
0
0
1
4
7
0
5
0
2
2
4
2
3
3
1
5
3
3
2
2
2
3
4
1
5
3
6
5
3
3
1
3
2
3
1
4
4
3
0
7
3
0
2
2
3
0
4
0
5
2
3
3
0
3
3
2
1
6
1
3
3
4
0
0
1
1
4
0
0
3
4
1
0
5
2
1
1
3
0
1
4
0
4
4
0
1
1
2
0
1
0
3
2
3
2
5
5
2
2
0
6
6
2
2
4
3
2
0
3
5
1
1
2
1
1
2
5
0
0
4
1
3
3
4
6
0
3
4
2
0
4
0
2
1
4
4
3
1
2
4
2
0
2
3
4
5
2
2
2
0
5
3
4
5
5
2
2
6
5
3
4
4
4
1
3
0
5
6
0
1
1
1
4
0
0
1
3
2
0
1
2
6
14
2
5
0
0
0
2
3
2
2
3
3
3
2
4
1
7
1
1
3
2
4
3
4
2
1
0
6
1
2
4
4
2
2
0
2
4
0
0
4
1
2
2
0
2
1
2
2
5
3
2
1
0
3
1
1
4
2
1
0
4
1
2
4
2
1
2
3
3
3
3
5
1
3
1
4
2
1
2
0
4
0
2
3
2
2
1
4
2
1
2
4
4
7
3
1
4
3
1
3
1
2
5
7
5
0
1
1
2
1
3
2
9
0
0
4
1
5
2
0
3
1
4
2
2
4
2
2
2
5
0
8
3
2
1
3
1
3
2
2
3
3
1
2
2
2
3
10
6
3
1
2
5
3
0
5
1
2
2
3
3
3
3
0
0
3
4
1
5
0
5
2
0
1
1
4
0
1
3
0
2
3
2
2
0
4
0
0
4
1
2
2
4
0
5
5
4
1
0
1
0
2
2
3
3
5
1
0
5
2
0
2
2
4
3
4
0
0
1
7
2
2
3
3
3
1
2
1
2
3
1
0
0
4
3
2
4
5
0
2
5
3
5
6
2
2
6
3
5
3
2
2
0
1
2
3
0
1
1
5
0
2
3
2
3
1
4
3
1
5
4
2
1
4
4
0
2
2
5
1
4
4
0
5
2
1
2
1
0
2
1
4
2
2
2
3
5
3
4
5
3
2
5
1
1
4
0
4
2
1
0
2
2
4
2
1
0
0
1
4
6
6
4
1
3
2
2
0
2
4
0
5
3
4
2
0
3
2
3
2
4
4
0
3
4
4
0
1
6
2
1
4
2
0
0
4
4
4
1
4
1
2
2
0
4
1
3
3
0
6
4
1
3
3
0
6
2
3
1
2
2
1
0
0
0
2
7
5
0
1
5
4
5
2
2
5
5
1
1
2
4
2
4
1
6
0
0
4
0
2
3
2
1
3
3
2
1
1
3
2
2
3
3
1
1
6
0
0
4
2
3
2
6
2
4
1
2
3
4
1
2
1
1
1
7
2
1
6
3
2
1
1
2
0
3
1
3
1
2
3
5
3
4
1
0
2
0
0
4
1
1
3
3
1
3
0
3
1
2
2
0
2
0
4
4
4
3
3
1
4
4
3
1
4
0
3
2
1
1
0
3
4
2
1
1
1
5
4
3
1
3
0
1
0
1
3
1
0
1
4
5
6
1
4
3
5
7
4
2
0
6
5
3
0
5
3
2
1
4
2
5
2
1
2
2
8
2
1
8
6
0
4
1
4
3
3
3
0
2
0
0
4
2
1
3
1
2
2
7
0
0
3
0
0
4
0
0
6
2
3
2
4
4
5
1
0
1
5
9
2
0
1
2
6
0
4
2
2
5
2
3
5
0
3
4
1
0
1
1
3
2
1
1
1
0
5
2
2
1
2
1
2
0
3
3
4
0
1
1
4
6
1
0
2
2
3
3
3
6
1
1
4
2
0
4
2
2
2
0
1
1
3
1
6
6
2
5
3
2
0
2
1
2
3
7
3
3
5
1
0
1
6
2
2
3
3
2
5
1
2
3
1
1
2
0
1
0
3
0
1
5
1
5
1
2
5
3
6
3
3
2
1
4
0
1
3
4
5
3
2
1
1
1
3
1
0
2
1
0
2
5
2
0
6
1
3
3
3
2
0
1
2
0
4
1
4
5
1
8
2
3
4
1
4
0
0
2
1
4
2
2
3
0
2
0
2
2
2
3
3
1
2
0
1
4
0
8
1
0
1
4
2
5
2
0
2
3
6
2
3
5
1
1
1
2
1
3
4
4
2
4
1
1
4
0
1
2
0
4
2
0
5
1
2
5
5
1
3
0
3
0
3
4
1
3
6
4
2
1
6
0
2
2
5
1
1
5
4
1
1
3
0
3
4
6
2
0
0
4
4
4
1
5
3
2
2
6
2
2
2
0
4
3
2
2
4
3
1
2
2
3
1
3
1
1
5
1
1
4
2
3
0
0
6
3
1
4
2
2
3
1
1
5
4
3
3
1
1
5
5
3
5
1
4
2
6
3
1
0
1
3
1
2
3
1
3
1
4
4
3
1
0
1
2
2
5
0
2
0
3
3
0
1
6
2
4
1
0
5
5
4
2
2
3
3
0
4
3
3
2
1
2
0
3
2
1
2
0
0
3
3
1
1
2
3
2
1
1
1
0
6
2
5
0
0
6
0
3
2
1
4
2
4
1
1
1
3
1
2
1
2
1
3
0
2
1
1
3
0
0
0
2
1
0
1
1
2
1
1
2
0
1
4
1
3
0
4
4
3
1
1
3
4
7
2
0
2
2
0
2
1
1
4
2
1
2
0
8
2
1
3
2
3
3
5
1
4
1
4
2
1
4
0
0
0
1
2
3
1
5
3
5
3
0
0
7
5
1
1
3
0
1
3
0
1
5
2
3
1
2
0
3
4
2
2
6
3
2
2
2
4
1
7
1
0
0
3
0
0
3
1
2
3
1
0
2
4
3
7
5
2
1
3
3
2
0
2
2
3
4
0
2
2
5
3
1
7
0
5
3
1
1
2
2
3
2
3
3
1
2
3
2
6
1
2
1
1
4
2
0
5
4
1
4
2
3
3
3
2
0
0
2
3
2
1
10
3
3
0
1
1
1
0
1
3
0
2
3
4
0
1
2
2
0
1
1
2
3
2
0
2
3
0
0
0
1
2
0
1
2
6
4
5
3
3
3
4
3
1
2
2
1
5
0
1
3
3
0
2
2
1
1
0
2
2
2
0
2
2
0
2
2
2
3
5
2
0
1
2
2
1
1
5
0
1
1
1
1
3
1
0
3
5
3
2
4
15
3
0
0
5
4
1
6
3
4
0
1
1
1
0
0
2
4
4
0
5
2
0
1
0
2
0
2
3
2
1
1
2
3
4
3
4
2
3
1
3
2
1
2
2
1
3
0
2
2
0
1
4
1
1
3
0
1
1
1
3
1
3
3
1
1
3
0
6
0
5
5
1
0
0
0
0
2
0
1
2
4
0
1
3
2
0
2
3
1
4
1
3
3
1
0
3
2
2
2
2
1
1
4
0
4
2
1
0
4
1
0
2
4
2
1
4
1
0
2
2
4
0
0
1
6
5
2
1
2
1
1
0
2
5
0
1
1
5
3
2
3
1
5
6
0
0
6
3
0
3
1
1
0
2
3
3
3
3
2
2
1
2
3
3
3
0
5
3
1
0
1
0
1
1
1
1
1
2
1
2
3
2
2
0
1
0
2
1
2
1
2
3
4
3
0
5
1
0
0
2
0
0
1
3
1
6
1
1
0
1
3
2
3
0
0
2
4
3
0
2
0
0
2
0
1
1
0
0
3
2
2
1
1
0
2
2
0
2
1
3
5
0
1
0
5
3
2
2
3
1
3
3
4
4
1
2
0
2
4
3
2
2
0
3
3
3
5
4
0
1
3
4
4
2
5
3
1
2
4
2
3
0
3
1
3
2
2
2
1
1
2
3
0
2
5
3
0
2
1
0
1
1
0
2
2
1
6
2
4
1
0
1
2
6
2
4
0
2
0
1
0
0
1
0
5
1
1
0
0
1
3
1
3
4
4
4
1
2
3
3
1
6
1
2
0
2
4
0
3
3
2
2
4
2
4
3
1
6
4
0
5
0
0
0
5
20
3
1
1
1
2
2
0
2
6
0
1
4
0
0
6
1
4
4
2
2
0
3
1
2
3
0
0
2
3
4
2
4
2
1
1
6
1
4
3
5
2
3
4
5
1
2
5
1
5
2
0
0
1
1
2
0
4
1
2
2
5
3
1
2
2
5
1
7
0
5
1
3
0
4
1
1
3
3
2
3
2
3
3
2
3
2
5
0
4
1
0
3
2
2
2
0
0
0
2
4
5
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
6
1
3
1
3
1
0
4
7
2
3
3
1
0
3
2
1
1
3
3
4
1
0
1
3
3
1
5
6
1
0
1
4
2
2
4
4
4
0
0
1
2
1
0
0
2
1
1
2
2
1
1
3
3
1
2
1
5
1
3
4
0
3
3
0
1
0
3
1
2
1
4
1
2
3
0
2
5
2
3
0
1
1
3
3
0
1
4
4
0
1
3
3
0
5
2
3
1
1
1
2
0
1
6
2
1
5
1
4
1
1
3
3
1
1
2
1
2
6
0
1
1
1
4
2
3
0
0
0
3
1
7
4
3
3
2
1
3
1
4
1
5
2
2
0
2
3
0
1
2
2
0
2
2
3
1
0
1
1
2
1
4
3
1
5
2
2
3
3
3
2
4
0
1
4
1
0
4
1
0
0
3
3
4
0
4
1
4
2
0
2
0
1
0
5
4
3
5
0
4
4
1
3
3
0
2
3
0
3
1
3
2
4
2
1
3
1
2
3
3
2
4
5
0
0
1
1
0
0
1
1
2
0
2
1
2
1
3
3
4
3
2
0
3
2
5
2
0
2
3
0
5
1
1
3
2
3
1
4
3
0
2
4
2
1
0
1
4
2
3
1
3
3
5
0
1
1
1
0
2
0
2
0
0
2
2
1
3
3
3
4
4
1
2
0
2
2
6
1
3
5
2
3
0
1
3
3
2
0
2
3
4
1
1
1
2
0
4
4
3
1
2
2
6
1
0
1
2
3
2
4
3
0
3
3
2
3
1
1
3
2
3
3
1
2
1
1
2
2
0
1
5
3
2
0
0
3
4
2
4
5
3
0
0
2
1
8
3
1
0
3
0
4
2
7
3
1
7
1
3
1
0
0
5
2
5
7
4
1
3
2
3
3
2
1
1
1
2
1
0
0
6
2
2
1
3
4
0
0
0
3
0
2
1
0
2
3
0
1
3
5
1
1
2
3
1
3
3
5
2
5
2
3
2
6
3
0
3
0
2
2
1
7
1
1
2
3
1
2
4
0
1
2
1
3
0
5
0
4
4
2
4
0
0
4
0
0
1
6
3
1
0
2
1
1
2
0
2
1
2
6
3
2
0
1
1
2
0
4
4
3
4
0
5
2
4
2
2
2
0
1
4
2
5
2
0
4
0
0
4
2
1
4
0
2
2
5
2
4
2
0
2
1
5
1
0
1
2
6
0
1
3
0
3
2
0
0
4
2
2
2
0
2
1
5
1
3
3
3
2
3
5
1
4
3
7
2
1
2
0
2
1
5
0
4
2
1
5
1
3
1
0
1
2
3
1
0
3
1
1
1
0
1
1
0
4
3
5
1
4
3
1
1
3
1
3
1
2
1
4
0
1
0
0
4
4
1
3
1
4
1
0
2
1
1
0
2
4
3
3
0
1
3
1
0
2
1
0
1
1
1
1
2
4
2
4
4
0
0
5
2
2
0
0
1
1
8
0
5
5
5
2
0
2
0
1
2
2
1
2
0
1
0
0
0
5
1
3
3
0
2
1
1
1
0
1
5
2
1
0
0
2
1
0
3
5
2
0
3
6
0
5
1
5
0
3
3
5
0
0
0
0
3
6
1
3
2
3
0
6
1
1
1
1
0
2
0
1
3
2
1
1
2
3
2
0
3
0
1
4
5
1
0
3
1
6
0
0
2
2
4
5
6
5
1
2
2
1
3
1
0
1
0
1
2
1
0
2
0
1
4
3
3
4
0
2
2
0
2
2
2
1
1
1
0
4
2
2
0
2
2
0
2
4
2
2
2
4
1
0
2
3
4
3
3
3
0
3
1
1
0
2
0
3
2
5
2
2
3
3
4
3
2
1
4
1
0
2
3
3
1
2
4
6
3
2
1
1
5
1
4
2
2
4
3
6
2
2
5
1
2
1
1
6
3
1
4
2
3
3
0
3
2
1
2
4
0
0
0
3
2
0
2
2
2
0
2
2
1
2
0
0
1
0
4
3
3
7
0
3
1
3
3
0
2
0
1
1
3
1
2
3
0
0
3
0
2
1
2
2
0
5
1
1
1
0
0
1
5
3
4
0
1
1
1
2
2
3
2
1
0
1
2
3
3
3
0
0
1
4
2
0
4
1
2
2
0
0
2
0
0
1
0
2
0
2
0
4
3
2
1
3
0
4
0
5
4
2
0
0
1
5
0
0
4
0
1
2
3
3
1
2
2
1
2
0
0
1
2
2
3
5
3
3
1
1
4
4
0
1
2
1
2
1
1
1
1
6
1
7
1
2
2
1
0
5
2
2
0
1
9
4
4
8
3
0
3
4
1
0
2
2
3
1
1
2
0
2
1
2
1
0
1
1
6
1
3
3
1
0
1
2
2
2
4
4
2
2
3
3
2
2
1
1
1
2
0
1
1
1
0
0
1
2
3
2
2
2
3
2
2
5
1
1
3
3
2
1
4
3
2
2
1
1
0
1
1
2
1
1
0
5
2
0
1
1
0
1
2
4
2
0
0
6
1
2
1
3
1
2
2
0
0
0
1
1
0
1
2
0
2
3
2
5
1
5
3
6
7
4
5
0
0
1
0
4
5
2
5
0
0
4
3
5
0
5
3
0
4
0
1
1
2
4
2
3
2
2
0
0
0
2
4
1
5
2
2
2
6
3
0
1
3
1
3
2
1
4
0
1
1
3
1
2
7
1
1
6
0
5
1
2
4
1
3
1
5
3
1
0
1
0
6
1
1
0
3
1
3
2
4
2
2
1
2
2
4
1
1
7
1
1
3
0
3
1
4
0
3
2
1
0
3
1
2
3
2
4
5
4
2
2
0
1
0
1
0
5
1
1
3
4
1
1
2
1
1
3
0
1
5
1
2
1
4
1
3
3
4
1
1
1
0
3
1
0
3
2
0
1
3
3
1
3
4
0
2
0
0
1
0
0
0
2
1
0
1
1
2
2
1
7
3
2
4
4
2
2
5
0
2
1
1
1
0
1
6
4
3
0
1
3
4
3
0
0
0
3
0
5
2
3
0
3
1
1
2
0
5
3
1
1
3
2
0
0
4
3
1
1
0
0
3
1
4
1
0
1
1
1
5
1
6
1
3
2
1
2
1
1
3
4
1
5
1
2
0
3
0
6
0
1
0
3
0
3
2
0
1
2
1
3
5
2
4
1
0
1
0
3
2
4
3
1
2
5
1
0
0
0
0
1
0
4
0
1
3
3
3
3
1
4
1
0
0
1
2
3
0
0
3
2
4
0
4
0
1
1
1
3
3
0
1
0
6
2
0
2
2
1
0
3
3
0
1
5
2
1
1
3
0
0
5
4
0
0
1
1
0
1
2
1
1
1
4
0
0
1
2
2
0
2
0
2
3
5
0
3
1
1
3
1
1
0
2
0
1
3
4
1
0
1
1
3
3
4
1
2
0
1
0
1
1
2
3
7
1
1
2
2
2
0
5
1
2
3
1
0
3
4
1
2
5
2
3
1
1
3
2
1
1
1
4
0
2
2
1
6
1
2
0
0
4
2
2
5
3
2
1
1
1
1
0
4
1
5
3
0
0
2
0
2
2
2
1
1
1
3
0
3
1
2
1
0
2
1
1
1
0
1
0
1
1
2
5
2
2
2
3
1
1
3
1
0
2
2
1
3
0
0
0
3
0
1
0
0
1
0
2
0
2
0
2
0
2
3
3
1
3
2
1
3
3
0
1
2
0
1
1
1
4
1
3
2
0
2
1
2
1
0
0
4
1
0
2
5
2
0
2
3
2
1
1
1
2
1
2
3
5
5
4
2
1
1
1
0
2
0
3
6
3
2
2
1
1
3
3
0
3
1
2
1
3
3
5
0
5
0
4
2
2
1
1
3
3
5
1
4
3
0
2
0
3
2
2
0
3
0
1
0
3
2
0
6
2
2
2
1
5
6
1
0
0
0
2
0
2
2
2
2
2
2
1
3
1
0
0
1
0
1
0
4
1
3
0
3
0
3
0
2
0
5
1
0
0
3
4
0
0
1
4
4
4
1
1
3
1
1
3
2
5
3
7
2
2
1
1
1
2
3
5
1
3
2
2
2
2
2
2
4
1
0
3
4
4
1
2
1
4
2
4
2
1
3
1
3
1
0
6
5
3
3
2
1
1
3
2
3
1
3
3
2
0
1
1
0
1
0
0
4
2
2
2
0
1
4
4
5
2
1
2
0
1
2
1
3
0
2
3
3
1
3
1
2
3
0
1
4
0
3
3
0
2
2
0
2
4
4
1
250
1
0
0
4
4
1
6
3
5
1
0
3
1
0
1
4
0
0
2
0
2
0
3
2
4
1
3
2
1
2
0
4
1
5
0
1
2
4
0
1
0
0
1
3
0
2
2
1
1
6
1
1
4
2
1
3
5
3
2
3
0
0
3
0
3
4
0
3
1
0
0
1
4
5
0
3
0
5
2
2
1
0
1
2
3
1
3
3
1
1
2
1
2
1
1
1
0
4
3
3
2
0
1
4
1
0
0
0
6
2
0
2
3
1
2
2
2
2
1
4
2
0
4
2
2
1
0
3
0
1
1
3
1
4
3
1
1
2
1
1
2
1
0
0
1
2
3
3
2
0
2
4
1
3
1
4
1
2
0
3
1
0
1
4
1
2
1
4
1
4
0
2
1
5
0
3
4
0
0
1
1
0
4
2
2
1
3
2
1
1
0
1
0
3
2
0
3
2
2
3
0
1
1
0
3
1
2
1
2
5
0
3
0
0
0
0
0
7
1
0
3
2
0
3
3
1
4
0
0
1
2
1
4
0
3
2
4
0
1
1
3
0
2
1
3
5
0
0
2
2
2
0
3
0
1
0
0
3
3
0
7
5
1
0
3
1
3
5
2
0
0
4
0
2
3
2
1
1
4
3
3
2
2
0
4
1
0
1
0
4
3
4
5
1
3
2
5
2
5
2
0
2
5
2
1
0
2
1
2
1
0
4
1
0
0
1
3
3
4
4
0
3
3
0
1
2
3
2
0
1
1
0
2
0
2
1
1
0
0
1
0
1
0
0
4
2
0
4
1
1
1
2
3
1
0
2
2
0
9
2
1
3
0
2
1
0
1
6
1
2
0
1
0
2
0
5
4
1
2
1
0
1
1
3
1
0
4
2
2
3
2
1
3
0
2
0
2
1
3
1
1
2
1
2
1
2
1
0
0
0
3
1
3
4
0
1
2
3
3
1
2
1
3
1
2
0
2
1
1
1
4
0
2
1
2
1
12
1
4
1
1
2
2
0
1
5
1
3
3
1
1
1
1
2
1
0
4
1
2
0
0
4
3
1
2
0
1
5
2
3
2
0
2
2
0
2
0
2
1
1
3
1
0
4
1
0
6
3
2
3
1
0
0
0
1
1
0
1
2
2
0
1
2
0
2
0
1
2
0
1
2
6
1
1
6
2
4
0
1
0
2
2
6
4
4
0
3
0
2
1
3
1
0
1
2
2
2
3
3
4
2
2
3
6
4
4
1
2
2
1
2
0
1
2
3
2
4
7
0
3
2
4
2
4
3
0
2
3
4
3
0
2
2
1
1
2
0
0
0
0
1
5
1
1
3
2
1
2
0
3
1
3
5
1
0
4
1
2
1
2
4
1
1
0
0
3
1
0
4
4
1
3
1
1
3
1
2
7
1
0
1
2
2
2
2
3
4
1
1
1
2
4
1
2
2
3
2
0
2
2
0
2
2
0
4
0
1
2
2
5
0
2
0
1
0
0
0
0
1
4
1
0
4
4
0
0
3
1
1
1
2
0
6
1
1
3
1
1
0
2
3
4
3
2
0
3
2
1
2
3
0
6
3
1
1
1
1
0
1
1
0
4
2
4
2
3
5
3
2
1
0
5
2
0
1
0
3
4
3
3
10
2
1
3
0
0
1
1
2
2
5
0
3
3
2
3
0
0
2
0
1
0
1
2
1
2
5
5
0
2
4
1
2
4
0
0
3
4
2
1
1
2
4
1
2
1
1
0
5
0
4
0
3
0
2
1
0
1
3
0
2
2
1
1
2
5
3
0
3
0
0
3
5
2
1
3
1
0
2
1
2
3
0
3
2
1
0
1
5
2
2
0
2
0
2
1
0
3
1
1
0
4
2
4
2
1
2
2
2
5
0
1
0
0
1
3
4
2
2
2
0
1
1
3
0
0
3
5
1
0
2
1
4
0
2
3
1
0
3
0
2
0
0
2
1
0
1
3
4
4
2
4
1
3
3
0
3
1
4
0
0
6
2
0
1
0
1
1
2
1
0
0
1
0
2
1
0
8
2
2
0
3
2
1
0
3
4
0
3
5
0
3
1
3
3
0
0
1
2
1
1
1
1
1
0
2
6
2
1
1
2
1
0
3
2
1
2
5
1
2
3
2
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
3
3
3
3
2
1
2
3
3
0
0
0
0
1
0
0
1
0
1
0
0
3
1
0
5
1
0
2
0
0
3
1
2
3
5
3
0
3
2
2
4
0
1
1
1
1
0
2
4
0
0
0
2
1
2
0
2
2
0
2
4
1
0
0
0
5
1
2
3
0
1
1
2
1
0
3
5
3
0
5
3
1
4
0
2
5
0
0
1
2
2
1
0
2
2
2
4
1
0
3
2
3
1
2
0
3
2
4
1
0
0
5
3
2
2
1
1
1
0
1
3
1
3
4
1
3
3
1
2
0
3
2
2
3
0
0
3
2
0
0
1
1
0
0
0
3
1
1
1
2
0
0
6
2
2
1
3
2
4
3
0
0
2
2
1
2
2
1
1
0
2
1
2
0
1
1
7
4
0
1
5
1
3
2
1
1
2
4
0
2
4
0
3
1
3
2
1
1
0
2
2
1
6
2
1
1
1
2
4
2
0
3
2
1
1
0
5
3
1
2
1
1
1
4
2
2
3
2
3
3
3
3
2
0
0
4
5
1
0
5
1
3
4
2
2
1
0
0
0
1
1
0
3
0
2
1
1
0
7
25
0
2
2
3
0
3
3
4
4
2
2
1
4
1
2
3
3
1
5
3
2
1
2
2
0
1
1
6
5
0
1
2
1
1
1
3
1
1
3
0
5
2
5
4
3
6
0
4
2
0
3
6
1
1
3
2
1
2
6
2
3
2
0
2
2
1
0
2
1
2
0
3
4
2
4
1
2
4
0
0
1
3
2
1
3
1
4
2
2
0
4
0
3
2
1
2
1
2
2
2
3
1
2
1
1
3
1
0
0
3
2
3
1
3
0
2
2
1
2
3
3
4
0
1
0
0
3
0
4
1
2
3
2
2
1
3
0
0
1
4
3
0
1
0
0
0
1
4
2
2
0
0
4
1
2
0
3
1
2
0
1
2
1
2
4
2
1
1
2
4
3
2
0
4
4
1
1
2
1
1
2
0
2
0
2
4
0
4
0
3
2
1
4
2
1
4
2
3
0
1
1
1
2
4
6
2
6
1
2
2
1
2
2
0
0
3
0
0
4
1
4
0
0
2
2
4
2
0
2
1
0
2
3
3
1
2
0
1
0
0
2
3
3
3
3
3
2
4
0
2
4
2
1
0
3
1
2
4
1
2
0
0
2
2
2
2
0
2
4
3
2
3
5
3
2
6
2
0
3
3
3
4
1
1
1
1
1
3
2
1
0
1
1
3
1
0
1
5
2
2
1
0
5
2
0
5
0
1
4
3
1
0
1
0
2
0
4
0
0
0
3
3
1
2
4
3
2
2
0
4
2
2
0
2
1
1
2
0
0
4
4
1
1
0
2
2
0
3
1
2
3
1
3
2
1
0
3
2
0
2
2
2
0
0
5
8
2
0
2
1
0
3
2
4
3
1
3
0
0
3
4
2
8
3
3
1
1
0
0
1
4
1
1
0
2
3
1
3
1
1
1
0
2
0
0
0
3
4
3
3
0
4
2
1
0
0
2
0
2
1
3
1
2
4
1
0
1
1
2
0
0
4
1
2
1
0
1
3
2
0
2
3
2
1
0
5
1
0
0
1
3
1
2
3
3
0
1
2
0
1
1
1
2
3
3
1
1
0
3
0
6
0
2
1
1
4
7
5
1
5
2
2
0
0
2
1
3
2
1
2
2
3
1
3
3
3
2
2
3
7
5
2
2
0
0
3
2
0
4
1
3
1
2
2
5
2
3
1
1
2
4
1
0
2
0
0
1
4
0
1
1
1
2
3
0
0
0
1
1
2
2
5
3
1
1
1
0
2
3
3
3
2
2
1
0
3
3
3
3
2
0
1
1
2
3
0
0
3
3
5
1
2
0
1
0
1
0
1
2
2
1
3
3
1
3
2
1
3
2
0
1
0
2
1
1
1
0
1
5
0
4
0
3
4
2
1
2
3
0
0
3
1
2
1
2
0
0
0
0
2
1
1
0
1
2
0
0
2
0
1
1
4
0
0
1
0
1
1
1
2
0
1
0
1
2
2
0
1
5
0
0
2
2
3
2
2
1
2
0
1
2
0
0
2
0
0
2
3
2
3
2
5
1
1
0
2
1
5
2
0
3
4
2
1
1
1
1
3
1
2
0
3
3
1
0
1
2
3
1
0
1
4
1
4
1
1
2
4
3
1
0
1
1
4
43
5
1
1
4
1
0
0
2
0
2
0
1
1
0
4
1
0
1
0
2
3
2
1
1
2
2
0
0
0
1
0
0
4
1
4
0
1
0
3
0
1
2
3
4
3
0
1
4
1
2
1
1
0
2
2
2
1
0
2
0
1
1
1
1
0
1
2
1
1
5
3
3
2
4
2
3
2
2
2
4
3
1
1
2
1
1
2
2
6
4
2
1
2
0
1
2
1
2
1
1
1
3
2
0
2
1
0
0
0
2
3
1
3
1
0
1
0
2
1
3
1
3
0
3
3
2
4
5
1
2
0
1
0
3
1
0
1
1
1
1
1
0
1
4
2
2
2
2
2
3
0
0
0
1
0
3
1
1
3
1
3
3
0
1
1
1
2
2
4
3
0
7
2
1
2
1
5
1
1
3
6
0
3
0
3
0
0
0
2
4
1
1
2
0
1
3
0
1
5
3
2
1
0
5
0
3
0
3
0
1
2
4
1
0
0
1
3
3
0
2
0
1
0
4
3
3
4
4
1
1
3
1
0
2
0
2
1
1
2
4
2
1
4
1
3
1
0
0
1
3
2
1
3
4
4
4
2
2
1
5
1
2
1
2
1
0
2
2
1
3
4
0
1
0
1
0
0
0
1
0
2
1
1
1
1
3
2
0
0
0
1
2
2
0
2
2
0
2
1
0
2
1
5
0
3
2
2
1
1
2
2
0
0
2
2
2
3
2
2
1
1
3
0
1
2
0
0
0
2
4
3
0
4
2
4
4
0
0
0
1
2
3
0
0
2
0
0
4
4
1
1
1
5
1
1
2
0
3
1
3
2
2
3
3
1
1
2
2
2
1
0
6
2
2
0
0
0
3
2
4
2
1
1
1
3
0
1
3
1
1
2
1
0
2
0
1
1
6
4
2
0
1
2
0
4
2
0
2
1
1
2
4
1
3
1
5
2
3
2
0
3
2
1
6
3
0
2
1
1
2
1
5
0
0
3
1
0
1
0
0
1
3
3
0
1
1
2
0
3
1
2
2
1
2
1
2
3
0
0
3
2
2
0
3
1
0
1
1
1
2
1
4
2
1
2
2
4
1
4
2
2
1
2
0
3
0
0
3
1
2
1
3
4
5
1
1
0
5
1
0
4
1
2
0
1
1
2
1
0
1
0
0
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
3
0
3
4
3
4
0
3
5
0
1
4
3
1
0
0
7
0
6
0
2
6
0
1
2
2
3
1
0
2
2
4
3
4
1
2
1
0
1
1
0
2
2
2
2
1
1
2
2
3
0
1
2
3
2
0
3
2
3
4
2
0
3
1
0
0
0
3
0
3
0
2
1
2
0
0
3
2
2
1
2
0
0
0
0
3
1
1
0
6
2
4
2
2
3
1
1
0
6
1
2
0
2
1
3
1
1
3
1
1
1
4
0
3
3
6
0
3
0
0
3
0
0
1
3
1
0
1
1
0
0
3
0
1
2
2
2
2
1
2
4
2
2
0
1
4
0
2
2
0
5
3
2
4
2
2
2
3
1
2
1
1
1
3
3
3
2
2
2
0
1
1
2
1
1
1
4
2
0
2
0
1
2
1
1
3
0
1
4
4
2
0
2
3
1
2
1
5
0
0
3
2
0
2
1
1
3
2
3
3
0
0
1
5
2
8
0
1
2
2
1
4
2
0
1
2
2
0
2
2
1
3
5
1
2
1
1
1
2
0
1
0
1
1
3
2
1
2
2
0
2
3
0
1
1
3
2
1
3
1
1
1
3
1
0
0
0
1
0
2
2
4
5
2
2
3
1
3
5
2
2
2
0
2
1
1
0
3
2
1
2
3
0
0
2
4
2
1
4
1
4
5
0
4
0
1
4
3
0
1
1
2
0
3
1
2
2
2
2
0
1
4
0
3
1
7
2
2
0
6
0
0
3
3
2
2
0
0
0
2
2
2
2
0
1
4
2
2
2
0
6
1
2
1
1
2
2
1
2
1
0
1
2
0
1
3
3
0
1
0
0
4
2
2
1
0
2
3
4
2
2
1
0
0
1
3
5
2
0
0
5
1
0
0
1
3
1
4
0
0
1
1
1
4
1
0
1
2
3
1
1
4
0
3
0
1
0
1
2
4
1
0
0
4
2
1
3
1
4
3
5
0
1
2
3
0
4
1
1
2
2
4
3
2
1
1
7
3
1
0
2
1
3
2
2
2
1
1
1
2
0
4
3
0
4
3
2
0
1
0
1
3
1
0
3
2
2
2
0
1
3
1
1
2
7
1
0
1
1
1
2
0
3
1
2
2
1
1
2
1
0
3
2
3
4
0
4
2
3
2
1
4
5
1
1
0
2
0
1
0
3
1
0
0
2
0
0
1
1
5
4
3
3
1
2
0
3
4
2
4
2
4
0
0
0
0
0
1
0
0
1
0
1
6
0
0
1
2
3
0
0
1
0
2
1
0
0
5
8
0
4
2
1
0
0
1
0
3
2
0
0
2
0
3
4
0
3
1
0
1
2
2
3
1
2
0
1
1
2
1
1
1
1
1
0
0
3
3
2
0
1
1
0
1
2
0
0
1
1
2
0
0
1
0
2
1
1
0
1
1
3
0
6
1
0
6
1
3
1
0
3
0
1
2
1
2
4
3
2
0
1
2
0
1
2
1
3
1
3
5
1
0
5
2
1
1
3
0
3
2
3
4
0
3
1
0
2
4
0
4
2
1
1
1
3
1
2
1
3
2
0
0
1
4
2
0
0
5
2
0
1
1
1
2
0
1
3
1
0
5
2
0
2
4
0
0
1
2
1
0
9
1
1
1
2
2
1
0
1
0
2
1
0
1
3
4
0
2
1
0
1
2
1
3
4
0
6
1
2
2
3
0
0
2
2
2
2
2
1
1
2
0
1
4
0
1
6
0
2
2
0
2
2
3
1
0
5
1
0
1
1
5
4
1
5
0
2
1
2
0
5
1
1
1
3
1
1
2
0
0
3
3
2
0
1
3
3
4
2
1
3
1
2
1
3
2
2
0
1
0
1
6
2
1
2
1
2
4
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
1
4
2
2
3
3
1
3
2
1
4
2
3
0
1
1
2
0
1
1
3
0
2
1
0
3
2
0
4
0
2
0
5
1
1
0
0
2
3
0
3
4
2
3
2
0
1
1
0
3
1
1
2
3
0
1
2
0
2
2
0
4
2
2
2
2
1
1
2
0
2
1
1
5
3
0
0
3
1
1
4
3
0
4
1
4
4
1
3
1
3
0
2
2
6
2
3
0
1
1
0
2
2
1
4
0
1
1
23
1
1
2
3
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
5
0
0
1
0
1
0
2
2
2
2
1
3
0
2
2
1
4
2
0
1
1
2
2
1
2
0
4
4
1
3
0
1
4
3
0
0
0
1
3
0
0
2
2
1
2
3
2
0
2
0
2
0
3
2
1
1
0
2
1
0
4
3
2
2
3
0
4
4
4
1
4
2
3
2
0
0
0
1
6
1
3
1
0
0
2
1
3
2
2
1
2
1
4
0
0
3
0
2
0
0
1
1
0
0
1
2
2
0
2
2
0
2
1
1
3
1
5
1
2
2
1
3
5
1
3
14
2
1
1
5
2
3
0
1
1
4
2
5
1
3
0
1
0
3
1
0
1
3
2
4
2
1
2
2
1
0
3
1
0
4
2
2
5
3
2
4
0
6
2
3
0
1
0
1
1
0
2
4
1
0
2
0
0
2
0
5
2
1
0
6
2
0
0
2
0
2
0
0
2
3
2
2
0
2
2
3
3
2
0
1
0
3
2
0
3
1
1
4
0
2
1
2
2
4
2
1
1
1
1
4
1
2
4
4
2
4
2
3
0
1
4
2
1
2
1
2
0
2
3
1
0
1
1
3
3
1
2
2
2
3
2
3
3
1
3
2
2
1
3
1
4
3
3
0
3
1
5
7
1
1
1
1
2
0
2
2
3
2
3
1
1
1
1
0
3
1
0
3
1
0
0
0
1
2
1
0
4
2
1
1
3
3
0
0
2
1
3
2
0
2
0
2
3
0
0
2
2
5
4
1
1
2
1
6
0
0
1
2
0
1
1
1
1
2
1
2
0
2
2
2
2
0
4
0
2
2
1
1
2
1
3
2
0
2
2
1
0
4
0
2
1
7
2
1
2
4
0
2
1
2
1
6
3
0
0
0
2
1
1
4
0
1
3
0
5
0
2
2
4
2
2
1
0
1
0
3
0
0
0
4
1
1
2
3
0
3
3
0
5
0
1
0
2
2
5
1
4
1
5
0
1
2
2
0
3
1
4
1
1
2
2
1
4
2
1
2
0
1
3
3
3
2
3
1
2
2
2
4
4
3
5
3
3
0
0
3
7
3
3
1
2
1
0
2
1
4
5
3
3
0
1
2
3
2
3
1
3
3
0
3
0
0
1
0
1
7
1
4
3
0
2
3
1
2
2
1
2
1
2
0
1
1
1
2
5
0
1
0
1
0
2
1
0
3
2
2
0
3
0
2
2
5
2
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
1
1
1
1
5
0
2
0
2
2
0
1
0
1
0
4
2
1
1
2
4
0
1
1
1
4
2
2
1
0
4
5
1
1
1
3
0
3
3
1
0
5
1
6
0
2
2
2
3
2
0
0
2
0
2
2
0
0
3
1
1
0
1
0
1
0
3
2
2
0
1
1
0
1
1
2
3
5
1
2
2
2
1
2
0
2
3
0
2
3
0
0
1
2
0
4
3
0
0
1
0
1
0
3
2
3
1
0
1
0
2
1
1
0
2
3
2
0
3
2
3
2
3
4
18
0
3
32
1
0
2
1
3
2
4
0
2
0
2
2
2
1
0
1
1
3
2
0
2
0
0
3
1
1
1
0
0
2
0
2
3
2
0
0
2
2
0
0
3
0
2
1
2
0
0
1
4
0
1
2
3
1
0
1
3
3
0
2
3
4
0
0
1
3
2
2
1
0
2
1
2
2
0
2
2
1
2
3
1
3
2
1
2
0
0
1
0
2
1
1
3
2
4
1
1
0
0
4
3
0
3
0
5
0
2
1
0
2
0
1
0
2
8
3
4
1
1
1
5
4
1
5
4
1
2
0
4
1
1
1
5
1
0
0
3
1
1
1
0
0
0
1
0
0
0
3
0
0
0
2
3
1
1
1
1
5
5
0
1
1
1
2
0
2
2
0
1
2
1
3
0
0
0
3
1
0
4
0
0
1
1
1
0
1
0
2
0
3
3
2
1
2
0
0
1
1
0
1
1
3
1
2
1
0
1
3
1
0
2
0
1
3
0
0
2
5
4
0
3
1
1
2
1
0
2
0
0
1
1
2
3
1
0
3
2
4
0
3
2
2
0
2
1
1
0
2
0
1
0
1
0
0
1
2
0
2
2
1
1
1
0
1
0
1
1
1
0
2
2
2
1
2
1
2
2
2
0
4
2
1
1
0
1
2
2
1
1
3
2
0
2
4
1
3
2
1
3
1
0
0
2
1
0
1
2
0
1
1
2
0
1
1
4
3
1
2
2
1
1
4
2
3
2
2
0
3
2
1
2
1
2
1
2
0
2
2
3
3
2
0
1
4
1
1
4
2
1
2
3
1
2
1
0
0
2
1
2
1
0
3
0
2
0
3
3
0
0
5
2
3
0
0
2
2
1
3
1
1
1
1
1
0
1
1
1
3
3
4
1
0
0
1
1
4
0
1
0
3
2
0
3
0
5
1
4
1
1
2
1
0
1
0
0
2
2
0
0
1
3
0
0
2
3
2
1
1
1
3
2
0
0
2
5
2
0
2
1
0
0
0
2
2
4
1
2
1
1
2
2
1
0
1
2
3
1
1
1
4
3
1
1
5
0
2
1
3
0
1
4
0
1
0
3
1
2
3
1
3
1
4
0
1
1
2
2
0
4
1
4
0
1
0
1
3
0
2
2
3
1
3
0
1
2
3
0
0
2
0
5
2
1
0
4
0
3
0
0
1
0
3
3
0
1
1
2
4
3
1
2
1
1
0
0
3
0
7
1
1
2
1
3
1
1
2
1
1
0
0
0
1
0
1
2
0
2
1
0
0
1
1
1
2
4
1
3
0
1
2
5
0
1
3
1
0
2
2
0
1
0
1
2
2
0
0
1
2
0
0
3
2
1
0
2
3
1
1
0
1
0
3
0
2
0
3
2
2
1
4
1
2
2
2
1
2
0
1
2
5
1
2
3
1
1
1
1
1
2
2
0
2
0
1
1
1
2
2
3
3
0
1
2
2
1
0
2
1
3
1
1
1
1
2
1
2
6
0
0
1
2
0
3
3
3
1
1
0
1
1
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
1
1
3
1
1
1
0
1
1
3
1
2
0
0
3
3
1
2
1
0
1
0
0
1
2
0
2
2
2
0
0
2
1
2
1
1
0
0
1
0
0
5
1
1
2
1
1
1
8
1
2
1
2
1
1
3
0
2
0
3
2
0
1
3
0
1
2
2
0
3
2
1
1
0
2
0
1
0
0
3
0
0
1
3
1
3
7
0
2
1
2
5
1
1
0
3
3
0
3
3
0
2
3
2
5
0
1
1
0
3
0
0
0
2
3
4
3
3
1
0
2
3
1
1
0
0
1
4
4
1
1
2
2
3
0
3
2
1
3
3
3
1
1
1
0
1
2
4
0
0
2
2
1
2
3
5
2
1
1
3
0
2
0
3
3
3
1
6
1
0
3
1
1
1
2
1
0
3
0
2
1
0
2
0
1
3
2
1
2
2
0
1
1
2
1
2
1
2
4
2
2
1
2
5
1
2
0
1
2
1
0
1
2
1
3
1
0
0
2
2
2
1
2
3
2
1
2
1
2
0
0
0
0
0
4
1
4
0
1
2
1
3
3
2
1
1
2
0
1
2
1
0
1
4
1
4
3
3
0
0
1
2
2
4
0
3
2
1
0
2
1
1
3
2
0
0
0
3
1
0
1
0
1
1
3
0
7
0
0
0
1
1
3
1
2
0
1
4
1
1
0
2
1
2
0
0
3
5
2
1
3
2
2
2
0
4
0
1
1
1
3
1
2
2
1
2
0
2
3
1
0
2
0
1
0
2
2
1
2
0
1
0
2
2
0
1
2
1
1
1
0
3
1
3
2
4
4
1
1
2
0
1
2
0
0
0
1
1
0
3
2
1
3
0
0
1
1
0
2
0
4
1
0
1
1
1
3
1
1
1
0
2
2
1
1
4
3
1
3
0
1
1
3
1
1
3
1
2
0
1
2
3
2
1
2
0
2
0
1
0
1
3
0
0
0
0
1
3
0
2
3
2
3
0
2
0
7
1
1
1
2
1
3
0
0
1
0
1
2
0
0
5
1
1
0
2
0
2
2
1
0
1
1
4
1
0
2
1
2
1
2
0
4
2
4
0
1
2
3
0
2
2
4
0
1
4
0
0
1
1
0
1
2
1
1
1
1
0
4
0
0
1
0
3
2
2
0
0
0
4
2
3
2
0
1
0
1
1
2
0
0
0
0
4
2
1
2
0
0
0
0
0
1
4
0
2
1
0
1
1
1
3
1
0
1
2
1
0
1
1
0
2
3
2
3
1
1
1
0
0
0
0
1
0
2
0
1
0
3
2
3
3
0
2
5
1
3
2
3
3
1
0
0
0
3
0
5
0
2
6
1
2
2
2
3
1
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
1
0
1
0
1
0
1
0
0
3
0
2
1
2
2
3
0
2
3
0
0
1
2
1
2
2
2
3
0
3
3
1
4
1
2
3
3
2
0
1
0
0
1
1
1
0
0
1
2
1
3
2
2
2
1
0
0
0
1
1
2
3
1
0
1
0
1
2
1
1
1
1
0
1
1
2
0
0
0
0
3
2
1
0
1
0
1
1
0
3
1
3
3
4
2
0
3
2
2
2
3
2
1
4
3
0
3
0
3
0
2
0
1
5
0
5
1
1
3
1
0
0
1
0
3
4
4
0
3
0
4
0
3
0
0
2
0
4
0
1
2
1
2
3
3
0
1
1
1
1
2
0
1
5
0
3
0
1
1
2
0
1
3
1
1
0
3
2
2
0
3
2
1
3
2
1
13
1
4
3
2
2
2
0
1
3
2
2
0
2
1
3
1
1
0
1
0
0
3
0
0
1
3
0
0
0
1
0
1
1
1
1
2
2
2
1
2
2
2
4
1
1
2
1
0
3
2
0
4
3
0
2
1
0
0
2
2
5
1
2
0
0
1
2
2
2
1
2
2
0
1
3
0
2
0
4
0
3
3
3
3
0
10
0
5
0
2
1
0
3
2
3
1
0
1
2
1
2
0
1
3
3
7
1
1
0
3
0
2
2
0
0
3
0
6
2
0
1
3
2
1
0
2
4
1
1
2
2
2
3
4
1
1
0
1
1
2
1
3
0
3
2
4
0
4
2
1
2
3
0
3
1
1
2
0
1
3
0
0
0
1
3
3
1
2
0
3
1
1
3
2
3
1
2
1
1
1
2
4
0
1
0
0
1
1
2
1
0
0
1
1
3
0
0
2
2
2
1
1
0
3
0
0
0
1
1
1
3
1
1
1
3
0
3
1
2
0
0
2
2
1
1
0
1
1
0
3
1
0
1
0
0
0
0
1
0
4
3
0
1
1
1
0
3
4
0
1
3
2
1
2
0
2
0
1
0
1
2
1
1
2
3
1
0
1
0
0
4
1
3
0
0
2
0
0
0
1
0
1
1
5
0
1
3
0
0
0
1
1
1
0
2
2
1
3
3
3
0
0
0
1
7
1
0
1
0
0
4
3
0
0
1
2
1
2
0
0
2
4
1
2
3
0
0
2
1
0
1
1
2
4
0
2
1
1
1
2
0
0
0
4
1
0
4
4
3
1
3
0
0
0
1
3
1
2
0
0
1
1
1
3
3
2
0
1
6
3
1
1
3
4
1
0
1
2
3
2
0
2
0
5
1
0
0
3
2
0
3
0
2
1
0
2
1
1
0
0
2
2
0
0
3
3
1
1
3
0
1
0
0
2
1
1
2
0
0
2
3
1
2
1
4
4
1
2
0
0
2
1
0
2
0
4
0
1
1
1
2
2
1
0
0
2
1
1
1
1
0
2
1
3
2
1
1
0
0
1
1
0
4
2
0
2
4
0
2
2
2
1
1
1
1
1
1
1
0
4
2
1
2
1
0
0
3
3
2
0
0
0
3
2
1
0
3
2
2
1
1
0
0
0
0
4
1
0
2
3
2
2
2
0
1
0
2
2
1
0
0
3
1
3
1
3
2
0
1
2
0
2
0
1
1
1
1
3
0
2
0
1
0
2
2
2
0
0
2
0
1
0
2
0
0
2
0
0
3
1
3
0
2
0
0
0
2
2
0
1
2
0
3
3
0
2
1
0
2
0
1
3
0
1
2
0
3
0
1
0
1
1
1
0
0
3
0
0
2
4
2
1
1
1
2
1
4
1
1
1
1
6
1
0
2
1
2
2
1
1
0
2
1
2
3
0
0
1
3
1
0
2
3
1
0
3
0
3
2
2
2
3
0
1
1
1
1
0
0
1
1
1
0
0
1
5
0
4
0
1
1
2
1
0
0
4
1
0
0
4
1
2
1
2
2
0
2
2
0
0
0
2
1
1
1
1
5
3
0
1
2
0
4
0
1
4
0
0
1
1
3
2
2
0
3
0
2
2
0
0
1
2
2
3
2
1
2
1
2
0
2
2
1
3
0
0
0
1
3
0
3
3
6
3
1
1
0
1
0
1
0
1
0
3
1
4
0
3
1
1
3
0
0
1
1
0
0
1
0
3
1
0
0
0
3
2
2
1
2
1
2
0
2
0
2
3
4
1
2
1
4
0
2
1
2
3
3
2
1
1
0
0
0
2
0
1
0
1
2
0
1
3
2
3
0
3
1
5
2
0
0
2
0
3
1
1
1
0
1
3
0
0
2
2
0
2
3
0
2
0
0
1
1
0
0
1
3
0
0
1
0
0
2
4
0
4
1
2
1
1
1
1
0
0
2
0
3
3
0
1
1
2
2
0
3
2
1
0
6
1
2
1
2
1
1
1
4
2
1
0
1
0
0
2
1
0
3
1
0
2
1
1
1
0
0
0
0
1
1
1
0
4
0
2
0
0
0
3
1
0
6
2
4
1
1
0
2
0
2
3
1
4
3
2
0
0
2
9
1
2
1
1
0
0
3
1
3
3
0
3
0
1
4
1
0
1
1
2
3
0
4
3
1
0
0
1
1
0
2
4
3
1
2
0
0
4
1
1
4
2
0
1
0
0
4
1
3
0
2
1
1
0
3
0
0
0
1
2
0
2
1
2
2
3
0
0
2
1
2
1
2
1
0
1
3
0
0
2
1
3
0
2
2
2
0
1
1
0
2
3
0
1
0
1
0
0
1
3
0
1
1
0
2
2
0
3
2
1
3
1
0
2
2
3
0
1
3
1
0
3
0
3
0
1
1
0
3
2
1
1
0
1
4
5
3
5
0
0
0
0
3
1
0
2
1
0
2
1
0
1
1
1
2
3
1
0
1
2
1
2
1
2
3
4
3
1
1
0
1
0
240
0
1
1
1
2
0
4
0
0
3
3
4
3
1
4
4
1
0
0
0
2
0
0
1
2
0
0
1
0
1
2
4
1
1
1
1
4
0
2
2
0
0
0
3
2
1
1
0
2
1
1
2
0
3
0
3
3
1
4
2
2
0
2
1
0
3
0
2
0
2
1
0
5
1
3
1
3
1
1
2
2
0
0
0
0
1
1
1
0
2
5
2
0
2
0
1
1
1
2
0
3
1
2
3
3
1
5
5
3
3
3
2
0
4
2
1
1
3
1
5
4
3
1
0
2
0
0
1
1
0
1
1
2
0
3
3
3
6
1
1
0
3
0
1
2
1
3
2
10
1
2
1
3
0
2
0
0
0
1
4
4
0
1
3
1
1
0
4
3
1
0
1
1
4
3
2
2
0
4
3
1
0
0
1
0
0
1
2
0
3
1
3
2
4
1
1
3
2
0
1
1
3
0
0
2
2
2
0
0
1
2
1
1
2
0
2
3
2
6
1
3
3
0
1
1
0
2
1
1
2
0
2
3
0
1
0
0
1
1
2
0
1
1
2
0
0
1
3
2
2
0
2
1
3
1
1
3
1
0
2
0
0
4
1
4
0
0
0
2
1
3
2
3
2
1
3
1
1
2
1
1
2
0
0
1
0
3
1
1
1
2
0
3
1
4
3
2
4
1
1
0
3
0
0
1
0
7
2
1
2
3
5
0
2
3
3
2
0
1
1
1
2
2
1
2
1
0
0
1
2
0
0
0
3
3
2
2
0
0
3
2
5
2
1
0
1
3
0
2
1
0
0
4
1
2
1
0
2
0
4
1
1
3
5
2
0
0
1
0
0
1
2
2
1
1
0
1
1
1
2
0
0
0
2
0
1
0
1
3
3
0
3
0
1
1
0
0
2
2
4
1
2
1
2
0
3
2
1
3
1
0
1
3
2
1
3
3
4
0
0
3
2
3
0
0
2
2
2
0
0
1
1
1
3
0
4
1
0
0
1
2
1
0
2
1
1
1
0
1
0
2
0
4
0
2
1
2
1
0
3
3
2
2
6
0
6
0
4
6
2
1
0
1
1
2
4
0
0
1
2
1
2
1
1
0
1
1
1
1
4
4
1
5
2
2
2
1
2
0
0
1
3
1
0
2
0
1
0
0
1
2
1
1
1
1
1
1
0
2
0
4
0
1
1
2
0
4
2
3
2
2
2
2
2
1
0
0
3
1
1
0
0
0
0
1
0
0
1
1
3
1
1
4
2
0
4
3
2
0
3
0
0
0
2
1
0
2
0
4
3
0
0
0
2
0
1
2
0
6
1
3
4
4
2
3
1
3
2
2
2
0
1
0
0
1
1
1
0
2
3
3
0
2
0
2
1
0
2
2
0
0
2
2
0
0
2
1
1
3
1
1
2
1
0
1
2
1
0
0
0
3
7
0
1
0
2
1
0
1
2
1
0
1
1
7
0
1
0
1
1
0
0
0
1
2
1
0
0
2
0
5
1
2
4
0
1
1
0
1
0
0
0
1
1
1
3
2
3
2
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
3
1
0
4
1
1
0
0
4
2
0
0
2
4
2
2
2
2
1
0
4
1
1
1
0
1
1
2
1
2
2
3
2
2
1
2
0
1
3
2
1
0
6
0
1
2
2
1
0
1
3
4
1
1
0
1
0
3
1
0
2
1
1
3
1
6
0
4
1
2
1
0
0
2
2
1
1
2
1
3
2
1
2
0
1
1
1
0
1
2
3
1
0
2
0
1
0
0
2
0
0
1
2
1
2
0
1
0
0
1
1
2
3
0
2
1
1
0
1
3
1
0
4
5
0
2
1
2
1
0
1
0
2
0
2
0
5
2
3
0
1
2
1
2
2
0
2
4
7
0
1
1
1
1
1
1
0
1
0
0
3
0
2
0
4
0
0
0
2
1
1
0
2
1
3
6
1
1
1
1
0
5
0
1
3
2
0
4
0
1
0
3
2
2
2
1
1
2
3
4
4
1
2
1
0
2
3
0
3
0
1
2
3
0
4
3
0
1
2
0
0
2
0
1
0
1
2
2
1
1
1
0
0
2
2
0
0
2
1
3
4
3
4
3
1
1
0
1
0
1
2
1
0
0
1
2
1
4
0
1
3
2
3
2
2
0
0
1
2
0
1
0
4
0
2
1
1
0
1
0
1
2
2
4
2
1
1
1
1
0
4
1
0
1
2
3
0
1
0
0
1
2
1
4
7
1
2
0
0
2
2
1
1
2
2
1
1
1
2
2
0
4
6
0
2
1
3
0
0
0
1
0
2
0
1
2
0
0
3
5
1
1
0
2
1
1
0
4
0
1
0
0
1
2
0
1
1
2
0
1
4
2
1
1
0
1
2
0
3
2
2
1
4
2
1
3
1
2
4
0
1
1
12
0
1
0
2
0
2
1
0
2
3
2
2
3
0
2
1
1
0
0
3
0
0
2
1
0
0
2
1
3
2
1
2
1
0
2
4
1
0
0
1
2
2
3
5
2
2
2
0
2
1
2
0
0
3
0
1
0
0
3
2
3
2
1
1
1
1
2
1
2
1
0
2
1
0
0
1
2
3
0
4
4
3
0
1
1
1
2
1
1
1
1
1
1
0
2
0
5
4
1
1
2
4
3
0
2
1
0
2
0
0
0
0
0
2
0
3
3
0
3
1
6
0
2
1
0
0
2
0
5
0
0
2
0
0
1
0
1
1
4
0
3
2
2
1
2
2
0
1
1
1
1
1
1
0
2
1
0
7
1
0
2
2
2
0
1
2
2
3
0
0
1
2
0
0
3
0
0
0
1
1
5
0
5
4
2
0
2
3
0
3
1
1
2
1
2
0
0
4
1
3
1
1
0
1
1
3
2
1
1
2
3
1
2
2
2
5
0
3
1
1
0
1
0
0
3
1
0
3
0
1
1
5
2
1
2
0
2
2
0
3
1
1
1
1
0
1
3
0
0
0
2
1
0
2
2
0
2
0
0
2
5
0
0
3
4
1
1
0
0
2
2
0
2
1
1
0
0
1
3
4
0
2
25
2
2
0
2
1
0
5
0
0
1
1
0
3
1
0
3
0
2
1
3
0
0
0
0
1
3
5
1
0
1
2
1
2
2
2
2
0
0
3
1
1
1
0
3
0
1
0
0
0
1
0
2
2
2
0
0
3
0
0
0
1
1
4
1
1
0
0
1
2
2
1
1
0
0
0
3
3
0
0
0
1
1
1
2
2
1
0
0
3
3
0
0
1
3
4
0
1
0
0
1
2
3
2
1
2
0
1
2
0
4
0
1
1
0
1
2
1
0
1
3
1
5
1
2
1
1
2
1
0
0
0
1
1
1
1
4
0
1
2
1
0
0
4
0
1
0
1
2
0
2
1
0
2
4
2
0
2
2
3
3
0
1
1
0
0
0
2
2
0
2
0
0
2
1
0
2
3
0
1
1
3
5
1
0
1
0
0
1
4
3
1
1
0
1
4
0
2
1
0
1
2
1
3
1
0
3
2
3
2
0
2
0
0
1
0
2
2
1
0
1
1
1
2
0
2
1
3
2
1
0
1
0
1
1
2
2
0
2
3
2
2
1
1
0
1
1
2
4
1
2
1
1
0
0
1
0
2
0
0
4
1
0
0
2
1
0
2
1
1
0
1
2
1
2
2
1
0
1
3
1
1
0
1
0
0
2
0
5
2
0
1
0
1
3
5
0
3
1
0
2
1
1
1
0
1
2
1
2
0
4
1
3
1
3
0
2
1
3
3
1
1
2
2
1
0
2
0
2
0
1
1
1
0
1
3
0
8
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
2
1
3
0
0
1
1
1
2
2
1
1
2
3
0
1
1
2
1
0
1
4
1
1
2
3
2
1
0
1
2
0
15
2
2
2
1
0
2
0
1
2
1
0
1
2
0
1
0
0
2
1
4
1
1
1
5
2
0
6
0
2
0
1
0
1
1
1
3
0
1
1
0
0
1
1
0
2
0
0
1
3
0
0
4
3
4
0
1
4
1
0
1
0
3
2
0
0
0
2
2
1
1
1
0
0
3
3
2
1
1
1
0
1
0
1
1
2
0
0
5
0
2
3
1
0
1
1
4
1
0
2
1
2
0
0
2
0
0
0
2
2
3
1
2
3
1
3
1
1
0
1
0
0
0
1
1
4
3
2
1
1
0
5
1
1
0
1
1
1
0
0
0
1
1
2
0
2
1
0
2
2
4
0
0
3
2
3
0
1
2
0
0
1
0
4
2
2
0
0
1
950
0
2
0
11
0
1
1
3
0
3
2
0
1
0
10
1
0
0
0
1
0
1
5
0
0
3
2
3
0
4
0
5
2
2
3
0
0
0
0
0
1
2
0
2
1
0
2
1
0
2
1
2
1
3
2
1
1
0
1
0
1
2
1
1
1
2
0
2
3
5
1
1
0
2
0
3
0
1
1
1
2
1
3
3
1
3
0
5
2
0
0
0
2
2
6
3
0
1
0
2
1
1
3
0
4
0
2
1
2
2
1
1
0
3
3
3
0
3
3
0
1
0
2
0
1
1
4
0
1
2
2
0
0
0
2
3
3
2
1
2
0
1
2
1
4
1
0
1
2
5
3
2
4
6
2
2
1
1
2
2
0
0
2
2
3
0
0
2
3
2
0
1
1
5
1
1
0
2
2
1
1
1
1
0
1
2
0
0
0
0
2
4
0
3
1
4
2
3
0
4
0
2
2
0
4
3
3
1
2
0
0
0
0
3
4
0
4
2
1
3
4
0
2
0
1
1
2
2
0
5
0
1
1
5
0
2
0
1
3
3
4
3
2
5
2
1
0
6
1
3
1
1
1
1
2
1
3
3
0
0
0
1
4
2
2
4
8
4
2
2
0
2
1
4
2
2
0
3
0
1
0
3
0
2
1
0
0
0
2
1
1
1
1
0
2
0
2
0
1
1
1
2
2
0
0
2
2
4
1
3
0
0
1
2
3
2
1
1
0
0
0
2
3
1
0
1
0
0
0
2
0
0
0
2
1
1
2
2
0
3
0
0
1
0
0
1
1
0
0
1
2
3
2
2
4
3
0
2
0
0
1
0
4
0
3
1
2
1
6
2
4
2
3
3
1
1
0
2
1
1
3
2
1
0
1
1
1
1
0
3
6
4
3
4
1
1
3
1
3
5
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
1
2
2
0
0
0
3
0
0
1
2
3
5
0
2
5
0
1
0
0
1
0
0
1
1
0
0
2
1
4
2
0
0
0
1
2
1
1
0
0
2
1
0
0
1
3
0
0
4
2
1
4
1
1
0
1
1
1
4
2
3
0
2
1
0
0
1
4
0
2
1
2
3
1
0
1
4
0
0
0
1
3
0
1
3
2
0
0
2
4
1
1
0
1
0
1
0
0
1
1
0
3
0
1
1
1
0
0
7
0
2
1
0
0
2
0
0
2
1
3
0
1
6
0
0
1
0
5
0
0
0
0
0
0
1
2
4
0
1
0
0
0
0
2
2
2
4
1
7
0
2
0
2
0
1
1
3
0
2
1
0
2
1
1
1
2
3
2
1
3
1
2
0
4
3
2
0
2
0
1
1
1
1
3
0
1
3
3
2
1
1
3
3
2
0
1
2
0
0
4
0
0
0
3
1
3
0
1
1
1
2
1
0
1
1
3
3
2
0
2
0
4
4
2
3
2
0
5
1
2
2
3
2
3
1
0
0
4
1
4
0
1
1
4
0
2
2
2
1
0
0
1
2
4
2
0
1
1
1
1
4
1
1
0
0
1
2
2
0
1
0
2
1
3
1
1
2
1
2
2
1
1
1
0
2
0
2
0
0
3
1
2
0
1
0
0
1
1
0
1
0
3
0
1
3
2
0
2
0
0
0
0
0
3
0
0
1
8
4
0
0
4
0
0
1
0
1
0
0
0
3
5
1
1
1
1
2
1
1
4
0
0
0
1
4
0
2
3
1
1
2
1
1
3
2
0
2
1
1
1
0
3
2
1
1
2
0
0
0
1
4
2
0
0
0
10
0
3
2
0
4
1
1
0
2
0
2
2
2
1
3
4
0
2
0
2
1
0
1
0
2
0
1
3
1
0
1
2
0
0
3
1
2
4
0
0
1
3
2
5
2
1
1
5
10
0
0
1
2
0
1
0
0
1
0
1
1
0
2
3
1
1
4
2
2
1
0
1
0
2
2
0
3
2
5
1
1
1
0
1
0
0
1
0
2
2
0
0
0
2
3
1
1
4
4
0
2
1
3
1
2
0
1
0
3
1
0
1
2
2
3
1
0
2
22
1
2
1
0
2
1
0
2
3
1
0
0
2
3
0
1
0
0
0
0
4
2
2
0
0
0
0
2
0
1
0
1
1
4
0
0
1
2
0
1
3
3
1
1
2
0
2
2
0
3
2
3
0
2
1
0
0
0
1
2
0
1
1
3
5
0
5
0
2
0
1
1
0
5
1
1
5
2
3
1
0
0
1
1
0
3
3
1
0
1
2
0
2
1
0
5
9
0
1
0
2
1
2
1
1
1
2
2
1
1
2
2
3
1
4
0
1
0
1
2
0
4
4
1
0
0
2
0
0
2
2
0
0
3
1
1
1
1
0
0
3
0
5
3
0
1
1
1
1
2
1
2
2
0
1
0
1
1
0
0
0
1
1
2
1
1
1
0
0
2
2
1
0
0
0
30
0
0
0
2
3
0
2
0
1
1
0
1
2
0
3
1
1
1
2
1
2
1
0
3
0
2
1
2
1
2
0
0
1
1
2
0
2
0
2
0
1
0
4
2
1
0
4
2
2
0
0
3
3
3
0
0
3
0
1
1
0
2
2
0
1
2
3
1
0
0
0
2
2
1
1
0
1
1
1
0
1
3
0
0
2
3
3
3
1
0
1
0
1
4
1
2
0
0
1
0
1
0
0
3
4
2
2
1
2
1
2
0
0
0
0
1
3
2
3
2
0
0
0
0
2
2
2
0
1
0
2
0
1
3
1
0
2
1
1
3
1
0
1
0
1
2
3
2
0
0
1
2
1
1
1
0
0
0
0
0
2
0
1
5
0
0
0
0
0
3
0
0
0
2
2
2
1
0
0
0
1
0
1
1
4
1
2
2
2
1
1
4
0
2
2
0
5
0
0
0
1
1
0
2
2
2
0
0
3
0
0
1
2
2
1
2
1
1
0
1
0
3
1
0
3
3
1
3
1
2
1
0
6
1
5
1
0
0
1
4
0
4
0
1
1
0
1
0
0
1
0
1
2
2
1
3
0
2
1
0
1
3
1
2
0
4
0
1
1
0
0
1
0
0
0
1
2
2
1
0
0
2
2
3
1
0
1
0
4
0
4
0
1
1
0
1
0
5
2
4
1
7
2
4
4
2
2
4
2
1
0
0
2
0
1
0
1
2
0
0
1
1
2
3
2
1
0
0
0
0
2
0
4
2
1
4
2
2
1
1
1
2
2
1
2
2
1
3
2
4
2
0
0
0
0
3
1
0
1
2
4
1
2
0
0
0
0
0
1
1
1
1
3
1
2
4
0
3
1
2
0
1
0
3
0
0
1
1
1
3
2
2
2
1
1
1
1
0
1
3
2
0
0
7
1
0
2
0
0
2
0
4
0
2
1
0
1
1
0
5
0
1
1
0
0
2
4
2
2
1
2
0
0
1
2
4
2
1
1
3
0
0
1
0
4
3
1
0
2
0
0
4
1
1
1
0
3
1
0
2
2
0
0
2
0
2
1
1
2
3
1
2
2
0
1
1
0
2
0
1
5
0
1
3
3
1
4
0
1
0
2
2
0
5
1
0
0
2
1
2
2
3
2
1
0
2
2
1
1
3
1
0
0
1
1
1
2
3
0
1
0
2
3
0
5
0
0
3
1
1
0
1
0
0
3
0
0
2
0
1
0
1
2
1
1
3
3
1
1
0
2
2
1
2
3
1
1
1
0
0
0
0
2
0
3
1
2
1
1
1
1
0
0
1
1
1
0
0
5
1
0
1
1
1
0
0
4
1
1
1
3
6
0
4
1
1
3
1
1
0
1
1
1
2
0
2
0
0
5
0
0
1
0
1
1
0
1
0
4
0
2
3
2
0
0
2
0
1
2
2
1
1
2
8
0
0
3
2
1
2
0
2
3
1
1
1
2
2
0
0
1
0
2
1
0
1
0
1
0
2
1
1
3
3
0
3
3
0
0
1
0
1
1
2
0
3
0
0
1
0
0
2
0
2
0
3
2
3
1
0
2
2
2
2
3
1
0
0
0
0
0
2
0
4
1
1
1
5
1
3
1
0
2
0
3
2
0
0
0
2
3
2
1
0
2
0
1
5
1
1
1
0
3
4
2
2
1
0
1
3
3
0
1
1
0
0
1
1
1
1
0
2
0
0
2
0
5
0
0
3
1
3
2
1
0
0
1
0
1
2
1
2
0
0
1
3
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
4
0
2
0
0
1
0
0
1
4
1
1
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
1
0
0
1
3
2
0
0
3
0
4
1
1
1
3
2
3
3
0
1
1
0
2
0
0
2
2
1
2
1
0
0
1
4
0
1
2
1
3
1
2
1
2
4
2
0
1
4
0
0
0
1
2
0
1
1
2
0
2
0
3
0
0
4
1
4
0
1
2
0
1
2
1
3
1
1
2
1
0
0
2
2
3
2
1
3
3
2
4
0
2
0
0
3
3
1
0
2
1
1
1
2
4
1
0
0
3
3
2
2
1
2
2
1
0
0
4
1
2
0
3
1
0
0
4
4
0
2
3
0
0
0
1
3
1
2
0
0
2
0
1
4
0
2
0
1
1
1
0
2
0
0
0
0
2
3
0
1
0
0
2
2
4
0
1
1
2
1
0
0
0
2
1
0
1
1
2
0
2
1
1
0
0
4
0
0
0
1
0
0
0
2
2
1
0
2
2
3
1
1
1
3
1
0
0
2
1
0
0
0
4
0
0
0
5
0
1
3
0
0
0
4
0
1
3
3
2
2
0
2
0
1
1
1
1
0
0
1
0
0
2
3
1
2
2
0
2
3
0
0
0
1
0
2
2
2
2
2
2
2
0
1
1
1
1
0
3
0
0
1
1
0
3
4
4
0
2
0
1
4
1
0
2
1
1
1
1
1
0
4
2
4
0
0
1
1
0
0
2
0
0
2
1
2
1
4
1
1
7
2
2
1
0
1
0
2
0
1
2
2
2
1
1
0
2
1
0
1
0
2
3
0
4
2
1
1
0
2
3
2
1
2
0
1
2
1
2
4
0
0
0
0
0
0
3
3
2
3
2
0
1
1
0
3
2
0
0
0
0
0
0
0
0
1
2
0
1
0
3
2
1
1
3
2
0
1
1
1
0
2
2
1
3
1
0
1
0
3
1
1
0
0
3
0
1
2
0
0
0
0
2
0
4
1
2
3
2
0
1
2
1
0
0
4
1
4
3
2
0
1
2
0
4
1
0
0
2
1
0
0
3
3
0
4
1
2
0
0
1
0
1
1
1
6
2
0
0
3
1
0
2
1
3
1
3
0
1
2
1
2
1
0
1
0
0
1
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
5
1
1
2
0
2
1
3
1
0
0
2
1
0
1
0
3
0
2
1
2
0
0
2
1
0
1
0
2
0
1
3
0
3
1
3
0
0
1
1
0
3
0
2
1
1
0
0
1
1
0
0
3
0
0
2
2
1
1
1
1
3
0
0
3
3
2
1
4
2
0
0
2
1
2
4
2
1
0
1
1
4
0
1
0
2
2
1
0
0
0
0
0
0
1
3
2
0
1
1
0
0
1
1
1
1
1
0
5
0
0
2
2
1
3
1
2
1
4
1
0
4
1
1
3
1
4
1
2
0
0
2
1
1
0
1
4
2
0
0
0
0
2
0
0
1
0
5
0
2
3
3
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
4
0
0
1
1
1
0
1
0
3
1
0
2
0
0
1
0
4
2
0
0
1
0
0
2
4
3
1
2
1
5
0
0
0
2
1
3
4
1
0
1
2
1
1
1
2
1
1
0
0
2
2
1
1
3
0
1
3
0
1
0
0
4
3
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
4
0
0
1
1
3
2
0
3
0
3
1
0
2
2
4
1
1
3
0
2
1
0
1
1
0
0
0
0
1
2
1
0
2
5
0
2
2
0
0
0
1
1
1
0
2
2
0
2
2
1
0
0
1
0
0
0
0
4
0
2
2
0
1
3
0
1
2
2
0
2
1
6
2
1
1
0
2
3
4
1
0
0
0
0
0
1
7
0
1
3
0
2
2
2
2
0
0
1
1
1
0
1
0
0
0
0
2
4
1
1
0
0
2
0
0
1
0
0
1
1
0
2
2
0
1
1
3
1
1
2
0
0
0
3
4
0
0
3
1
0
1
0
2
0
1
1
0
0
2
0
2
6
3
0
4
1
0
1
0
1
0
0
2
1
2
1
0
1
0
3
1
1
1
1
0
1
0
0
4
3
0
0
3
1
0
2
3
1
1
2
2
1
2
0
0
0
1
0
0
0
0
1
0
1
6
3
1
0
0
0
4
1
0
0
1
0
0
2
1
1
1
3
2
6
0
5
2
0
0
1
0
1
1
0
3
2
0
3
0
1
1
2
2
0
2
0
1
2
0
2
0
2
1
0
0
0
0
0
3
1
1
1
1
1
0
3
1
3
0
1
0
0
2
0
1
0
0
5
0
0
1
0
2
0
0
2
2
3
1
3
0
0
0
2
0
1
1
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
4
0
2
2
2
2
3
1
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
1
3
0
0
0
2
1
1
3
1
1
0
0
0
1
1
0
1
0
2
0
1
1
0
4
1
0
3
0
1
0
5
2
0
1
2
0
1
3
1
1
1
0
2
2
0
1
1
1
0
2
1
0
1
0
2
3
0
2
0
0
2
3
3
3
0
2
0
0
2
2
2
0
4
0
0
3
0
0
1
1
2
2
0
0
2
1
2
1
1
0
1
3
0
0
3
2
0
0
1
0
0
5
1
2
1
0
4
2
3
1
2
1
0
5
2
3
2
3
0
0
0
1
22
2
1
1
0
0
0
0
0
1
0
3
1
0
1
1
0
1
0
3
0
0
1
2
1
2
0
2
2
0
2
1
5
0
1
1
0
0
1
0
0
4
0
0
2
2
1
3
5
3
1
1
3
3
0
1
1
1
0
5
0
0
0
0
1
0
3
0
1
2
2
0
0
0
1
0
4
0
1
2
2
0
0
0
0
2
3
0
1
2
0
0
1
1
0
1
3
0
2
2
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
2
0
1
3
0
3
0
1
0
2
0
0
1
2
0
0
3
2
0
0
2
1
0
2
1
2
3
1
0
1
2
1
1
0
1
1
1
3
4
4
2
0
0
3
0
0
2
0
0
0
1
1
2
1
0
1
0
3
0
1
8
1
4
1
2
3
0
1
1
2
1
1
2
1
1
3
0
2
0
4
2
2
2
1
1
1
1
2
0
5
0
1
0
2
2
1
4
2
0
1
1
0
2
5
0
2
0
1
3
0
3
0
0
2
1
1
2
2
1
2
2
0
5
3
1
4
0
2
1
0
1
0
1
2
2
4
0
1
0
2
0
1
0
0
4
1
0
1
3
0
1
5
0
1
0
2
1
0
2
0
0
0
0
2
0
2
4
0
0
0
1
0
2
0
0
1
0
0
4
1
1
0
0
1
2
0
0
1
2
1
2
1
3
4
2
1
1
1
3
1
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
4
1
0
0
1
2
0
2
1
1
2
0
1
1
1
2
4
1
0
0
7
0
0
2
2
0
0
0
2
0
0
2
1
1
0
2
6
5
3
0
2
1
3
0
4
3
1
2
3
4
0
1
3
1
0
0
0
1
0
1
2
0
3
0
0
4
2
1
1
2
1
0
1
2
2
1
1
4
1
1
0
0
1
0
0
0
2
1
1
2
1
2
0
1
1
0
1
1
0
0
2
3
0
1
0
0
3
1
0
1
0
3
2
3
4
1
1
1
0
0
0
4
0
0
1
0
0
3
0
1
2
1
1
4
1
1
3
0
0
1
5
2
3
0
0
1
2
0
1
1
1
0
0
2
1
0
2
2
4
2
0
1
0
2
0
2
1
0
0
2
0
2
2
4
2
0
0
1
0
0
2
0
3
1
4
0
0
4
1
3
0
2
0
1
0
0
0
3
0
1
2
0
2
0
2
1
2
2
3
3
1
1
0
0
1
0
0
1
2
2
2
4
1
2
3
0
2
3
2
2
1
2
3
0
3
0
1
3
2
1
0
0
0
1
1
0
1
1
0
1
5
0
1
2
0
1
0
0
0
0
1
2
1
2
1
2
3
1
1
2
0
2
1
0
0
1
2
1
2
1
1
2
0
1
2
3
0
0
0
1
0
0
3
2
2
1
1
1
2
2
2
0
0
1
3
0
0
1
0
1
0
2
0
0
3
5
2
1
0
1
1
0
2
3
0
3
1
1
1
0
2
0
0
0
2
3
0
3
2
2
0
2
2
0
2
3
1
0
3
0
2
5
1
2
5
4
5
1
1
0
4
0
0
2
0
1
1
0
0
0
1
2
2
3
2
1
3
2
2
4
0
1
1
0
3
2
2
0
1
2
0
0
0
2
0
1
0
0
2
0
2
0
2
1
1
2
1
0
1
1
0
1
1
2
0
1
2
0
0
5
0
0
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
1
1
0
2
0
3
1
0
0
1
0
1
3
1
0
0
1
1
0
1
2
0
0
3
1
1
1
0
0
2
0
2
0
0
1
1
0
0
4
0
0
1
1
0
0
2
0
3
1
2
1
0
3
2
0
0
0
6
0
0
0
1
0
2
0
0
0
2
0
4
0
4
0
0
4
0
1
1
2
1
2
1
0
2
0
2
0
0
1
0
4
0
0
2
1
0
1
0
1
3
2
4
0
1
0
2
2
0
1
1
0
1
0
2
1
2
0
5
1
1
2
1
1
1
1
0
1
0
0
1
0
1
3
0
0
1
0
2
1
2
0
2
0
0
0
2
1
1
4
2
1
0
0
3
0
1
0
4
0
0
0
0
0
1
2
0
0
1
2
1
6
2
2
1
0
1
0
3
1
2
2
2
2
4
1
2
3
1
0
4
2
3
2
0
2
0
3
0
0
1
2
0
0
1
2
1
0
0
1
0
2
0
3
0
3
1
2
0
0
2
0
0
3
2
3
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
1
0
3
2
1
0
1
0
0
1
1
1
1
1
1
4
0
0
1
3
0
0
1
0
2
1
0
2
2
2
0
1
2
1
0
1
0
0
0
0
1
4
1
0
0
1
0
1
3
2
1
2
2
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
8
0
4
1
1
0
1
1
1
4
0
2
1
2
5
0
0
1
0
4
0
1
3
0
0
1
1
2
1
2
0
1
1
0
0
0
3
0
0
0
3
0
0
1
1
3
0
1
2
0
2
0
0
2
2
0
1
0
2
1
0
2
0
2
1
0
6
1
1
1
1
4
0
1
1
2
0
1
1
0
0
0
5
1
0
0
0
1
5
8
2
0
0
0
1
3
0
0
1
2
1
1
1
2
0
3
1
4
1
0
2
0
0
1
0
1
0
3
0
1
3
0
1
0
1
1
0
0
2
0
0
2
0
5
0
1
1
1
0
0
3
0
0
2
2
3
0
0
1
1
1
1
0
1
2
0
9
2
1
2
1
0
2
0
3
0
2
0
1
4
0
0
1
0
0
2
0
0
0
0
0
2
1
2
3
1
1
0
1
2
1
0
0
1
2
1
2
0
3
0
2
1
0
3
1
1
2
0
3
3
2
1
2
1
1
0
1
3
1
0
2
0
0
2
1
0
1
1
0
2
1
1
1
0
1
3
2
1
1
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
0
3
2
1
0
4
3
0
0
2
2
12
1
0
2
0
4
3
2
1
0
1
1
0
0
0
2
0
1
0
0
0
6
1
0
3
2
1
0
0
1
2
1
1
1
1
1
3
0
0
1
0
0
3
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
3
1
2
2
0
2
0
0
0
3
0
0
1
0
1
1
1
1
0
1
1
0
0
3
3
1
0
0
0
1
0
0
1
1
0
0
1
2
2
1
3
3
0
0
1
1
2
2
0
0
0
0
1
0
0
8
0
1
3
0
1
1
0
0
1
2
2
1
2
1
4
0
0
0
0
2
3
0
8
2
1
3
2
2
1
4
1
0
1
1
4
0
2
0
2
1
0
2
0
2
2
3
0
0
1
0
1
2
2
0
0
2
1
3
1
1
1
2
1
0
1
2
1
0
2
2
4
2
0
4
1
0
1
0
2
0
3
6
2
1
3
2
0
0
2
0
0
0
1
3
1
4
0
1
0
1
2
3
3
0
2
1
0
1
0
0
3
0
2
3
0
1
2
2
1
0
2
0
0
0
0
1
1
0
1
2
1
4
1
0
3
0
0
0
4
2
0
1
2
1
0
0
1
1
4
2
1
4
0
1
2
2
1
0
1
2
1
0
1
1
2
2
4
1
1
0
0
1
2
2
0
1
3
0
0
1
0
1
0
1
1
2
1
3
1
0
3
0
1
0
0
2
0
3
2
2
1
0
1
1
1
113
1
1
1
1
1
0
2
0
0
1
1
2
1
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
3
0
0
0
3
1
1
1
2
1
2
2
0
2
0
0
1
1
0
3
0
2
2
5
0
0
0
0
1
1
1
0
1
3
0
2
0
3
1
0
3
1
3
0
0
1
1
0
1
1
3
0
3
0
1
2
2
1
2
0
0
1
1
4
0
3
1
0
1
2
1
1
3
4
0
4
2
0
0
0
3
2
1
3
1
0
0
1
1
3
0
0
2
0
0
2
1
0
3
0
0
1
1
1
2
1
0
2
1
0
1
0
3
1
1
4
2
0
1
0
0
0
3
1
2
2
2
1
0
0
0
1
0
3
1
4
0
1
0
2
0
0
3
1
2
1
0
0
0
0
1
0
3
2
0
0
2
1
1
3
2
2
2
0
4
1
0
0
2
2
0
0
0
1
2
3
0
1
1
2
1
0
0
0
3
3
0
1
0
0
1
1
2
2
0
1
1
2
3
1
0
2
1
3
5
0
3
0
1
0
0
0
58
1
4
0
1
0
1
1
1
1
3
3
1
1
2
3
2
1
2
1
0
1
3
2
1
3
0
1
1
0
0
2
1
0
0
2
0
2
1
0
2
0
0
4
0
2
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
3
4
0
2
3
0
1
2
3
0
2
2
1
1
1
1
0
2
1
1
1
2
0
1
0
3
2
1
2
0
0
2
0
0
0
0
2
57
4
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
2
1
2
1
2
1
1
4
2
1
0
2
0
1
1
0
2
0
1
1
0
1
4
1
1
1
0
2
0
0
1
1
1
0
0
1
0
0
3
1
2
1
5
1
0
0
3
1
0
2
2
1
2
1
0
1
2
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
3
1
0
2
2
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
4
0
0
1
4
0
2
1
1
1
1
3
0
0
1
0
1
1
1
0
0
0
2
1
0
1
1
0
3
2
1
2
0
2
0
0
0
2
1
4
3
3
0
0
4
0
2
1
3
1
1
2
0
0
0
1
1
0
2
1
1
0
2
0
5
1
2
1
0
0
1
1
0
0
3
1
2
0
1
0
2
0
1
0
2
0
1
0
2
1
1
0
0
2
3
3
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
3
0
0
2
0
2
0
4
1
2
0
1
2
3
1
0
0
0
2
4
1
0
0
0
1
2
2
1
0
0
0
1
1
1
1
1
0
0
3
0
2
0
1
1
1
4
1
1
3
1
4
0
0
0
0
1
1
0
1
0
4
4
1
0
0
3
0
0
4
4
3
3
1
1
3
1
2
1
0
0
0
1
0
3
0
3
3
2
0
2
1
0
0
0
0
1
2
0
2
2
2
4
1
1
1
0
1
1
4
0
1
0
3
4
0
2
0
0
1
0
2
0
2
4
1
0
0
0
0
0
1
2
1
0
1
0
0
5
2
0
0
1
1
0
2
0
2
4
0
2
0
0
1
0
2
1
2
1
0
0
1
3
0
3
0
2
3
1
2
2
1
0
2
2
1
1
1
0
2
1
0
0
2
1
1
1
3
3
1
1
1
0
3
7
3
0
2
4
0
0
0
0
3
2
3
1
1
2
1
0
5
0
1
2
2
3
3
2
1
0
1
0
0
4
2
1
1
4
1
0
2
1
1
0
0
3
4
0
0
1
1
2
1
2
2
0
0
2
0
1
0
3
0
1
1
3
0
3
1
0
2
0
2
1
0
2
0
2
4
1
0
3
2
1
0
0
2
2
3
2
1
0
1
2
6
0
0
2
1
2
1
0
0
3
1
1
2
3
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
2
3
1
0
0
3
0
0
0
1
2
0
1
1
4
2
1
2
2
3
1
1
1
5
1
1
0
0
0
2
2
0
4
0
0
1
4
0
1
1
1
1
0
2
0
1
2
1
0
2
1
1
1
1
0
2
3
1
0
3
3
2
1
0
0
1
1
2
0
3
1
0
0
2
1
0
2
1
1
1
2
1
0
1
2
0
1
0
1
0
4
0
1
0
0
0
1
0
0
2
2
0
0
0
1
5
2
0
0
4
2
3
0
1
0
1
1
3
2
3
0
2
0
0
0
1
0
2
1
1
1
0
1
5
0
0
1
0
0
1
1
5
4
0
1
1
4
0
0
0
4
1
0
0
0
0
1
0
2
2
2
0
1
4
2
2
2
0
0
1
0
0
2
4
0
1
1
0
2
4
0
2
0
0
4
0
1
0
0
1
0
1
3
1
1
1
0
0
0
1
0
2
2
0
0
0
3
4
1
0
1
2
0
1
1
1
2
0
1
0
1
3
0
1
2
4
1
0
2
1
2
1
0
1
0
1
0
1
0
2
0
0
1
1
1
0
1
4
0
2
0
0
1
1
1
4
0
0
1
0
3
0
1
1
1
1
2
2
2
0
2
2
3
0
2
2
0
0
1
1
0
0
2
0
1
1
1
0
1
3
2
1
0
0
1
0
1
2
0
0
1
0
2
1
0
2
1
3
1
0
0
2
1
0
5
1
2
0
0
1
1
0
1
1
1
0
2
0
0
1
1
2
0
0
5
0
0
0
2
1
2
0
0
0
0
3
0
1
2
2
1
2
2
2
1
5
0
4
4
1
0
6
1
2
1
1
2
0
1
0
1
0
1
0
5
3
2
0
3
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
4
2
0
2
3
1
0
2
1
2
0
0
2
0
5
1
1
3
2
4
0
4
1
1
0
2
0
1
0
3
2
0
0
0
3
3
2
1
4
0
2
2
1
2
3
1
1
1
0
0
2
0
1
0
0
1
4
0
0
2
1
1
0
0
1
0
1
0
1
5
2
1
0
1
0
0
1
2
2
0
1
2
1
2
1
0
3
0
0
0
3
4
3
1
4
3
0
0
1
2
4
1
2
0
0
0
0
0
2
0
2
2
2
1
6
0
1
3
1
1
2
2
0
9
1
3
4
1
2
0
3
0
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
1
1
1
3
1
1
1
2
2
0
3
0
0
4
0
1
0
2
2
0
0
2
0
0
1
0
1
0
2
1
2
0
0
1
1
0
0
1
0
1
1
1
0
8
0
0
0
0
0
1
1
6
1
3
1
0
1
2
2
1
3
5
1
0
2
1
0
0
0
0
0
2
0
1
0
1
2
2
1
1
4
0
5
2
0
0
1
4
1
0
1
1
2
1
0
1
1
2
1
0
0
1
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
2
1
0
2
1
0
2
1
0
2
1
0
2
0
2
1
1
0
1
4
1
1
0
1
2
1
0
1
0
3
1
0
2
0
4
0
1
0
0
3
3
0
0
1
1
1
0
2
0
2
1
2
3
0
1
1
0
1
4
0
0
0
1
2
0
0
1
3
0
3
2
5
1
1
2
1
4
0
3
1
3
1
1
0
0
1
1
2
0
0
0
0
2
3
5
0
0
1
2
13
0
2
2
0
2
0
0
2
0
2
1
3
1
1
0
1
11
0
0
3
0
4
1
0
1
3
0
0
4
0
0
0
0
1
1
2
1
0
1
2
1
0
1
2
2
1
1
3
0
1
1
2
1
1
2
2
0
3
0
0
2
5
1
2
0
3
1
0
2
1
1
3
1
1
0
3
1
2
1
1
1
1
1
4
1
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
4
0
0
0
1
6
0
1
1
1
2
1
2
4
0
1
0
2
0
1
1
1
1
0
2
0
0
0
1
1
2
0
0
1
2
0
3
3
0
1
0
1
0
0
1
1
1
2
0
2
2
2
2
0
2
0
1
1
0
0
0
3
1
2
4
0
0
3
0
3
3
2
1
1
1
0
2
1
1
0
0
5
0
0
1
1
0
2
0
0
3
2
0
0
3
1
0
3
2
0
2
2
0
0
5
0
0
3
0
0
1
1
1
0
1
3
0
0
1
0
0
0
1
0
0
4
1
2
0
2
1
2
2
0
0
1
2
0
2
4
0
2
2
0
0
0
0
1
0
2
0
2
3
1
0
0
1
2
2
1
0
0
1
1
1
1
2
0
1
1
0
1
1
222
1
1
2
1
1
0
0
0
1
1
3
1
2
0
1
0
1
2
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
1
3
1
0
4
1
1
0
2
1
3
1
1
2
3
3
1
1
1
1
0
1
0
2
1
2
0
0
4
0
1
0
4
0
1
1
0
2
0
0
1
1
3
0
0
2
2
0
1
1
1
0
2
1
1
1
0
0
1
1
0
1
0
2
4
1
2
1
0
2
0
2
1
2
1
0
0
2
2
1
0
2
4
2
0
1
0
2
1
1
2
0
4
1
1
0
2
0
0
1
0
1
1
0
2
1
0
1
1
0
2
1
5
1
0
2
1
0
0
3
3
0
1
2
6
3
1
3
3
0
2
2
1
1
1
0
1
0
1
1
5
1
0
1
0
3
3
0
8
0
2
2
5
2
0
0
1
0
0
3
1
1
0
3
0
0
1
1
0
1
0
1
0
1
2
0
2
1
0
0
1
3
1
2
1
0
1
0
1
1
1
0
0
4
1
0
0
4
1
0
0
2
0
1
4
1
0
1
2
16
0
3
3
1
1
1
0
0
1
1
2
5
2
3
1
0
1
1
89
1
0
2
1
3
2
0
3
0
3
0
2
0
0
0
0
0
1
1
3
1
1
2
0
3
0
0
1
0
2
0
0
1
1
0
1
0
4
2
2
1
0
2
5
1
2
1
3
1
3
0
0
1
1
2
0
4
0
2
1
1
1
2
2
1
2
1
1
3
2
1
1
3
1
3
2
1
1
2
1
3
1
2
0
0
2
2
1
2
1
1
2
0
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
0
0
0
1
2
0
2
3
0
0
2
1
1
0
2
3
1
0
0
0
0
3
1
0
0
0
0
1
1
0
3
2
5
1
2
2
1
2
0
2
1
1
1
0
1
0
3
0
3
0
2
3
3
1
0
2
0
1
0
0
0
3
1
0
2
2
4
0
0
2
2
0
1
0
0
1
2
0
1
0
2
1
1
2
1
0
0
1
1
10
0
1
1
0
0
1
3
3
1
1
0
0
1
1
0
1
1
2
1
1
3
0
1
0
1
1
0
0
3
0
9
0
2
2
2
1
2
0
2
0
0
2
1
3
0
0
2
1
0
2
6
1
0
7
1
1
1
1
0
0
1
2
1
0
0
2
0
1
0
1
0
3
2
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
3
0
2
2
0
1
2
1
0
6
0
0
2
1
0
2
1
1
1
0
1
0
2
5
2
2
2
3
2
1
0
1
0
1
1
0
0
1
4
0
0
0
11
1
1
0
0
1
1
0
0
1
1
0
0
0
0
2
1
1
1
1
0
1
3
1
3
0
1
4
0
1
1
0
0
2
1
2
0
1
1
2
1
0
1
3
1
1
3
0
0
1
1
2
0
1
3
0
0
5
1
4
1
0
0
4
2
0
1
1
1
2
2
0
0
0
0
0
3
0
1
0
1
1
0
0
3
1
1
2
1
1
1
0
1
1
0
2
0
2
1
2
0
1
1
0
3
0
0
4
2
0
2
1
0
0
1
0
3
1
1
0
1
1
1
2
3
1
1
0
2
1
0
0
0
1
0
2
2
1
2
2
3
1
0
0
1
1
2
0
2
1
1
1
0
0
2
0
2
1
0
0
0
3
0
1
1
2
2
2
0
1
0
0
2
0
2
1
0
2
3
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
5
0
1
3
0
4
1
3
0
4
0
1
0
1
1
0
0
0
1
3
4
5
1
4
0
0
0
2
1
1
1
1
0
1
2
2
1
2
1
3
0
1
1
3
1
0
0
1
1
0
3
2
1
0
1
1
1
2
2
2
0
3
1
0
1
0
1
0
4
1
0
0
0
2
1
0
0
0
1
0
1
3
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
1
4
0
2
1
0
2
2
2
0
0
1
0
1
0
4
3
0
3
0
2
0
1
2
1
0
3
0
2
1
2
2
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
0
6
0
0
0
1
2
1
0
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
4
0
1
3
1
2
0
0
0
2
0
6
1
0
1
2
1
0
1
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
1
1
1
3
2
0
3
2
0
1
1
1
0
2
0
0
1
1
2
0
1
2
0
4
3
2
1
2
1
3
1
2
3
0
1
2
0
0
2
2
0
4
6
0
0
0
0
2
2
2
0
2
1
1
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
3
3
1
0
1
0
3
2
1
2
3
2
1
3
1
0
3
0
4
1
2
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
1
1
0
3
1
0
0
3
0
0
1
1
1
1
0
0
0
0
1
3
0
1
1
1
0
1
1
1
0
1
0
0
0
0
3
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
2
1
0
1
1
1
0
1
1
3
2
1
0
4
0
0
0
0
0
1
1
3
1
0
0
2
0
0
1
2
0
1
1
0
1
2
1
0
0
1
1
0
1
4
0
1
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
4
1
1
0
1
2
4
2
2
1
0
0
0
0
2
0
4
0
0
7
3
0
1
4
2
0
0
1
0
1
2
0
1
1
0
1
4
2
0
1
1
3
0
1
0
1
1
0
0
0
0
5
1
1
3
0
1
0
1
0
0
1
1
1
0
3
1
0
1
0
0
0
0
1
0
1
1
1
3
0
1
4
0
1
0
0
0
0
3
0
0
3
2
5
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
3
0
3
0
0
4
0
1
0
0
5
1
0
1
2
1
3
2
0
2
0
0
2
0
0
0
5
0
1
0
0
1
0
0
1
1
0
3
1
0
0
2
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
5
1
1
0
0
2
1
1
3
0
1
2
1
1
1
1
1
0
0
0
2
1
2
0
5
0
1
1
5
1
2
0
1
0
1
1
1
1
0
1
2
3
0
0
4
5
2
2
2
2
1
1
0
1
0
2
1
3
1
0
2
1
1
3
2
3
1
4
2
3
0
0
2
1
1
1
1
1
1
3
0
0
1
0
0
2
2
2
0
0
0
1
0
2
4
1
0
2
2
3
0
0
2
0
0
2
3
0
1
0
2
0
1
1
0
1
3
2
0
1
2
1
0
2
1
0
2
1
0
2
3
0
2
2
2
1
0
1
1
1
1
1
0
2
1
0
4
3
1
1
3
0
2
0
0
0
2
0
0
3
0
1
1
2
0
0
2
2
0
0
3
2
1
6
1
1
0
0
1
0
3
0
1
1
1
1
1
0
1
2
0
0
1
0
0
0
1
2
0
2
2
1
1
2
1
3
0
1
1
2
2
1
0
7
3
0
0
0
0
3
4
2
1
1
2
2
3
1
0
0
3
0
0
2
4
1
2
2
0
2
1
3
1
2
4
3
3
3
1
0
0
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
3
0
0
0
2
0
2
0
1
1
1
1
1
1
1
2
0
0
1
0
0
2
2
0
0
0
2
4
0
2
3
0
3
0
1
1
0
2
2
2
0
4
0
1
2
2
0
1
1
0
0
3
1
1
2
5
3
1
3
2
1
0
3
1
4
0
0
0
2
1
0
0
0
0
1
1
2
1
0
1
0
3
1
1
1
3
1
2
0
4
1
0
0
1
0
1
1
0
3
2
2
0
0
2
1
0
2
0
4
4
4
1
0
0
2
0
0
1
1
2
0
0
0
1
1
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
3
1
2
1
1
3
1
0
1
0
1
0
1
3
0
1
0
1
1
4
1
0
0
2
2
0
1
2
0
5
0
1
0
3
2
3
2
1
0
2
0
0
2
1
4
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
3
2
0
1
0
0
1
0
1
0
3
0
2
4
1
0
1
1
1
1
0
0
0
0
1
2
1
4
1
5
0
1
2
1
0
1
2
0
0
2
0
1
1
0
2
1
0
0
0
1
1
0
2
0
1
2
0
5
1
1
1
3
3
0
1
1
1
0
2
0
4
1
1
2
1
3
0
0
1
1
3
1
1
2
0
1
2
1
0
0
1
1
2
1
1
1
2
0
2
0
0
1
2
0
1
1
0
2
0
0
0
3
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
2
1
0
0
0
0
0
2
4
1
3
0
4
2
1
3
2
0
1
0
0
0
3
0
0
1
1
0
1
0
1
4
0
1
0
3
0
0
0
1
0
2
2
1
0
0
1
1
1
2
3
0
1
0
0
2
0
0
0
4
0
1
1
0
0
2
0
1
0
0
1
4
4
1
2
2
1
2
0
3
0
2
0
2
0
1
0
0
0
2
0
1
3
1
0
3
1
0
0
1
0
1
2
1
2
2
1
0
1
0
1
2
0
0
1
1
1
1
1
0
0
0
2
0
1
2
3
0
0
3
1
0
0
0
2
12
2
0
2
0
1
1
1
0
1
1
1
0
0
1
2
1
4
3
0
1
0
1
1
1
1
2
2
1
0
1
4
2
1
1
2
0
0
0
1
0
2
2
0
0
2
1
0
0
2
1
1
0
2
1
0
4
0
1
2
0
2
2
2
0
3
1
1
0
0
0
1
0
1
5
3
3
0
1
1
1
0
0
1
2
3
2
0
2
2
1
0
2
1
0
2
1
3
1
0
1
1
1
1
3
1
0
1
1
3
2
1
0
1
0
0
1
0
1
3
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
3
2
0
1
1
2
0
1
1
1
0
0
0
1
1
0
3
1
1
3
1
0
1
0
2
1
0
2
2
1
4
2
1
0
1
0
3
0
3
1
1
0
0
0
2
0
0
0
4
2
2
1
0
1
0
0
0
0
3
0
1
1
0
1
1
0
2
4
0
2
1
1
1
0
1
1
2
1
0
1
2
2
0
3
0
0
1
2
2
3
0
1
2
2
1
2
1
0
2
1
0
0
2
1
1
2
1
0
3
3
2
3
2
0
1
0
1
2
1
3
1
0
1
1
1
1
2
1
1
0
1
0
0
1
3
1
0
2
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
1
4
1
2
1
0
0
2
0
1
0
2
2
1
0
1
1
2
2
2
0
3
0
1
0
0
1
3
0
0
0
2
0
2
1
0
1
1
2
0
1
1
1
0
1
0
2
0
0
1
0
1
0
2
1
0
2
2
0
2
0
2
1
0
1
0
1
1
0
3
2
1
2
2
0
0
0
0
0
0
1
3
0
0
3
2
1
1
1
3
2
0
1
2
2
1
1
0
0
3
1
0
2
1
0
0
1
0
2
1
2
2
1
1
1
1
1
1
0
0
1
0
6
0
1
1
0
2
4
0
0
2
1
0
1
1
0
1
0
1
3
1
2
0
4
0
4
6
0
1
0
2
1
0
2
1
2
2
0
1
2
0
3
0
0
0
3
0
2
2
1
0
3
5
0
2
2
0
1
0
4
0
0
0
0
2
2
0
0
2
1
2
1
0
1
1
1
2
0
1
1
1
5
0
3
0
1
2
2
0
1
0
3
2
0
2
0
0
1
2
1
2
2
1
0
0
0
3
0
2
0
0
1
0
2
0
1
1
0
0
2
2
0
2
0
2
0
0
0
1
2
1
0
2
1
1
0
1
2
0
2
2
1
1
2
0
0
0
0
0
1
1
1
0
1
3
1
2
0
1
0
1
0
2
1
0
2
0
2
4
3
1
0
2
1
1
1
1
0
0
1
0
3
2
1
0
1
1
0
3
1
2
1
2
1
2
0
2
2
0
1
1
1
0
2
1
0
1
1
3
1
0
2
1
0
2
0
2
1
4
0
2
0
1
4
1
0
1
3
2
1
5
1
1
2
1
1
0
4
0
2
0
1
0
2
1
0
1
0
1
0
0
0
1
0
2
4
3
1
2
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
2
4
1
0
3
0
2
1
0
3
2
0
0
1
1
0
1
1
1
1
0
3
3
2
1
0
4
1
1
0
1
0
1
0
2
4
4
0
3
0
0
1
0
1
1
1
0
0
0
1
3
0
0
0
1
0
1
1
1
0
1
2
1
0
5
0
0
0
1
0
4
2
0
0
0
1
1
2
2
1
1
2
2
0
2
4
3
1
3
3
1
3
2
0
1
0
0
2
2
1
0
0
1
3
0
3
1
0
4
1
1
3
0
0
18
0
0
0
2
0
0
0
0
0
2
1
4
3
2
1
0
1
0
2
0
1
1
2
1
2
0
0
2
3
0
1
3
1
1
0
0
0
0
2
1
1
0
2
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
5
0
1
1
1
1
2
0
0
1
0
3
1
0
2
0
0
0
3
1
1
0
2
0
0
3
0
2
2
0
0
2
0
0
0
0
0
1
3
0
3
2
0
1
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
1
0
1
2
0
0
4
0
1
1
0
0
0
0
3
0
3
0
0
1
1
1
3
1
1
2
2
0
4
2
0
1
2
0
1
0
2
5
1
0
3
2
1
0
1
0
0
2
4
2
0
0
0
1
1
0
3
1
0
2
1
0
0
1
0
4
0
0
0
4
1
3
2
0
1
3
5
2
0
2
0
0
1
1
1
4
1
3
0
1
2
0
1
2
0
3
1
1
1
1
2
1
2
2
0
3
0
2
1
0
1
1
1
3
0
82
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
1
0
3
1
1
0
1
0
0
0
0
2
1
3
0
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
0
3
0
0
2
0
0
1
2
0
3
3
0
1
0
1
1
2
0
3
0
1
2
1
3
1
1
1
0
0
1
3
1
0
1
0
1
3
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
1
0
1
0
0
0
1
3
0
2
0
1
2
2
1
2
1
2
1
1
0
0
0
0
1
1
0
0
1
0
2
3
1
0
0
0
2
1
1
4
0
2
1
6
0
0
1
2
1
0
4
1
2
3
1
1
1
1
2
0
0
0
0
0
4
0
3
0
0
1
1
1
1
2
0
0
0
1
1
0
1
1
4
1
0
0
0
3
4
1
0
0
3
0
1
2
0
2
0
0
2
0
1
0
0
0
0
3
0
1
3
1
1
1
1
2
0
0
4
0
0
2
0
6
0
1
0
2
0
4
0
0
1
0
0
2
0
1
2
2
0
3
1
1
2
4
0
1
1
1
0
0
4
1
1
1
2
2
0
0
2
1
0
2
0
1
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
3
1
0
3
1
2
4
1
0
0
2
6
1
0
1
34
1
1
1
2
1
0
3
2
0
2
2
0
0
2
1
1
2
1
3
2
0
0
2
0
0
0
1
2
0
2
0
2
0
3
1
1
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
1
1
7
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
2
2
0
2
2
2
0
0
2
0
1
1
2
0
0
3
0
0
7
1
2
2
2
2
1
0
3
2
0
0
0
2
2
0
3
1
2
0
2
0
3
2
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
2
0
0
2
3
1
0
1
2
2
1
3
5
4
1
1
3
1
1
1
0
1
1
4
1
1
2
3
0
1
0
0
0
0
0
2
5
0
1
2
0
1
0
2
0
4
5
0
5
0
2
1
1
0
1
1
1
2
1
0
4
1
0
1
2
4
1
0
3
2
1
0
0
3
0
1
0
3
1
4
1
1
1
2
0
0
0
1
2
1
3
0
1
1
0
1
2
0
0
0
1
3
3
2
0
0
1
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
1
2
0
1
0
1
1
2
0
2
0
1
1
1
0
0
0
0
0
4
2
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
1
2
1
1
2
1
1
1
3
2
0
0
1
0
1
1
1
5
1
0
2
2
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
1
0
1
0
2
2
1
0
0
0
0
1
2
2
1
1
0
0
0
1
1
0
0
1
0
2
1
2
3
0
1
0
2
2
1
0
2
0
0
1
3
2
2
0
5
0
1
2
1
2
0
0
0
0
0
3
2
0
2
0
2
0
1
0
0
2
2
3
0
5
0
0
1
2
2
0
1
1
0
3
2
1
0
1
3
1
3
1
0
2
1
0
0
1
2
1
3
0
1
0
3
1
1
1
0
1
1
1
2
0
0
0
0
3
5
0
0
0
1
0
0
3
2
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
2
0
1
0
1
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
1
1
4
1
2
1
1
3
0
0
5
2
1
1
0
1
1
0
0
0
2
0
0
1
2
2
0
1
2
0
2
0
4
1
1
3
0
2
0
1
0
0
1
2
0
1
0
1
0
1
0
3
2
2
1
1
0
0
0
0
3
3
0
0
3
3
2
1
0
0
0
2
0
0
1
0
1
1
3
2
0
1
1
2
1
5
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
2
0
0
2
0
1
3
2
0
0
0
2
1
2
1
0
2
0
9
4
0
0
0
1
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
2
0
4
0
2
0
1
1
1
3
2
1
0
0
2
1
0
1
2
3
1
4
0
1
0
0
2
2
1
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
2
1
0
1
2
5
1
2
0
1
2
1
1
3
3
2
0
1
0
4
1
1
2
2
2
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
0
4
0
0
0
0
0
2
3
1
0
0
0
1
0
0
1
1
0
0
4
0
2
1
0
1
1
0
1
1
1
0
4
2
1
2
0
2
1
0
2
1
2
2
0
0
1
0
1
0
3
1
0
0
3
1
4
1
0
0
2
0
1
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
3
0
7
0
1
1
0
1
1
1
3
0
0
0
1
5
1
0
0
4
1
3
2
2
0
0
0
0
2
1
0
3
2
0
1
1
1
1
1
1
2
0
0
1
2
1
0
2
0
0
1
2
1
0
0
1
1
0
5
0
0
0
2
2
0
3
0
0
0
0
0
1
0
2
1
1
0
1
0
2
0
1
0
2
1
2
2
1
0
3
0
0
0
2
1
2
2
1
2
0
1
1
1
1
0
1
4
1
0
2
0
1
3
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
1
0
1
2
0
0
1
0
2
2
2
1
2
2
2
0
0
1
0
1
0
2
0
1
0
0
1
1
0
2
4
3
0
1
0
2
0
0
0
2
0
0
1
1
1
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
1
2
0
1
1
4
2
1
2
3
0
0
1
0
2
3
1
2
2
0
1
0
1
0
0
0
0
1
2
1
2
1
2
1
8
1
2
2
0
0
0
0
2
3
2
2
0
1
0
1
3
3
2
0
1
1
0
0
1
0
0
0
20
0
0
2
1
2
0
0
0
0
0
0
1
0
0
3
3
1
1
0
2
0
0
0
1
1
1
0
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
1
1
3
0
3
0
0
1
1
0
1
4
0
3
2
0
2
0
0
0
2
0
2
1
0
0
0
1
2
0
0
2
0
0
2
1
2
0
4
2
12
0
0
2
0
2
0
0
6
1
1
3
0
2
0
2
0
1
0
2
1
1
2
3
1
0
0
3
2
0
0
0
2
0
0
0
1
0
1
0
5
1
3
2
1
2
2
0
0
0
25
0
0
0
0
4
0
1
0
0
2
2
1
3
1
1
0
1
1
0
0
5
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
1
2
1
3
2
2
1
0
3
0
0
1
0
1
1
0
0
1
0
1
2
2
0
1
0
0
1
4
4
0
3
3
0
1
0
1
1
3
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
1
2
1
0
3
0
2
1
2
0
0
0
0
2
0
0
1
2
2
0
2
1
496
1
2
3
0
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
3
5
4
0
4
1
24
1
1
2
0
0
2
0
2
0
0
4
0
1
2
1
0
1
2
0
2
0
2
0
0
0
1
1
2
1
0
1
2
0
0
1
0
5
0
0
0
3
3
0
0
1
2
0
2
0
2
1
0
0
2
1
3
0
2
2
1
1
0
1
1
2
0
2
1
1
1
0
1
1
4
2
0
1
2
0
1
2
1
1
1
2
1
1
0
17
0
0
0
0
0
0
0
1
3
0
1
2
0
0
1
0
1
1
0
5
0
1
3
1
0
0
1
2
1
0
2
3
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
1
8
0
1
2
1
0
0
2
1
1
2
0
2
0
1
1
3
0
2
2
0
2
0
0
4
0
0
1
2
3
0
0
1
0
0
2
1
0
3
2
4
1
1
1
5
0
0
3
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
2
3
0
0
3
1
1
1
2
1
1
1
0
1
2
2
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
3
1
0
0
1
0
2
4
1
0
0
4
1
0
3
0
1
1
0
0
0
4
0
1
2
1
3
5
0
0
2
4
1
1
1
2
0
2
0
1
0
1
1
1
2
1
2
0
1
2
1
2
0
1
0
0
3
0
1
3
1
1
0
0
0
1
0
1
2
0
0
5
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
2
0
2
3
0
1
0
2
1
1
1
0
0
2
0
3
5
2
2
1
0
0
1
1
1
1
1
0
1
0
1
1
4
1
2
2
0
3
2
0
3
1
1
12
2
3
0
3
2
1
0
0
0
0
4
1
2
1
1
3
0
2
0
1
0
3
2
6
0
0
0
2
1
3
0
0
2
0
1
3
1
4
1
2
0
0
0
1
4
2
2
2
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
1
0
0
5
1
0
0
2
0
1
0
3
1
4
0
4
2
1
1
3
0
1
1
1
0
2
0
3
1
0
1
0
2
2
0
0
1
1
0
2
2
2
0
1
2
0
2
1
3
0
3
0
2
3
1
0
0
0
2
1
0
0
1
0
1
4
0
0
0
2
0
1
1
0
2
0
0
2
0
2
0
0
1
1
0
1
3
0
1
3
0
0
1
1
0
0
1
1
1
2
0
2
0
1
2
0
0
0
1
0
3
0
5
2
2
0
1
2
2
0
2
4
1
1
1
1
0
1
1
1
0
2
0
1
0
2
1
0
0
0
1
2
1
3
3
0
1
5
0
0
2
1
0
2
0
0
0
3
0
1
0
1
3
0
1
0
1
0
0
1
3
1
0
4
1
1
1
0
3
1
2
1
3
0
0
1
1
3
1
4
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
1
4
0
3
2
2
2
0
1
3
1
1
1
1
1
2
1
0
2
1
1
1
2
0
0
2
1
1
0
0
1
3
0
0
1
0
0
1
1
4
0
2
0
2
0
4
0
10
5
1
0
1
0
1
5
1
0
1
1
2
2
2
0
4
1
1
0
1
0
2
0
1
1
0
0
3
0
2
2
0
1
0
1
0
1
1
0
1
4
0
1
1
0
0
0
1
2
1
3
1
0
1
0
2
3
0
2
0
1
0
1
0
1
3
1
1
3
1
2
1
1
2
0
3
0
2
1
0
0
0
0
0
3
0
0
1
1
0
0
2
1
1
0
0
2
0
3
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
1
7
0
2
2
0
0
0
1
19
0
2
1
0
1
0
2
1
0
0
1
1
2
0
0
1
3
0
0
0
0
1
1
1
0
1
4
1
1
1
0
1
1
3
0
0
1
0
0
2
1
0
1
0
0
2
1
1
0
0
2
1
0
2
0
1
0
3
1
1
1
0
1
6
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
2
0
0
2
0
1
0
1
0
0
2
1
0
0
3
0
1
0
0
2
0
0
3
1
2
0
4
0
1
0
1
3
0
0
1
1
0
2
1
2
0
1
0
0
3
3
0
0
2
3
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
2
1
3
1
47
1
0
0
0
1
1
1
0
2
0
0
0
0
0
4
1
0
1
1
1
1
0
2
1
0
1
1
2
0
2
0
1
0
0
3
1
0
2
0
1
0
0
1
0
0
3
0
3
0
0
1
4
1
1
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
3
0
1
3
1
1
2
1
1
2
1
0
1
1
1
1
0
4
1
0
0
1
0
2
0
0
1
1
0
2
0
1
1
1
0
0
0
2
1
0
2
0
2
0
2
2
0
1
0
0
1
1
3
0
0
0
2
0
0
1
1
0
7
3
1
1
0
1
1
0
2
0
3
2
0
1
1
0
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
3
3
2
3
2
0
2
2
1
2
0
1
0
0
1
0
0
2
3
0
0
0
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
0
2
1
1
4
3
0
0
0
3
3
1
1
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
3
3
0
2
0
2
3
0
4
0
1
1
0
3
0
2
3
0
0
5
1
0
4
1
1
1
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
1
1
3
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
1
1
1
2
0
2
0
2
0
2
4
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
2
0
1
1
2
0
1
1
2
0
0
0
1
2
0
0
1
0
3
1
0
1
1
1
1
0
1
2
1
1
0
4
0
3
2
0
0
0
0
0
2
1
2
0
4
0
0
2
1
0
3
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
3
3
4
1
0
3
0
0
1
0
0
3
3
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
2
0
0
0
1
3
1
3
0
0
1
0
1
3
0
1
2
0
1
0
0
0
1
0
2
0
5
2
0
0
0
0
1
0
5
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
2
4
0
1
4
0
0
2
0
1
1
1
0
3
2
0
0
2
1
1
1
3
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
4
0
1
2
0
0
1
1
2
2
0
3
0
1
0
0
1
0
3
3
0
0
2
1
0
3
0
0
1
1
2
0
1
1
0
1
2
1
0
2
1
3
0
0
2
0
0
2
3
0
2
0
2
0
0
1
1
0
0
1
0
0
3
1
0
1
1
0
0
4
0
0
1
1
2
0
0
3
3
0
2
1
4
3
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
3
1
1
3
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
1
1
2
9
4
0
0
3
1
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
0
2
4
0
0
1
3
1
2
3
1
0
0
3
0
4
2
1
3
2
0
1
0
1
0
8
0
1
1
0
2
3
0
2
1
0
1
0
0
1
1
0
2
3
1
0
2
1
2
0
0
0
0
1
1
2
0
0
0
4
0
0
5
0
2
0
0
3
0
0
2
2
0
1
1
0
1
3
0
0
4
0
0
2
2
1
3
0
0
2
1
0
2
3
4
0
1
3
0
1
1
0
3
0
0
0
2
1
1
0
1
2
1
4
1
0
1
1
1
0
1
0
0
1
0
0
1
2
0
1
3
0
1
0
1
2
1
1
0
0
0
0
0
4
0
1
0
2
1
3
0
3
0
0
1
0
1
1
0
2
2
2
0
1
1
1
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
2
1
1
1
0
0
1
2
0
5
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
1
2
1
2
0
3
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
1
2
1
1
2
0
1
2
0
2
3
3
2
1
1
0
2
1
0
2
1
1
1
0
0
0
2
2
0
2
0
1
0
2
0
1
2
3
0
3
1
2
1
1
0
0
1
2
1
1
0
1
1
2
2
0
2
1
0
0
1
1
0
0
0
3
1
0
4
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
4
1
0
0
1
1
0
3
0
0
1
2
4
0
2
0
0
0
1
1
0
0
0
3
3
4
1
0
0
1
1
0
2
4
0
1
0
0
4
0
0
2
3
0
0
0
1
1
0
2
2
1
3
1
0
2
1
0
2
0
2
0
0
3
0
2
1
2
1
0
1
1
1
2
0
1
1
0
4
0
2
0
0
1
0
2
2
1
0
0
1
1
2
1
0
2
0
1
2
0
0
2
0
1
0
1
1
0
0
2
2
3
1
1
0
2
3
0
0
0
0
0
0
0
2
2
0
0
1
0
7
0
0
2
0
2
1
0
1
1
1
0
0
0
3
1
0
1
0
0
0
0
2
1
1
0
2
1
0
1
0
1
0
1
5
1
0
4
3
0
0
0
0
0
1
0
3
0
1
3
0
0
0
3
1
2
3
5
1
2
0
0
1
1
0
2
0
0
1
2
2
1
0
0
1
0
1
0
2
0
1
3
1
0
0
0
3
3
1
4
2
0
1
1
0
0
2
0
1
1
0
0
3
2
1
0
1
0
1
0
0
1
0
1
1
3
3
0
0
0
0
0
2
1
6
1
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
2
3
1
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
4
1
5
0
3
3
2
3
0
2
1
1
1
1
4
1
0
2
1
1
3
2
2
0
1
2
0
1
1
1
0
1
3
2
1
1
0
1
0
1
2
0
2
4
0
0
2
0
2
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
1
0
1
2
4
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
5
0
1
1
0
1
0
0
1
0
0
0
0
0
1
3
1
0
2
0
1
2
2
0
1
0
0
2
0
0
0
1
0
4
0
0
1
1
0
1
4
2
0
2
1
2
0
2
1
0
0
1
2
2
0
1
0
8
0
0
3
0
0
2
0
2
1
0
2
2
2
0
0
2
0
0
1
0
0
1
2
0
2
2
1
3
5
0
0
0
1
0
0
5
3
2
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
4
1
2
0
0
0
1
0
1
0
2
0
1
2
4
0
2
1
0
2
1
0
0
0
1
1
0
0
1
2
2
0
4
2
1
2
1
0
0
1
0
0
1
1
1
2
0
2
2
0
2
0
2
5
1
0
0
0
1
0
0
2
1
1
1
2
0
3
1
2
0
1
2
0
1
0
0
1
0
1
4
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
1
1
0
2
1
3
2
1
0
0
2
0
2
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
3
1
0
0
1
3
1
0
1
1
1
2
0
0
2
1
1
0
1
0
1
0
1
1
0
15
1
0
0
0
1
1
1
0
0
0
1
0
0
2
1
2
0
2
1
1
0
0
3
0
1
0
0
0
0
0
1
1
1
0
2
2
0
2
5
0
3
0
3
1
2
1
1
4
0
0
0
2
1
1
2
1
0
2
0
0
7
2
2
1
0
0
2
0
1
0
4
0
1
0
0
1
3
1
0
0
0
0
0
1
0
4
0
1
2
1
0
0
0
1
2
1
0
4
4
1
2
3
2
8
1
3
1
0
0
2
2
1
2
1
1
1
0
0
1
0
0
1
0
1
0
1
3
2
2
2
1
1
0
3
0
1
1
1
2
0
1
0
3
1
0
0
1
1
0
1
0
0
1
2
1
0
1
0
0
0
1
0
3
0
0
2
1
1
1
2
1
1
0
2
0
0
2
2
2
1
4
0
1
1
2
2
0
0
2
1
1
0
0
1
1
0
6
0
0
2
0
0
2
0
1
2
2
1
2
0
3
2
2
5
1
0
1
1
2
1
0
1
1
0
0
1
0
1
2
1
1
1
0
0
1
0
0
1
2
13
0
0
1
0
0
2
1
1
0
3
2
2
1
0
0
1
0
0
0
1
0
3
1
0
1
21
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
1
0
0
1
1
1
3
1
2
1
1
0
1
0
0
2
2
1
1
1
1
2
0
1
0
2
1
0
2
3
0
0
0
0
0
1
1
1
2
0
2
1
0
0
1
1
0
2
2
0
1
1
0
0
0
42
2
1
1
4
0
3
1
1
0
1
2
1
1
4
0
2
1
0
1
1
1
0
1
1
3
1
0
2
2
0
0
0
0
2
1
4
0
1
0
0
3
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
1
3
4
2
1
0
1
1
0
0
1
4
0
1
1
0
2
0
1
0
2
1
2
1
1
1
1
0
1
1
0
4
0
0
0
0
0
1
1
0
2
1
2
2
0
0
0
0
1
0
1
6
0
0
0
0
0
3
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
2
0
2
3
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
1
0
0
2
0
0
1
0
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
3
2
0
1
0
0
2
3
2
0
1
0
1
0
1
1
1
4
0
2
3
1
0
0
1
0
1
1
2
2
0
0
0
0
2
4
1
1
1
1
1
1
1
0
2
0
0
2
0
1
3
1
0
0
0
1
1
0
1
1
4
0
0
0
1
1
1
2
1
0
1
0
2
1
1
1
0
2
0
2
0
0
4
5
0
3
2
0
0
1
0
0
2
1
2
0
2
2
0
0
1
1
4
1
1
2
0
1
2
1
1
4
1
0
2
0
0
0
2
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
1
1
2
3
0
2
0
0
0
1
1
0
1
0
1
1
0
1
0
2
0
3
0
0
0
3
1
2
2
0
1
0
4
0
0
0
1
1
0
0
4
0
1
6
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
2
1
4
0
2
0
1
1
0
0
0
5
1
1
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
2
1
0
1
5
0
1
3
2
2
0
1
1
0
0
0
0
1
0
0
2
1
3
1
2
0
3
1
2
0
0
1
0
1
1
1
0
0
2
2
1
1
1
4
0
0
1
1
3
2
0
1
1
1
2
2
0
4
0
1
0
0
1
1
0
3
1
0
0
1
0
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
4
1
2
0
0
2
1
0
1
0
2
0
2
0
1
0
1
1
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
3
1
1
2
1
1
1
1
0
1
5
0
0
0
4
0
2
0
2
0
0
5
3
1
0
1
0
2
0
0
2
0
2
1
0
4
0
0
3
0
0
0
1
1
2
0
2
0
3
2
0
1
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
2
1
0
0
3
1
0
1
1
0
0
0
1
0
1
0
1
0
3
6
1
1
1
0
0
1
0
1
3
4
1
2
2
0
0
0
4
2
2
1
1
0
0
0
0
1
2
1
0
0
1
2
1
1
1
1
2
1
0
4
1
0
0
2
0
1
0
0
1
2
1
1
0
0
1
0
1
1
0
0
0
3
1
0
1
1
0
1
1
5
1
0
0
0
2
0
0
1
0
4
2
1
1
0
1
0
1
1
2
0
2
1
0
1
1
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
6
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
3
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
1
0
1
0
1
0
3
2
1
1
0
3
0
1
1
0
0
2
1
2
3
2
0
0
1
2
0
1
0
0
3
0
2
0
0
0
2
1
1
0
0
0
1
3
4
1
0
1
0
2
0
0
1
0
0
0
0
0
3
1
0
1
2
2
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
2
1
1
1
0
2
1
1
8
1
4
1
1
1
1
1
0
4
2
0
4
0
0
2
3
1
2
1
1
1
0
0
3
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
3
1
0
0
0
0
1
3
0
0
3
2
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
4
1
0
0
2
2
0
0
2
1
1
0
0
1
3
0
0
0
0
1
1
0
2
1
3
0
1
3
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
3
1
5
1
4
0
1
3
1
0
0
2
0
0
3
2
2
1
0
1
2
0
2
2
1
0
0
1
3
1
0
2
2
1
1
1
0
1
1
1
1
1
3
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
1
0
2
0
0
1
4
2
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
1
1
1
1
1
1
4
0
1
0
2
2
0
3
1
2
0
1
1
4
2
2
1
0
1
1
0
0
3
1
2
1
1
0
0
1
1
1
0
1
5
2
0
1
3
3
0
1
2
1
0
1
0
0
1
1
0
1
2
0
0
0
3
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
2
0
2
0
2
5
2
0
1
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
2
0
0
0
2
0
3
0
0
1
1
2
1
1
1
3
1
0
2
0
0
4
2
1
0
0
0
1
2
3
0
0
0
0
3
1
2
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
0
2
0
0
0
3
1
0
0
0
0
2
0
0
3
1
0
6
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
1
1
0
2
1
2
2
0
2
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
2
1
3
3
3
2
1
0
0
0
1
0
1
1
0
0
0
3
1
0
1
1
1
1
2
1
1
0
0
2
0
0
2
0
1
2
1
1
0
2
1
3
1
0
1
2
0
1
4
2
1
2
0
1
0
2
2
1
1
2
0
1
3
2
0
0
0
1
0
0
0
0
3
1
3
1
1
1
0
0
1
0
2
1
1
3
1
0
3
1
0
2
1
1
1
2
0
4
1
0
1
1
1
1
2
2
3
1
0
5
1
1
1
1
0
0
2
2
0
1
1
0
0
0
0
1
2
0
3
0
1
0
0
1
0
2
2
1
1
3
2
0
0
1
0
0
2
2
1
4
3
0
0
1
0
3
0
1
1
0
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
2
1
0
1
0
3
0
0
3
2
2
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
4
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
4
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
3
0
2
0
2
0
0
1
2
0
1
1
0
1
1
1
0
0
0
1
2
1
0
1
1
0
2
1
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
3
2
0
0
0
2
2
0
0
0
2
2
4
0
2
0
0
2
1
3
1
1
1
1
0
1
0
1
0
0
0
2
2
2
3
0
0
4
1
4
0
3
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
0
0
0
2
4
1
0
0
0
0
3
3
0
0
2
0
0
1
1
1
2
2
0
0
0
0
2
0
1
2
1
2
0
3
0
0
1
3
1
1
1
2
0
0
0
1
5
1
3
1
1
1
0
3
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
1
2
1
3
0
2
4
0
0
0
1
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
1
0
0
0
1
2
0
0
0
0
2
2
2
0
1
1
2
0
0
2
2
0
0
1
3
0
0
1
1
0
2
1
1
2
0
2
1
0
0
5
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
2
2
1
0
0
0
0
1
1
2
2
0
0
1
0
0
4
0
1
0
1
1
0
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
0
0
1
4
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
1
1
0
0
0
1
1
0
4
0
1
3
0
2
0
1
0
3
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
1
0
5
0
3
1
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
3
1
2
1
0
0
1
3
0
0
1
0
2
0
2
1
0
0
0
1
2
0
3
0
1
1
2
4
0
5
0
1
1
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
3
0
0
3
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
2
0
1
1
1
1
0
4
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
3
2
2
1
1
1
0
1
0
1
3
0
1
3
1
0
6
2
0
1
1
1
2
2
0
1
1
1
2
0
2
1
0
1
0
10
0
1
2
0
3
3
0
1
4
1
2
0
1
0
1
2
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
3
2
3
1
1
0
2
1
0
3
0
1
2
3
0
2
1
0
3
3
1
2
0
2
1
0
2
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
1
1
1
0
1
0
0
0
2
3
0
0
0
0
0
1
1
0
2
3
0
0
0
2
1
0
3
1
1
2
0
1
2
3
2
0
2
0
0
3
0
2
1
0
0
1
0
0
2
1
0
0
1
1
1
0
0
1
2
2
0
0
0
1
1
0
0
1
0
4
3
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
1
5
0
2
2
0
2
1
1
1
1
1
0
0
1
2
0
1
1
0
3
0
0
2
2
1
0
3
0
0
1
1
3
0
2
1
0
0
1
1
0
1
1
1
0
0
1
2
1
0
0
0
3
0
1
0
1
3
0
0
1
1
1
1
1
0
1
1
0
0
0
1
3
2
1
0
2
0
0
2
0
4
1
2
1
0
0
1
1
0
0
0
0
0
3
0
0
4
0
0
1
0
1
2
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
3
3
0
1
0
0
1
0
1
2
1
0
2
2
0
0
0
1
2
0
1
1
0
2
1
0
0
0
2
0
3
0
2
2
3
2
0
0
1
4
1
1
1
1
0
1
1
2
0
109
0
0
1
0
0
2
0
0
1
1
0
1
2
1
3
1
0
0
0
3
1
0
2
0
0
1
0
0
2
1
4
0
2
1
2
0
0
1
0
2
1
0
1
0
0
0
1
1
1
1
0
0
2
2
1
1
0
0
0
3
0
1
2
1
0
1
0
1
0
0
2
0
1
3
1
1
0
2
1
0
0
0
0
2
0
2
1
0
0
0
3
0
4
2
0
0
1
0
1
1
0
0
1
1
1
3
1
2
0
1
2
1
1
1
3
1
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
0
0
1
1
0
1
2
1
1
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
3
0
2
0
2
0
0
0
2
0
1
1
0
2
1
0
2
1
2
1
2
0
2
1
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
2
1
1
0
1
4
1
2
1
3
0
1
0
1
0
1
3
2
2
2
1
1
1
1
2
1
0
0
1
1
0
2
2
0
1
3
3
12
1
1
0
2
7
0
2
1
0
0
1
3
0
0
0
0
1
0
2
1
2
1
2
0
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
1
1
0
2
3
2
0
0
1
0
1
0
1
1
0
4
0
1
2
0
2
1
0
1
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
2
0
2
1
2
0
0
4
0
0
1
2
1
3
0
1
0
0
1
0
1
0
4
1
1
0
2
1
1
0
1
1
0
0
2
0
1
0
2
1
0
2
2
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
2
2
0
1
1
1
0
1
2
1
0
2
2
0
3
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
2
2
0
1
3
0
0
1
1
0
0
1
0
0
1
1
1
3
0
1
3
0
3
2
0
2
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
12
0
0
2
4
1
1
0
0
1
0
2
3
0
1
38
0
0
2
0
1
0
2
1
0
2
1
0
0
0
2
2
2
7
2
1
1
3
3
0
0
1
2
0
0
0
0
1
2
5
6
0
0
0
1
0
1
3
0
1
1
2
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
3
1
1
25
0
1
2
1
1
3
1
0
3
1
0
1
1
0
1
1
1
2
1
1
2
0
0
0
0
3
1
2
3
1
1
1
2
0
0
0
2
0
1
1
2
0
1
1
0
0
4
1
0
1
0
2
4
1
0
0
4
5
1
0
3
2
1
0
0
3
4
0
0
0
0
0
0
1
0
0
2
4
0
0
0
2
1
5
0
0
0
2
1
4
0
2
2
1
0
3
2
3
2
0
0
1
1
2
0
0
0
0
0
3
1
3
0
2
0
1
1
0
2
0
0
1
55
0
2
1
3
0
0
1
1
3
0
2
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
54
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
2
0
6
0
0
1
1
1
4
0
1
3
3
1
1
4
2
4
0
0
0
1
1
2
2
0
0
1
2
1
0
3
0
0
0
0
0
0
3
0
0
0
1
0
1
1
1
0
1
0
1
0
0
2
1
2
0
1
0
0
0
1
2
1
0
1
0
3
2
1
1
1
1
1
2
0
1
5
0
1
0
4
1
0
2
2
1
0
0
0
0
1
0
1
0
1
3
2
2
2
1
0
0
0
2
3
0
0
1
0
1
2
0
2
3
2
2
0
6
3
1
0
0
0
0
0
3
1
2
1
0
0
3
2
1
4
6
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
4
0
2
1
0
4
0
1
0
2
2
2
1
1
1
0
2
1
3
2
0
2
0
1
0
3
1
0
0
0
1
1
1
1
2
2
3
2
2
1
0
0
1
1
1
1
0
2
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
3
9
0
0
1
0
1
2
0
4
0
1
0
1
0
4
1
0
2
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
2
4
1
2
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
4
0
2
0
1
0
2
0
5
0
0
2
1
0
2
1
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
1
2
1
2
0
0
1
0
0
0
1
0
1
1
3
0
0
2
1
0
0
0
1
3
1
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
4
0
0
1
4
0
0
3
1
0
1
0
1
1
2
2
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
0
2
0
2
1
1
1
3
2
1
2
2
1
1
2
0
0
1
2
0
1
0
3
0
2
1
3
2
0
0
2
0
0
1
0
3
1
0
1
1
3
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
3
0
0
1
0
1
1
1
0
0
1
1
0
2
0
3
0
0
1
0
2
1
0
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
4
1
0
2
1
0
1
0
0
2
3
2
0
0
1
1
0
0
1
1
0
2
1
1
0
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
2
4
1
1
0
3
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
3
0
5
0
1
0
0
0
1
0
1
0
3
2
2
1
3
5
0
0
2
0
1
3
1
2
0
1
0
1
1
0
2
0
0
0
2
2
0
0
2
1
0
1
3
0
0
1
1
0
1
0
2
0
0
0
0
0
5
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
1
2
1
4
2
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
2
0
0
4
0
1
2
2
0
1
0
3
0
3
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
3
0
0
0
0
2
0
2
0
0
0
6
1
1
1
0
1
1
1
0
0
0
3
1
0
1
3
1
0
0
2
0
1
4
2
0
1
0
1
1
0
1
1
0
5
0
1
0
0
0
3
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
4
0
0
2
0
0
2
0
1
2
0
1
0
1
2
1
1
1
2
3
2
1
0
0
0
1
1
0
1
0
1
0
1
2
2
1
2
2
1
1
0
1
0
1
1
0
1
3
1
1
0
4
1
1
1
1
3
3
0
1
0
3
2
2
0
0
2
2
0
0
1
1
2
0
3
2
4
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
4
1
0
0
0
3
0
0
2
1
1
2
1
3
1
1
4
0
1
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
1
1
1
1
2
4
0
3
2
0
0
1
2
1
2
1
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
2
0
1
2
3
1
0
1
0
0
1
0
0
0
3
4
3
1
0
1
0
1
0
0
0
1
0
0
1
0
4
0
1
1
0
1
2
1
0
4
2
0
0
1
1
2
1
0
0
0
2
3
1
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
1
5
2
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
5
0
1
3
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
2
1
3
1
0
0
1
1
1
1
2
3
0
0
2
0
0
0
0
0
1
2
3
2
0
1
0
2
1
1
0
0
0
0
0
4
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
0
1
0
0
2
0
1
1
1
1
3
0
3
1
2
0
0
0
0
2
0
3
0
2
0
0
1
2
2
2
3
2
1
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
7
0
0
0
1
1
0
0
0
3
0
1
2
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
2
1
1
1
0
0
1
0
0
0
5
1
0
3
0
0
1
0
2
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
1
1
1
2
1
1
0
0
1
0
0
2
3
0
0
0
0
1
1
2
1
0
2
1
0
2
0
3
2
0
0
1
0
3
2
2
0
0
0
1
1
1
2
0
2
2
0
1
0
0
0
1
0
0
1
1
1
0
1
3
2
1
0
0
2
0
0
1
2
0
2
0
0
0
1
2
1
0
1
1
2
1
0
1
1
1
2
2
0
0
3
0
0
2
1
4
0
1
1
1
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
3
0
0
3
1
1
2
2
1
1
0
1
0
0
3
1
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
10
0
0
2
0
3
0
2
0
1
0
1
4
2
2
0
0
1
1
2
1
1
0
0
2
2
1
2
0
0
1
0
0
0
0
8
3
0
0
0
1
0
0
0
2
1
0
2
2
0
0
4
1
0
0
2
2
1
1
0
0
0
1
3
0
1
1
6
1
0
0
0
1
0
4
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
1
0
3
0
0
1
0
0
0
1
1
2
1
0
2
0
0
3
1
0
0
1
1
4
2
1
1
3
0
1
0
2
2
0
2
1
2
2
2
1
0
1
1
2
3
0
0
1
1
1
1
1
1
2
0
0
2
0
2
1
0
0
0
0
0
1
0
10
0
0
0
0
1
1
0
1
2
0
0
1
0
1
0
3
1
0
2
0
1
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
1
1
1
2
2
0
1
4
1
1
0
1
2
2
0
1
4
1
3
1
0
1
2
1
1
1
1
3
1
0
0
3
1
0
2
2
1
0
4
0
4
0
0
1
0
0
0
1
0
0
1
2
0
3
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
0
1
2
1
1
1
2
2
0
0
1
0
1
0
0
1
4
1
0
0
2
0
1
1
0
2
2
1
1
7
1
0
3
0
0
0
2
0
2
4
1
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
1
0
2
1
1
1
1
0
0
4
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
3
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
3
0
0
1
3
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
1
3
1
0
1
1
0
0
0
2
1
2
0
0
0
3
1
2
0
3
0
0
1
1
2
0
2
2
2
0
0
0
1
1
0
2
1
1
0
1
0
1
0
2
1
3
0
1
1
0
1
2
1
2
0
0
2
0
1
0
4
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
3
1
0
0
0
1
2
0
1
0
2
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
2
6
1
0
1
0
0
3
1
0
0
1
2
2
2
1
3
0
1
1
0
0
2
3
1
4
3
1
3
0
0
0
1
0
0
2
2
1
1
0
3
0
3
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
3
0
1
5
2
2
0
2
0
0
1
0
3
0
1
1
0
2
0
1
1
1
1
0
1
2
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
3
1
2
1
1
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
2
2
0
1
2
5
1
4
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
3
2
1
0
0
0
1
45
0
0
1
0
2
0
0
3
1
0
1
0
2
0
2
2
0
1
0
1
2
0
1
1
0
0
2
0
0
1
2
0
3
0
3
1
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
2
0
1
2
1
2
1
3
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
3
0
0
1
0
0
1
0
0
1
0
1
1
2
1
1
0
0
0
1
0
1
7
1
0
3
2
1
2
0
2
0
0
2
1
1
1
0
2
0
1
0
1
0
0
3
3
1
1
1
1
3
0
1
0
2
2
3
1
1
1
8
4
1
3
0
2
0
1
1
0
0
0
1
0
0
3
1
0
0
3
1
0
0
1
2
0
0
2
2
3
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
2
1
2
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
2
2
3
1
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
2
2
2
1
5
0
0
3
1
1
3
3
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
1
3
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
9
2
0
0
2
0
0
1
2
1
0
1
0
1
0
0
1
1
1
2
1
0
1
0
0
0
3
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
3
1
0
0
4
3
1
2
1
1
0
0
0
1
0
0
0
2
4
3
0
0
1
1
1
0
4
0
0
1
1
1
0
0
2
1
0
1
1
4
2
2
0
1
0
0
2
1
0
0
162
1
1
0
0
2
1
1
2
0
2
0
1
0
1
0
5
4
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
2
2
1
0
1
0
2
1
1
1
0
2
0
0
0
1
0
0
3
2
1
0
1
0
2
3
0
2
2
0
1
1
2
8
0
1
1
2
2
1
1
2
0
1
0
0
0
2
0
0
1
2
1
1
1
2
1
2
2
1
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
2
3
0
0
3
3
2
1
1
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
2
3
2
3
0
1
2
0
6
0
0
0
1
0
0
0
2
2
0
0
1
1
0
1
0
0
4
0
0
0
1
0
1
0
0
0
5
0
2
0
1
3
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
1
1
1
0
0
3
1
2
0
4
0
0
0
4
0
0
1
3
0
2
1
0
0
2
2
1
1
1
2
0
1
0
4
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
5
4
0
0
0
0
5
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
3
0
0
2
0
2
3
1
0
2
0
0
1
1
2
1
1
1
2
0
0
0
1
1
1
3
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
1
1
0
1
1
0
1
2
0
2
1
0
2
1
0
1
0
1
0
3
1
0
2
3
1
1
2
0
1
1
0
3
0
0
0
0
0
1
0
0
3
3
3
0
2
1
1
2
0
1
1
2
1
2
1
3
3
1
3
3
3
0
0
2
1
5
1
0
1
0
2
0
4
0
0
1
0
0
3
1
2
2
0
0
1
0
0
0
0
2
8
2
2
1
0
3
0
2
0
2
0
1
3
2
0
0
2
1
0
1
2
0
2
1
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
1
0
0
0
3
1
0
2
1
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
4
1
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
3
3
1
2
0
2
1
0
1
0
1
0
0
1
1
0
1
3
2
2
1
0
2
4
0
0
1
1
2
1
0
2
0
2
1
3
0
2
1
0
1
0
2
1
1
2
2
0
0
1
1
3
1
0
0
3
0
0
0
3
1
0
2
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
1
6
1
0
0
1
0
1
0
1
0
0
4
0
0
0
1
0
3
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
1
4
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
3
1
0
1
0
0
2
0
0
0
1
1
3
2
1
3
2
0
0
1
0
0
1
4
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
3
3
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
3
0
1
4
3
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
1
0
1
1
1
0
0
1
1
1
2
0
0
0
0
1
0
2
2
0
1
2
0
2
2
0
2
0
0
0
2
3
0
2
2
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
4
0
0
1
1
1
2
0
2
0
3
0
1
1
0
1
0
1
0
4
0
1
3
0
0
1
0
0
1
0
1
3
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
3
2
2
0
1
0
0
4
0
0
3
0
0
1
0
1
0
0
3
0
3
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
2
3
0
2
5
2
1
0
3
1
2
0
0
2
0
0
0
2
0
0
0
6
1
2
0
0
0
2
1
0
2
1
1
1
2
0
1
2
0
0
0
1
2
0
2
1
1
1
0
2
0
1
1
1
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
2
1
0
4
1
2
1
0
3
0
0
2
0
0
0
0
2
1
0
1
2
1
3
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
1
2
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
3
2
2
0
0
1
1
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
1
2
1
1
1
1
0
2
0
0
0
0
3
1
0
1
1
0
0
1
0
1
3
1
1
0
0
3
0
1
1
0
1
1
0
0
1
2
0
0
1
0
2
2
1
3
0
2
0
2
0
2
1
0
1
0
0
0
0
3
3
0
0
1
1
0
0
0
1
0
2
0
3
1
1
2
1
3
0
0
2
0
0
3
0
1
0
1
1
0
1
1
0
1
0
0
2
1
0
1
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
3
1
1
3
0
0
1
1
0
1
0
1
1
0
0
2
0
1
1
1
0
1
0
0
1
0
2
1
2
2
1
0
0
0
1
2
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
3
1
0
0
2
4
0
0
0
0
1
1
1
2
1
3
1
1
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
2
1
0
1
1
2
4
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
4
0
1
0
1
1
0
1
0
2
2
1
0
0
0
3
1
1
0
0
0
1
1
0
0
1
0
3
1
1
0
0
2
0
2
3
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
3
3
1
0
3
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
2
1
0
1
1
1
1
0
0
2
1
0
2
1
0
1
0
0
0
0
2
4
4
1
1
2
1
1
5
0
0
1
0
0
1
1
0
1
0
1
0
1
0
2
2
0
1
0
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
1
1
1
1
6
2
0
0
1
1
1
1
1
0
1
0
0
0
1
0
4
0
1
4
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
4
0
0
1
0
3
1
3
2
1
1
0
0
4
0
1
3
1
0
1
3
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
3
1
0
1
1
0
2
2
2
0
0
0
1
0
0
1
1
1
2
8
0
1
1
0
1
0
2
3
1
1
0
0
0
2
2
2
1
1
0
2
0
1
0
1
1
2
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
1
2
0
0
2
2
0
1
0
2
2
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
2
3
2
1
1
0
2
0
1
1
1
0
3
0
0
0
1
1
0
0
1
3
0
0
3
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
1
0
2
2
2
0
0
1
2
0
0
0
1
2
4
0
1
0
0
1
0
1
1
0
3
1
1
0
2
3
1
0
0
2
2
1
1
0
0
1
2
0
1
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
0
3
0
0
0
2
0
2
1
1
1
2
0
2
1
0
0
0
1
3
1
1
1
5
2
1
0
3
1
3
2
0
0
0
0
1
1
2
4
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
2
0
2
1
3
0
0
0
0
1
2
1
2
0
1
2
0
2
1
1
3
1
1
0
1
0
1
0
1
1
0
0
3
1
2
1
0
2
0
0
2
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
0
2
0
0
1
2
0
1
0
3
0
2
0
0
1
0
1
1
2
0
0
1
1
0
0
0
1
1
6
2
0
1
0
0
0
1
2
1
2
2
0
0
0
1
1
0
0
1
0
1
3
0
1
1
0
0
1
2
2
0
0
0
0
0
4
2
0
1
0
0
6
1
1
6
1
0
3
3
1
1
0
1
2
1
1
2
0
5
0
0
1
1
1
0
0
2
2
4
1
1
4
1
0
0
1
0
6
1
0
1
0
0
3
1
0
1
0
1
1
3
2
0
0
3
0
0
1
2
2
0
1
1
2
1
1
4
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
3
2
0
1
2
0
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
3
0
0
2
1
0
2
5
6
0
0
1
4
1
0
1
2
0
0
0
3
0
0
2
0
0
0
0
1
0
1
2
1
1
0
1
0
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
4
1
1
0
4
2
2
0
1
0
1
0
2
1
0
4
0
4
0
0
0
1
1
0
0
0
0
3
0
1
0
0
6
2
0
0
0
1
1
1
2
0
0
0
2
1
1
0
2
0
0
0
0
1
1
1
2
1
1
3
2
0
1
0
0
1
0
0
4
0
1
1
4
0
1
0
2
0
1
1
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
3
1
1
1
1
0
0
2
3
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
4
0
1
2
0
0
1
8
0
3
3
1
0
0
0
7
1
1
0
2
0
1
1
2
1
0
0
1
1
1
0
0
1
4
0
0
0
2
1
0
0
4
0
1
4
0
0
0
0
2
2
1
0
4
0
2
0
1
1
0
0
1
3
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
1
2
2
0
1
0
2
1
1
2
1
2
0
0
1
2
0
4
1
0
1
0
2
0
1
1
0
4
2
0
2
0
1
0
0
0
0
1
0
0
0
0
19
1
0
0
0
0
3
2
1
0
0
1
1
1
1
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
3
2
0
1
0
1
1
1
1
2
1
2
2
1
1
0
0
0
0
0
0
1
0
0
3
0
1
1
1
0
1
2
2
0
0
1
0
0
1
2
1
4
1
0
0
2
1
1
1
3
0
0
0
0
0
2
0
4
1
1
0
3
0
2
0
1
2
2
0
1
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
3
1
0
1
1
0
1
2
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
1
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
3
1
1
2
1
0
1
0
0
5
1
2
2
1
0
1
0
1
1
1
1
0
2
2
1
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
1
5
0
0
3
2
1
1
0
2
1
0
0
0
1
1
2
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
3
1
2
0
2
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
3
1
0
1
2
1
1
1
1
2
0
2
2
1
0
0
3
1
0
2
5
0
0
1
6
2
1
0
2
1
0
1
1
0
1
1
1
1
0
0
0
1
2
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
0
1
3
0
0
1
2
1
2
0
2
0
0
0
1
0
1
1
0
2
1
1
0
1
0
2
2
0
1
1
1
1
2
1
3
0
0
0
0
3
0
2
2
1
2
0
1
0
2
2
0
3
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
6
0
1
1
1
1
1
3
0
3
3
0
1
3
0
2
1
1
0
2
0
0
0
4
1
1
1
2
0
0
27
1
0
0
1
2
1
1
2
1
0
0
1
1
0
1
3
0
2
0
0
0
1
1
1
0
1
2
1
2
0
2
2
0
0
0
5
1
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
0
0
2
1
1
1
1
1
0
2
3
2
0
0
0
1
1
0
0
1
0
0
2
3
0
1
2
1
0
0
4
1
1
0
0
2
2
0
0
1
1
2
1
1
0
3
1
0
0
1
1
1
1
0
3
1
0
2
2
0
1
1
0
0
3
1
2
0
1
1
1
0
1
0
1
0
0
0
0
0
1
3
0
0
3
0
1
1
0
1
2
0
2
0
3
0
0
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
1
2
0
0
1
1
1
0
0
2
0
3
0
1
2
0
2
2
4
1
1
2
2
0
1
0
0
1
1
0
1
1
1
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
2
0
2
2
1
0
1
3
1
0
1
1
1
0
1
1
1
1
3
1
1
0
0
3
0
0
0
0
1
3
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
35
0
1
0
2
1
2
11
0
0
1
0
2
0
0
0
2
3
1
0
0
1
0
0
3
0
0
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
3
1
2
0
1
0
1
1
0
2
1
0
1
0
0
0
0
2
2
0
1
2
0
0
1
2
2
0
0
1
0
3
1
0
1
1
0
0
2
1
2
0
0
1
1
1
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
1
1
2
1
0
0
1
2
0
3
3
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
3
1
1
0
0
1
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
3
0
2
1
1
2
7
0
2
1
0
1
1
2
1
1
1
0
0
0
1
0
2
0
1
2
1
4
0
1
2
2
0
2
0
0
1
0
1
2
2
1
0
0
0
2
1
1
1
1
1
0
1
0
2
1
0
2
1
0
0
2
2
0
1
3
1
0
0
0
2
2
8
0
0
0
4
0
1
0
1
3
1
3
0
0
1
0
1
0
0
1
0
1
0
0
4
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
3
0
0
0
1
3
2
0
0
2
0
0
0
0
0
2
2
0
0
1
1
3
2
1
1
0
0
2
0
1
1
0
2
1
1
0
0
1
1
0
1
1
2
0
1
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
1
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
3
1
2
0
0
1
1
2
1
1
1
1
2
1
1
3
0
0
0
4
0
1
0
2
1
0
0
3
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
2
2
1
1
0
0
0
0
1
1
0
0
1
1
2
0
2
1
1
1
1
2
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
2
1
0
2
1
0
1
0
2
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
4
0
1
1
4
1
0
20
2
1
0
1
1
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
1
4
0
2
4
1
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
0
11
2
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
2
1
1
0
2
0
0
2
0
1
2
2
0
0
3
0
0
1
0
0
1
0
1
0
2
1
0
0
3
0
4
0
1
1
0
0
2
0
1
2
0
1
0
2
1
2
0
1
0
3
1
1
1
0
2
1
2
1
0
2
2
1
1
0
0
0
3
1
0
3
0
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
3
1
1
1
1
0
0
3
1
0
2
2
0
0
1
0
0
1
0
0
1
2
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
3
0
1
4
1
0
1
3
2
4
2
1
0
1
2
3
0
1
0
0
0
4
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
1
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
0
3
0
2
2
0
1
3
2
2
1
1
1
0
2
1
0
0
0
0
0
0
0
5
3
0
0
0
1
2
0
0
1
0
0
1
0
1
3
2
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
0
2
2
0
0
0
2
1
0
1
0
1
1
0
1
0
3
0
0
1
0
1
1
0
0
0
2
1
0
3
2
1
0
0
0
1
0
1
1
2
1
2
1
1
1
1
3
1
1
0
1
0
0
1
3
5
0
1
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
2
3
3
0
0
1
0
0
4
0
1
0
1
0
0
1
0
0
1
0
0
6
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
3
3
1
0
0
1
1
3
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
3
1
2
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
1
1
0
1
1
0
0
0
1
2
1
1
0
3
1
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
1
1
1
0
0
0
2
1
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
2
0
0
3
1
1
0
1
2
0
0
1
1
0
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
2
0
1
4
3
1
0
2
0
2
0
1
0
4
0
3
0
1
1
1
0
2
2
1
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
2
1
0
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
2
1
0
3
2
2
1
0
1
1
1
0
1
0
5
0
1
1
2
2
2
1
1
0
1
1
3
1
0
0
0
0
2
1
0
1
3
1
0
0
0
0
0
0
0
8
2
1
0
3
0
0
0
2
1
0
1
0
1
1
0
0
1
0
2
0
2
1
1
3
0
0
0
0
0
3
0
2
0
22
0
0
0
1
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
3
0
0
0
1
0
0
3
0
2
0
2
3
3
2
0
1
0
2
0
1
1
3
0
2
1
1
0
0
1
2
1
2
0
1
0
1
0
0
1
1
1
1
1
1
2
0
0
0
0
2
2
0
1
0
1
2
2
0
1
3
1
0
0
1
1
3
1
0
0
0
1
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
4
1
2
1
1
3
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
3
0
1
0
2
0
1
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
1
0
3
1
0
0
0
1
1
0
1
3
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
0
0
1
3
3
1
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
3
0
0
1
2
1
0
3
0
0
0
3
1
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
2
0
1
1
0
1
1
0
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
1
0
13
1
0
2
0
0
0
0
0
0
2
1
1
2
2
1
1
0
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
1
6
1
1
0
1
0
0
0
1
0
3
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
1
1
2
0
0
1
0
2
1
0
0
1
3
1
1
1
0
0
1
1
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
2
2
0
0
0
1
1
0
1
1
19
0
0
0
0
1
0
1
0
0
5
2
0
0
1
0
1
0
1
1
0
0
4
2
1
0
0
0
0
1
1
1
1
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
2
0
1
0
2
0
2
1
1
1
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
2
0
3
0
2
2
0
1
2
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
3
1
0
0
0
1
0
1
0
0
0
0
1
0
3
2
1
1
2
1
1
1
1
1
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
1
2
0
2
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
1
0
0
2
3
0
1
0
2
0
0
0
2
0
0
0
0
1
1
3
2
0
1
2
15
0
1
0
2
0
2
0
1
2
0
0
1
0
2
1
3
0
0
1
1
1
1
3
0
1
0
4
0
2
1
1
0
2
1
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
1
2
2
0
1
1
0
1
1
3
0
1
0
4
0
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
3
0
1
3
3
1
1
0
2
2
0
1
1
1
0
0
0
2
6
0
0
0
0
3
2
1
3
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
1
3
0
1
1
0
0
1
0
0
0
0
1
4
2
1
2
1
0
0
0
0
1
2
0
1
0
1
0
4
0
2
1
4
0
1
0
1
1
1
5
1
0
0
1
1
2
1
1
2
0
1
1
2
1
1
0
3
0
3
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
3
2
4
1
1
2
0
0
2
1
1
0
1
0
2
4
0
0
0
2
0
1
1
0
1
0
1
0
2
0
2
1
1
0
0
1
1
1
2
1
1
0
1
0
0
0
0
1
0
1
1
0
4
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
4
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
5
3
1
1
0
0
1
0
0
1
0
4
0
2
0
2
0
0
1
0
1
1
0
1
0
2
1
2
3
1
0
0
1
0
0
1
4
0
0
1
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
2
2
1
1
0
2
2
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
1
1
0
4
0
0
3
0
0
103
2
0
4
1
0
3
1
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
2
1
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
3
1
3
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
1
0
0
2
1
0
0
0
2
2
1
0
4
0
0
0
1
0
0
1
1
2
1
2
1
1
0
0
1
1
2
1
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
4
0
1
0
0
1
1
0
0
1
1
0
2
0
1
1
0
0
2
1
1
0
3
0
0
0
1
0
1
1
0
0
0
1
0
2
0
1
0
1
1
2
0
1
0
0
1
2
0
1
0
1
1
1
1
0
0
2
3
1
0
0
5
0
0
0
0
0
1
1
1
2
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
1
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
3
0
5
0
0
2
2
0
0
0
3
2
1
0
1
0
1
0
0
0
1
3
0
0
1
0
1
1
0
2
2
1
3
2
1
0
0
3
1
1
0
0
1
2
0
0
2
1
0
0
2
0
0
2
4
0
0
1
2
0
1
1
0
2
2
0
3
2
2
0
1
0
2
1
0
2
1
1
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
1
3
2
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
3
3
0
0
0
1
0
1
1
1
1
2
2
0
0
1
2
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
3
3
0
2
0
2
1
0
0
1
1
1
1
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
2
3
1
0
1
0
0
0
0
1
0
0
0
1
1
2
1
2
2
1
3
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
1
0
4
0
0
0
0
1
0
0
0
0
1
1
2
1
0
2
0
0
1
2
0
1
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
3
2
0
0
1
0
3
1
2
0
0
1
0
0
0
2
0
1
1
2
0
1
2
0
2
1
0
0
0
1
1
1
0
1
2
0
1
1
2
0
1
1
0
0
0
2
0
3
2
1
1
1
3
0
0
0
2
2
3
0
1
0
0
1
1
0
1
5
1
3
3
1
2
0
0
2
1
1
0
0
1
1
3
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
1
2
2
0
0
1
3
0
1
1
2
1
1
0
0
0
0
0
0
1
3
0
0
2
3
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
2
2
2
1
0
1
4
3
0
0
1
2
1
0
0
1
1
1
2
0
2
4
0
0
0
0
1
0
0
3
1
2
1
0
0
0
4
1
0
0
1
0
0
1
3
0
1
0
1
6
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
3
2
1
1
1
1
0
2
2
1
0
2
1
0
1
1
1
1
0
3
1
0
2
1
1
2
0
1
2
1
0
0
0
1
0
1
0
1
1
1
1
2
1
0
0
0
0
0
1
1
0
3
0
0
3
3
0
0
1
2
0
0
0
1
0
0
1
4
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
5
0
1
0
0
0
7
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
5
3
0
0
3
1
2
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
3
0
3
0
0
4
1
0
0
0
0
1
0
0
1
1
0
0
0
5
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
1
1
1
0
0
0
3
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
3
0
2
2
1
1
0
1
2
0
2
1
1
1
0
0
0
1
1
0
1
4
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
7
0
0
0
2
2
0
0
2
2
1
0
0
0
0
1
2
1
0
0
0
2
0
1
1
2
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
2
1
1
0
1
1
0
0
0
0
1
3
0
2
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
3
0
0
1
1
0
1
1
0
0
0
1
1
0
2
1
3
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
3
1
0
1
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
3
1
1
0
0
3
0
3
1
0
0
1
0
0
1
0
0
3
0
3
1
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
2
2
1
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
3
4
0
1
2
1
1
1
3
3
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
3
2
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
2
0
2
1
0
2
0
0
3
2
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
3
0
1
1
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
3
0
1
0
0
0
1
3
0
1
0
2
0
0
4
0
0
1
0
1
0
2
1
2
0
2
2
3
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
1
0
2
2
1
0
0
0
3
2
1
0
0
3
0
3
0
0
1
0
2
1
0
1
0
0
1
1
1
0
0
2
0
0
1
1
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
4
2
0
2
0
0
0
0
2
4
0
1
0
1
1
1
1
4
0
0
4
0
0
0
0
2
1
0
0
1
0
1
0
6
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
0
0
2
0
2
0
1
0
1
0
1
0
2
0
0
1
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
1
2
3
0
0
1
0
1
0
1
0
4
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
3
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
2
1
1
0
1
1
0
3
1
0
2
0
0
0
2
1
1
1
0
0
1
0
4
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
2
2
0
0
5
0
1
0
3
0
1
1
0
0
0
1
0
0
0
2
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
1
0
0
4
2
1
0
1
0
0
2
0
3
1
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
6
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
1
3
0
2
2
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
8
0
5
0
2
1
3
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
4
0
0
3
0
2
1
1
0
0
0
0
1
0
3
2
1
1
0
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
3
0
0
1
0
0
4
0
0
0
0
0
1
1
3
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
4
1
1
0
1
1
0
0
0
0
2
4
0
1
0
0
1
2
0
1
1
1
0
2
1
0
1
1
0
2
0
1
3
0
2
0
0
2
1
2
0
0
0
3
0
0
2
1
0
3
1
1
0
1
3
2
1
0
1
0
0
0
1
4
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
4
1
0
0
1
0
3
0
3
0
1
0
0
1
2
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
1
0
0
31
5
1
0
1
0
1
0
0
0
0
0
2
0
22
1
1
2
0
1
4
0
0
0
2
1
5
1
0
0
0
1
3
1
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
1
4
1
0
3
0
0
0
1
0
0
0
2
1
2
0
2
1
1
1
0
0
1
1
0
3
2
1
2
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
2
1
0
2
0
0
0
9
1
0
2
0
1
0
0
20
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
1
1
0
1
2
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
6
2
0
4
0
0
0
0
0
0
1
1
0
1
0
4
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
2
3
2
0
0
1
2
1
3
5
0
0
0
0
2
2
4
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
2
0
1
0
3
0
2
0
0
1
0
0
0
1
3
0
1
1
0
0
1
3
2
0
1
1
0
2
2
2
1
1
0
0
3
1
2
1
0
0
1
2
0
0
7
1
0
0
3
0
3
0
0
2
0
1
0
0
1
0
0
3
0
0
0
1
1
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
3
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
1
1
2
1
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
0
3
0
2
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
3
1
0
2
1
1
288
0
0
1
2
0
1
1
1
1
2
1
1
5
2
0
1
1
0
0
0
1
2
0
1
3
0
1
2
1
0
5
0
7
0
0
2
0
3
0
0
0
11
0
1
0
0
3
0
0
0
1
2
1
0
1
2
0
1
0
2
1
0
0
1
0
2
1
0
2
0
1
0
0
1
1
0
0
1
0
1
3
0
0
0
0
1
0
3
2
0
1
1
2
1
0
1
0
0
0
0
3
0
4
0
0
3
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
0
0
1
0
3
1
1
1
1
0
1
1
0
0
1
2
0
1
1
1
0
5
1
2
0
1
0
0
0
1
1
1
0
0
2
1
1
2
0
1
0
0
6
2
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
3
3
0
0
9
1
0
4
1
0
0
0
0
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
1
0
0
2
5
1
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
1
2
0
0
1
1
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
2
2
0
0
3
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
3
1
0
1
3
0
0
2
1
0
1
2
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
337
0
1
2
1
2
2
0
0
3
1
7
6
0
1
1
0
1
0
1
1
2
0
0
1
0
2
1
2
0
1
1
1
0
1
1
4
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
1
2
2
2
1
0
0
0
1
1
2
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
1
0
0
1
1
1
0
0
1
4
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
10
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
3
1
2
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
0
1
1
0
1
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
3
2
0
0
1
1
1
1
6
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
1
1
0
0
1
1
1
3
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
2
2
0
1
1
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
2
25
4
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
5
0
1
0
0
0
0
1
3
0
0
0
0
1
1
0
2
0
2
3
0
0
1
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
1
3
0
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
1
1
2
3
0
0
1
1
0
0
1
3
3
0
6
0
0
2
0
0
0
0
2
2
3
3
0
0
2
0
0
0
1
1
2
1
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
3
0
1
0
0
4
0
1
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
6
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
5
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
2
0
2
0
0
1
0
1
0
1
1
1
1
2
0
1
1
0
4
0
2
0
0
0
0
0
10
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
1
1
2
2
3
1
0
0
2
3
2
2
0
0
0
1
2
2
0
0
2
0
5
1
4
1
0
1
2
1
2
3
1
0
0
0
1
2
1
0
0
0
0
0
3
0
1
1
1
0
35
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
2
0
0
3
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
4
0
3
2
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
0
10
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
31
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
3
0
2
0
1
0
3
0
1
0
1
2
1
0
1
2
0
2
2
0
0
0
0
4
1
0
2
0
4
0
1
1
1
1
1
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
2
1
0
1
0
2
3
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
2
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
2
1
2
0
2
0
1
2
1
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
3
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
3
2
0
0
0
1
1
0
1
2
2
0
0
1
0
1
1
1
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
1
0
0
0
10
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
3
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
2
2
0
0
1
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
1
1
1
0
2
2
2
0
0
2
2
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
3
0
1
0
0
3
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
5
1
2
0
0
1
0
1
1
0
1
1
1
0
1
0
4
0
0
0
1
0
0
3
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
3
0
2
0
0
1
3
2
0
2
0
0
2
0
1
0
0
1
2
1
1
1
1
2
0
0
1
2
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
4
0
1
1
0
3
3
2
0
2
1
0
1
1
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
0
3
2
2
0
0
0
1
1
0
0
1
0
2
0
0
1
1
1
3
2
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
2
1
1
3
1
0
0
0
2
0
0
1
0
1
0
2
0
0
1
3
0
0
2
3
1
0
0
0
0
1
0
1
0
1
1
1
0
1
2
0
0
2
1
2
3
6
1
0
2
0
0
2
0
1
3
0
1
0
1
3
2
1
0
1
0
0
0
2
0
1
0
0
1
1
0
1
2
0
1
0
2
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
2
0
0
0
1
1
0
2
1
1
1
0
2
1
1
0
0
1
0
0
0
1
0
0
3
2
0
2
0
1
2
1
1
1
0
1
0
1
3
0
4
2
2
0
0
1
0
0
1
1
2
5
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
1
2
2
0
0
1
0
0
1
1
1
1
0
2
0
1
1
2
1
0
0
0
1
2
0
3
1
3
3
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
3
0
1
1
1
0
2
0
1
0
0
1
3
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
23
0
11
0
2
2
4
0
0
0
0
1
0
3
0
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
4
0
2
1
0
0
0
0
1
1
4
2
1
3
0
0
1
0
1
3
0
1
0
3
0
0
2
1
1
0
4
2
1
0
6
0
0
3
0
3
0
3
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
5
0
4
2
0
1
1
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
0
1
1
1
1
1
0
6
0
0
0
6
0
0
3
0
1
1
3
0
1
1
1
1
0
0
1
1
0
1
1
0
2
1
0
1
2
3
3
2
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
2
2
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
2
0
1
1
2
2
1
1
1
1
0
0
1
3
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
0
3
1
0
0
0
0
2
1
0
3
1
0
0
0
2
0
1
2
2
0
0
0
1
0
0
3
0
3
0
0
1
1
1
2
1
1
0
0
2
1
0
0
1
0
3
0
1
1
3
0
0
0
0
2
1
0
0
1
4
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
2
0
0
1
1
3
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
2
2
0
1
1
2
0
0
1
0
3
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
0
3
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
4
1
0
2
1
0
1
2
0
0
1
1
1
4
4
0
0
0
0
1
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
4
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
3
3
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
2
2
1
4
1
1
3
0
1
0
2
1
1
0
1
1
1
0
1
1
0
0
0
2
0
3
0
0
1
0
1
1
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
1
1
1
2
0
0
4
0
1
0
0
0
1
0
1
1
0
1
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
2
1
3
1
2
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
0
1
1
0
5
0
1
0
0
1
2
2
0
0
0
1
3
0
0
0
1
0
3
9
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
3
2
0
2
0
1
0
1
0
0
1
1
0
1
2
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
3
1
1
0
2
0
1
3
3
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
4
0
1
0
1
0
0
0
1
0
1
1
7
1
1
0
0
1
4
0
0
0
1
1
2
1
0
1
1
3
1
4
2
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
5
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
1
0
2
1
0
1
2
2
0
0
2
0
1
0
1
0
0
0
2
0
0
2
1
0
5
1
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
2
0
0
2
0
0
0
3
1
0
0
1
1
2
2
2
0
1
0
2
0
1
0
0
0
1
1
1
0
1
1
1
1
2
3
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
24
1
2
1
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
3
1
1
1
1
0
3
0
1
2
0
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
2
2
0
1
1
0
1
0
4
0
2
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
3
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
2
0
3
1
0
1
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
3
1
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
1
0
1
3
1
1
2
0
0
0
3
1
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
3
0
1
0
0
2
0
0
0
0
0
0
1
18
1
0
2
0
1
0
0
0
1
0
14
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
5
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
4
1
0
4
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
1
1
3
0
0
1
1
0
0
0
2
0
0
1
1
0
2
1
1
1
3
0
0
0
1
0
1
2
2
0
1
0
1
2
0
1
2
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
1
0
2
4
1
0
0
0
1
1
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
1
0
2
1
3
0
0
0
0
4
1
1
1
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
4
2
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
2
1
1
2
0
1
0
0
1
2
2
0
1
5
0
0
0
0
3
1
0
0
0
1
0
6
1
0
2
1
0
2
0
0
2
1
1
1
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
2
1
0
5
1
0
3
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
4
0
0
0
1
1
1
0
1
0
6
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
3
1
1
2
3
4
2
0
3
1
0
1
1
1
0
2
0
2
1
0
1
1
1
2
0
1
0
0
0
1
0
0
2
1
1
1
0
2
1
1
0
0
1
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
1
2
0
1
3
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
2
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
1
1
1
0
1
1
1
1
3
2
0
3
0
1
0
0
1
1
0
2
1
0
2
1
0
0
0
0
4
0
1
2
0
0
1
2
0
0
1
5
0
0
1
1
1
2
1
3
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
1
1
0
10
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
2
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
3
1
0
0
0
1
1
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
4
0
1
0
1
1
0
0
0
3
0
0
0
0
1
0
2
16
1
1
0
1
1
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
2
3
0
1
0
1
3
1
3
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
1
0
2
2
0
0
1
1
2
1
0
1
0
0
1
0
0
1
0
0
0
140
0
1
7
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
2
3
1
0
0
0
0
1
0
3
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
8
0
2
0
2
2
0
0
1
0
1
2
1
0
1
7
1
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
11
0
0
0
0
0
1
0
2
0
1
4
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
1
1
0
0
0
0
2
0
3
1
6
0
1
1
1
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
2
3
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
3
0
1
0
3
1
2
0
4
1
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
3
0
1
0
1
0
0
2
0
0
1
0
1
1
1
4
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
0
1
1
1
0
3
2
0
0
1
1
0
0
2
6
2
2
0
4
0
3
2
0
0
2
0
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
2
1
1
3
1
1
4
0
1
1
0
0
0
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
6
1
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
3
2
0
0
0
3
0
3
1
1
3
1
0
0
0
1
1
0
0
1
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
0
1
0
3
1
1
0
0
1
1
0
1
2
0
0
1
0
0
0
3
0
0
1
1
3
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
5
2
0
0
0
0
0
0
3
1
8
0
1
2
0
1
1
0
0
2
0
3
0
1
1
0
2
1
0
1
0
0
1
4
0
0
0
0
1
0
1
0
2
0
3
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
8
0
0
1
0
1
0
0
1
3
1
2
0
0
2
1
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
0
1
0
0
3
4
0
1
1
0
2
0
1
0
0
1
0
6
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
3
0
1
0
1
0
3
0
0
1
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
0
1
0
1
3
0
2
0
0
1
4
1
1
0
0
4
1
0
0
1
1
0
0
1
2
2
0
1
4
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
3
2
3
3
1
0
0
0
2
1
0
2
0
1
1
1
0
0
2
1
0
0
0
0
1
1
1
1
1
0
1
20
0
1
3
0
0
6
1
2
1
0
1
1
0
1
0
0
3
0
0
1
0
3
1
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
2
1
5
0
0
0
1
1
0
0
0
2
1
0
0
0
1
5
0
0
0
0
1
0
0
0
4
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
3
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
14
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
1
1
1
3
1
1
0
2
1
1
2
0
1
0
1
0
1
1
1
1
0
4
1
0
0
3
0
0
0
2
1
2
0
0
1
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
1
2
1
2
2
0
0
1
1
1
1
0
0
0
2
2
0
1
0
0
0
3
1
1
3
1
3
1
1
1
5
0
3
0
0
0
1
2
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
4
1
0
2
2
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
1
0
2
1
0
2
1
0
0
1
1
1
0
0
1
1
0
1
0
4
0
0
0
1
1
0
0
0
2
2
0
3
0
2
1
1
2
5
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
3
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
6
1
1
0
1
0
1
1
1
2
0
1
0
0
0
0
1
0
0
7
0
1
1
2
0
0
1
0
2
1
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
5
0
1
0
2
1
1
0
0
0
1
0
0
1
0
2
2
0
1
2
0
0
3
3
1
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
3
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
3
2
3
1
1
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
3
5
0
1
3
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
18
0
0
0
0
2
0
0
1
2
0
1
0
3
0
0
0
0
2
0
1
8
1
0
0
1
0
3
3
4
1
0
1
0
0
0
0
0
0
1
0
0
1
3
0
1
1
3
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
3
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
0
0
0
1
1
0
4
0
1
2
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
3
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
2
3
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
1
3
0
1
0
0
0
1
0
31
0
1
1
0
0
1
0
0
4
1
0
0
1
0
1
1
1
0
3
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
0
1
1
2
1
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
4
0
1
1
0
0
0
0
1
0
0
1
3
1
0
0
2
0
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
31
1
1
1
10
0
3
1
1
1
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
4
2
1
8
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
6
0
3
1
0
2
0
0
3
3
0
0
3
2
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
2
0
2
0
1
0
1
1
1
3
12
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
2
0
1
1
0
4
0
1
2
0
0
5
1
2
0
2
1
1
1
2
0
2
0
0
1
0
0
1
3
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
5
0
0
1
0
0
0
1
0
3
0
3
1
0
0
0
0
1
1
1
5
0
0
1
1
0
2
0
2
3
0
3
1
0
2
0
2
0
0
2
4
0
1
0
0
1
1
0
0
2
6
0
0
0
1
2
0
1
1
3
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
1
1
1
6
0
4
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
2
3
0
1
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
1
2
0
2
0
1
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
1
0
1
2
2
1
0
1
0
3
1
0
0
0
0
0
1
2
0
0
1
8
3
1
0
1
3
1
0
2
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
1
0
2
0
0
1
0
2
1
1
2
0
3
0
0
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
2
1
0
1
3
2
2
0
0
0
5
0
0
2
1
0
1
0
1
4
2
0
1
0
0
0
1
0
1
0
0
0
1
2
2
2
1
3
1
0
12
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
1
0
1
2
1
2
1
2
0
2
1
1
1
0
1
0
2
0
1
0
0
0
2
0
7
0
0
1
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
4
1
1
2
2
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
8
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
2
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
2
3
0
1
0
1
0
0
2
2
0
3
2
1
0
1
3
0
0
0
0
0
0
15
3
0
1
1
2
1
2
1
0
2
1
0
1
0
0
3
0
0
0
0
1
2
1
1
0
1
0
0
1
2
1
1
1
3
2
1
0
0
0
2
1
1
0
0
0
1
0
1
2
1
0
1
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
3
0
0
0
2
1
0
0
1
1
0
0
0
0
4
0
0
0
2
1
0
3
0
3
0
0
2
92
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
0
2
3
0
0
1
0
0
7
0
2
0
1
0
0
1
2
1
0
0
0
1
1
1
1
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
34
1
0
4
0
0
1
0
0
1
0
2
2
3
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
3
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
4
0
1
2
0
0
1
0
0
1
2
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
1
1
2
2
1
0
5
0
1
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
1
1
4
0
0
1
0
0
1
0
1
1
1
0
39
3
0
2
2
0
1
0
0
1
0
0
1
1
1
0
2
0
3
0
1
0
2
0
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
4
0
2
0
1
1
0
0
0
4
3
1
0
1
0
0
0
0
1
2
1
3
0
0
0
1
0
1
2
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
5
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
1
1
0
3
1
1
0
1
0
3
0
0
0
2
1
0
1
0
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
4
3
0
1
1
0
0
0
2
0
0
0
2
6
1
0
0
2
0
0
1
0
0
0
0
17
2
1
1
2
3
2
4
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
6
1
4
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
1
1
1
0
1
0
0
0
0
4
0
0
1
1
0
2
1
0
0
0
0
0
3
1
0
0
18
2
0
5
0
1
0
1
0
0
0
1
0
2
4
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
3
0
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
0
2
2
0
1
1
2
2
0
0
0
3
2
0
1
2
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
4
0
2
0
0
1
0
1
3
0
0
0
0
0
0
3
0
0
1
1
0
0
11
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
2
0
1
2
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
1
2
1
2
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
5
1
1
1
0
1
2
1
1
0
2
2
3
25
0
0
0
1
1
0
2
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
1
0
0
2
0
0
0
2
0
2
0
21
0
0
0
2
0
2
1
0
1
0
0
0
1
0
1
2
1
0
1
3
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
3
0
0
3
0
0
1
0
0
1
3
0
0
2
0
0
1
0
4
0
0
5
1
0
0
1
1
0
2
2
4
2
1
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
1
0
1
2
1
0
1
1
2
0
2
0
0
4
2
0
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
2
3
1
1
0
1
1
2
1
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
0
1
2
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
0
1
1
1
1
2
1
2
0
1
4
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
4
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
3
1
2
0
0
0
1
1
0
0
0
1
1
0
1
2
0
1
2
1
0
0
0
0
2
1
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
1
1
1
0
1
0
0
0
1
0
0
0
28
2
0
0
1
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
6
3
0
2
0
0
1
0
3
0
0
1
0
0
1
0
2
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
6
1
1
0
3
0
1
1
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
1
3
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
4
0
1
3
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
1
1
1
2
0
0
0
0
3
0
0
1
1
1
1
0
2
0
0
3
4
0
0
5
1
0
3
1
0
2
1
0
0
0
5
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
5
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
4
0
0
0
3
1
4
1
2
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
2
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
8
4
0
1
2
2
2
0
0
0
1
0
1
0
0
1
4
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
3
1
0
0
1
0
0
1
1
2
1
0
1
0
2
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
6
0
1
1
0
2
1
0
1
1
2
0
1
1
0
1
0
2
2
3
0
0
1
0
1
2
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
2
1
0
1
1
0
1
1
3
3
1
0
1
0
1
1
1
0
0
3
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
1
1
0
2
2
0
2
3
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
0
3
2
1
0
1
0
0
0
2
2
0
0
2
1
1
1
0
1
2
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
3
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
1
2
0
1
2
0
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
3
2
3
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
5
0
1
0
2
1
1
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
5
2
1
2
1
1
1
0
0
2
0
4
0
3
1
0
1
1
0
1
1
2
0
1
0
0
1
3
0
1
1
1
0
0
1
0
0
2
1
0
0
1
0
1
3
0
2
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
2
3
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
2
3
230
1
0
0
1
0
0
0
2
0
1
0
1
4
0
1
1
1
0
1
0
3
0
0
1
1
1
0
2
1
0
1
1
0
3
0
0
2
0
1
0
0
2
2
1
0
1
0
0
2
0
0
0
2
1
0
1
2
0
3
1
0
0
0
0
1
1
0
2
0
1
3
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
2
0
0
1
0
1
0
0
3
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
1
0
2
1
1
2
0
2
0
0
0
8
0
1
0
1
1
0
0
0
1
1
0
0
4
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
2
1
0
0
1
1
1
0
0
0
3
1
5
1
0
0
1
0
2
2
1
1
0
0
0
1
2
2
0
1
0
2
1
2
0
0
1
0
7
0
1
1
1
1
17
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
3
2
0
0
0
2
1
1
0
6
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
3
0
1
0
1
2
0
0
1
4
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
0
1
3
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
6
0
1
0
0
1
3
1
0
0
2
1
3
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
3
0
0
14
5
2
0
0
3
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
0
0
2
2
8
1
1
0
0
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
3
2
2
2
1
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
0
4
0
1
0
1
0
0
0
0
1
2
2
5
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
4
0
4
0
1
0
3
0
1
1
3
1
1
0
0
1
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
0
1
0
3
0
1
0
1
2
0
3
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
3
2
3
1
0
0
0
1
0
4
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
2
1
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
5
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
3
0
1
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
5
1
0
1
0
3
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
1
2
0
0
2
3
0
0
0
2
0
1
1
0
1
0
0
1
1
1
0
0
2
0
1
1
0
48
2
0
1
1
1
2
1
1
0
0
1
0
0
0
0
1
0
1
1
4
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
2
0
12
0
0
1
0
3
2
1
0
0
0
0
0
1
1
0
3
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
3
3
1
0
1
1
1
0
0
0
0
1
0
13
1
0
0
0
2
1
2
0
0
2
0
0
4
1
0
1
2
1
0
0
0
18
1
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
3
0
1
0
1
0
0
1
0
0
1
2
5
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
3
0
1
1
0
0
0
1
2
0
3
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
0
0
1
0
1
1
2
1
0
0
3
2
3
1
0
0
0
0
0
1
1
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
2
1
4
1
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
3
1
0
0
1
0
2
0
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
4
4
1
0
0
1
0
1
1
1
2
1
3
0
0
2
0
0
1
0
0
3
0
3
1
1
1
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
1
0
1
3
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
3
0
2
1
0
3
0
0
0
0
0
0
1
0
2
0
1
3
0
2
2
0
1
0
5
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
3
0
0
0
1
2
0
0
4
2
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
1
1
6
1
0
1
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
3
0
2
0
0
0
1
1
1
0
0
3
1
2
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
3
2
2
2
1
0
3
0
1
0
0
15
1
1
3
0
1
2
1
0
0
1
0
0
4
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
1
3
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
3
1
6
1
2
1
1
2
1
2
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
1
1
0
0
2
2
0
1
1
1
1
3
1
0
2
1
0
0
2
0
0
1
0
0
0
1
18
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
1
1
0
0
0
1
2
2
2
1
2
0
1
0
0
0
1
3
2
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
3
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
2
0
4
1
0
2
1
0
1
3
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
3
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
2
1
1
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
4
1
2
0
2
0
0
0
1
0
0
3
1
1
0
1
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
0
0
1
6
1
0
0
0
1
6
0
0
0
1
0
0
3
1
6
0
1
2
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
1
1
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
5
1
0
1
3
1
0
2
0
1
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
6
0
0
0
3
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
2
1
1
1
0
0
3
0
0
0
0
0
1
3
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
1
0
0
1
0
0
2
1
2
0
0
1
4
0
0
2
1
0
2
0
0
0
0
2
1
2
0
1
0
0
1
1
0
3
0
1
2
2
0
1
1
1
0
0
0
2
1
1
1
0
3
1
0
0
0
1
1
1
1
5
0
3
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
1
1
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
12
1
1
1
0
1
1
0
0
1
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
3
4
1
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
1
3
0
0
0
1
1
1
0
0
1
1
2
0
3
0
0
2
1
0
0
0
0
0
2
1
0
0
1
1
4
0
6
3
1
0
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
1
1
1
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
1
3
1
0
0
1
1
0
0
0
0
1
3
3
0
4
0
0
0
1
0
3
0
1
1
1
0
0
1
0
2
0
5
2
0
1
0
0
1
3
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
41
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
3
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
2
7
2
1
0
1
1
2
0
0
0
0
0
3
1
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
2
38
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
5
0
1
1
0
0
1
4
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
2
1
1
0
2
0
1
0
1
2
0
0
3
1
3
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
1
2
0
0
0
4
1
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
6
0
0
0
1
3
1
0
0
0
2
0
1
0
0
1
1
0
3
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
1
2
0
1
0
0
1
1
1
0
2
3
0
3
0
2
0
1
1
0
0
2
1
0
2
2
1
0
3
0
1
0
0
0
0
0
1
1
1
0
3
0
1
0
2
1
1
0
0
4
1
3
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
0
2
2
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
3
1
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
3
3
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
2
2
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
15
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
2
0
3
1
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
2
2
2
1
0
0
1
1
0
2
1
1
1
0
1
1
2
0
1
0
0
3
0
2
0
1
3
1
0
0
0
0
1
2
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
4
0
1
0
0
3
3
0
0
2
1
0
0
1
1
1
3
0
2
0
0
0
1
0
0
1
0
0
1
1
1
2
1
1
1
0
0
1
1
3
1
1
2
0
0
0
0
0
13
0
1
0
1
0
0
3
1
2
0
2
0
2
3
1
0
1
0
1
1
0
0
1
0
0
1
0
3
1
0
1
1
0
0
1
0
2
0
1
0
2
3
1
0
3
0
0
1
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
3
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
5
2
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
17
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
3
1
0
1
1
1
0
3
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
4
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
1
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
5
3
0
1
0
0
0
0
0
3
0
0
2
1
1
0
0
1
0
0
0
1
2
0
4
1
0
0
0
0
1
0
1
1
7
1
0
0
0
0
0
0
1
0
0
0
1
1
1
3
2
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
4
0
1
0
1
0
2
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
3
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
10
9
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
4
1
0
1
0
1
7
0
0
0
0
2
0
1
6
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
2
1
3
0
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
2
1
1
1
0
1
0
0
2
0
0
1
6
5
1
2
0
1
2
0
0
4
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
5
0
1
0
0
1
2
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
2
0
4
0
2
3
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
2
0
0
1
1
2
1
0
2
0
0
1
2
0
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
3
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
3
0
2
0
0
3
0
1
1
1
0
2
2
1
0
0
0
2
0
0
0
0
2
4
1
1
0
0
2
1
0
0
0
0
0
0
9
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
3
1
1
1
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
1
0
0
2
0
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
3
1
0
0
1
1
0
0
0
1
0
1
0
3
1
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
5
1
1
0
0
0
1
3
1
0
1
1
0
0
0
0
0
0
1
21
0
1
0
2
1
1
0
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
0
1
3
2
0
1
1
1
0
0
0
2
0
0
2
1
0
2
1
0
2
0
1
1
6
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
1
4
1
2
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
5
0
0
3
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
2
1
0
0
0
1
0
4745
2
0
0
14
0
0
0
0
1
0
1
8
2
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
8
1
1
2
1
1
0
1
0
0
0
0
0
0
10
1
1
1
0
0
3
0
1
0
0
0
1
0
0
5
1
3
2
0
0
0
2
1
0
2
2
0
0
1
2
1
2
1
0
1
0
0
3
2
0
2
0
0
2
1
1
1
1
0
4
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
3
1
2
7
0
8
0
0
0
0
1
6
0
0
2
0
1
0
0
1
0
3
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
2
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
3
0
1
8
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
9
0
1
1
0
0
1
0
2
0
1
2
0
1
0
1
0
5
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
1
0
3
1
4
0
0
0
1
2
6
2
0
0
2
1
0
0
6
0
1
0
0
1
0
5
3
3
0
2
0
0
0
0
6
0
2
0
0
1
0
2
5
1
4
1
1
1
0
0
1
9
4
0
1
3
1
0
1
1
3
0
1
0
0
7
0
0
0
1
0
0
8
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
7
0
1
0
0
1
0
0
0
1
1
1
0
6
1
0
0
0
4
0
0
1
4
3
0
0
1
0
0
0
1
2
3
5
2
1
0
2
0
0
1
0
0
5
2
0
1
5
0
0
0
0
0
1
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
1
1
0
2
2
0
0
2
1
0
0
0
1
0
0
1
3
3
5
0
0
1
0
1
2
1
1
1
1
0
8
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
6
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
7
0
1
5
0
0
0
1
1
1
0
0
0
1
0
2
1
0
1
2
1
0
2
1
6
0
1
0
0
1
0
0
4
0
0
0
3
0
0
0
0
1
2
1
1
1
1
0
2
1
0
0
3
0
0
0
1
1
1
0
1
1
0
1
2
0
0
2
1
2
1
0
2
1
2
0
5
0
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
2
0
1
0
0
0
0
1
0
6
1
0
0
5
0
0
0
3
0
9
0
2
0
0
1
1
3
2
1
1
0
2
0
0
0
1
0
1
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
3
2
1
1
3
1
0
0
0
0
0
1
0
2
0
0
1
8
1
0
4
0
0
0
1
0
0
1
0
0
3
1
0
0
1
0
8
0
0
0
2
2
1
0
3
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
3
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
3
1
1
3
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
1
3
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
4
1
0
0
0
1
1
0
1
3
0
1
0
4
0
4
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
5
0
0
0
0
0
1
0
1
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
6
0
0
3
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
3
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
1
3
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
2
0
0
0
0
0
1
1
2
0
3
8
0
0
0
1
1
0
0
0
2
1
1
1
4
0
1
2
1
1
1
0
6
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
5
0
5
0
0
2
0
0
0
1
1
3
0
0
1
1
2
2
2
1
0
0
2
0
0
0
0
3
4
1
0
1
1
0
1
3
0
0
4
1
1
2
1
0
0
0
0
1
0
1
1
1
0
1
3
0
1
2
0
0
1
0
0
0
0
0
5
1
2
1
0
0
1
1
1
0
4
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
7
0
0
1
0
0
3
2
0
0
7
1
0
2
1
0
0
0
2
2
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
1
0
2
0
0
0
4
1
1
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
3
0
1
1
5
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
3
0
0
4
1
4
1
2
1
0
3
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
2
0
1
0
2
0
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
1
5
2
2
3
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
3
2
1
1
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
3
0
0
0
1
1
0
0
0
0
9
1
0
1
0
0
0
0
0
0
0
0
8
0
0
0
3
1
0
1
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
8
0
0
0
0
0
2
0
1
1
1
0
0
6
0
4
0
2
1
0
1
0
1
0
1
3
1
0
5
0
1
0
0
4
0
3
0
0
1
1
0
3
0
0
0
1
0
3
0
0
0
4
0
0
0
0
1
2
1
1
0
0
0
1
1
1
0
1
2
2
1
3
0
2
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
3
3
0
1
0
1
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
5
0
0
1
0
1
0
2
2
3
0
1
0
0
1
0
1
1
1
5
0
0
0
0
0
2
0
0
1
1
0
2
0
3
1
5
1
0
0
8
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
5
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
0
1
2
3
1
1
0
0
0
0
3
0
2
2
7
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
3
0
0
1
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
5
0
0
2
1
0
1
0
0
0
0
2
5
0
1
0
0
0
3
3
0
0
0
1
0
1
0
2
0
0
5
1
2
0
0
0
0
3
2
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
4
0
0
2
5
2
0
17
5
0
1
1
1
0
0
0
1
0
2
3
1
1
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
2
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
7
1
0
1
2
3
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
6
0
0
1
1
0
1
0
0
0
0
2
2
0
0
1
2
6
0
0
1
4
1
3
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
1
0
0
1
1
1
0
3
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
2
0
3
1
1
0
0
0
6
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
1
1
0
2
0
3
1
3
2
0
0
0
3
1
3
0
7
1
0
1
0
0
0
0
1
1
0
2
3
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
6
0
1
3
0
1
0
1
0
2
0
0
0
1
0
1
0
3
0
0
1
4
0
1
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
0
0
1
4
0
1
0
0
0
3
0
0
1
1
0
2
0
2
3
6
1
0
1
0
1
1
1
0
0
1
0
2
0
0
3
2
3
0
0
1
0
0
3
0
1
0
0
2
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
5
1
0
3
2
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
1
1
1
0
2
0
0
1
0
5
1
0
1
0
3
0
0
0
0
3
2
0
1
1
1
0
5
0
0
3
1
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
2
6
3
4
1
0
3
1
0
0
1
4
0
1
0
0
0
1
1
3
0
0
1
0
0
1
1
1
1
0
0
0
0
2
3
1
0
0
4
1
2
8
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
20
0
1
3
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
3
1
0
0
2
0
1
1
0
0
4
0
0
2
1
1
0
1
0
0
0
0
0
0
3
0
0
1
1
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
1
0
1
1
0
0
0
1
0
0
0
1
4
0
0
0
0
1
1
0
2
1
1
2
0
4
0
0
0
1
0
0
2
1
1
6
0
0
0
3
0
2
1
1
1
0
1
1
0
0
0
0
1
1
0
4
0
1
3
0
0
1
1
1
0
6
2
0
0
0
1
3
0
1
0
1
3
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
0
1
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
5
0
0
1
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
2
0
3
6
1
0
2
0
3
2
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
1
0
1
0
0
1
2
5
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
4
0
1
2
1
0
3
0
1
0
0
0
0
0
0
20
1
1
0
1
0
0
0
4
2
1
0
1
1
1
0
3
2
0
0
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
4
0
0
9
1
0
0
0
0
3
0
1
1
0
1
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
2
1
0
0
2
0
0
0
6
4
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
6
1
0
0
0
0
0
3
3
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
1
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
1
0
4
0
0
1
1
2
1
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
7
1
1
0
0
0
0
0
0
6
1
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
1
9
2
2
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
1
0
1
3
1
1
1
0
1
0
0
0
3
0
2
0
1
0
1
0
0
0
1
4
0
2
2
1
6
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
1
1
1
2
0
2
0
0
3
0
2
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
1
0
0
1
0
3
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
2
2
6
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
3
0
0
1
1
0
1
0
1
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
1
4
1
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
1
1
1
2
0
2
0
1
0
1
1
0
0
0
0
0
0
5
0
0
0
0
1
0
1
1
2
0
0
0
2
3
0
5
2
3
0
2
0
0
2
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
4
8
0
1
3
0
1
2
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
3
0
2
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
2
0
0
2
5
0
0
0
0
0
1
1
0
3
1
1
0
1
0
0
0
0
1
1
0
2
6
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
1
0
5
0
1
2
2
0
0
1
0
0
1
2
0
3
2
1
1
1
0
1
1
1
0
0
1
3
2
1
0
2
0
2
3
0
5
1
0
5
0
0
0
2
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
3
4
1
1
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
1
0
0
0
1
3
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
6
0
5
4
0
3
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
0
1
0
2
1
0
1
0
5
1
0
0
0
1
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
4
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
3
0
0
1
0
0
0
0
1
2
1
0
0
2
1
1
0
0
5
0
0
1
0
0
0
0
0
2
0
1
2
0
3
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
5
0
1
1
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
2
1
3
2
3
0
1
1
0
1
1
0
4
0
0
0
1
6
0
3
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
1
1
2
1
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
5
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
4
0
3
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
3
1
0
3
0
0
0
0
3
1
1
0
2
2
1
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
0
0
0
0
5
1
0
0
0
2
0
3
0
0
0
0
0
0
3
1
1
0
5
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
29
0
0
1
0
1
1
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
4
0
0
0
1
1
1
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
1
0
0
3
0
2
1
0
0
0
0
0
0
1
0
2
1
5
2
0
2
2
0
1
0
0
3
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
0
0
0
3
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
1
2
1
2
2
1
0
2
2
4
0
0
0
3
0
1
1
1
3
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
4
2
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
2
0
0
0
4
3
2
0
0
0
2
1
0
1
3
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
0
1
0
1
1
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
1
1
1
1
0
0
0
5
0
3
0
1
2
0
1
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
2
0
1
2
1
1
1
1
3
0
0
3
0
0
1
0
1
2
0
1
0
1
0
1
0
3
0
1
4
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
3
1
1
0
0
0
1
0
2
0
0
1
1
4
0
3
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
3
3
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
6
0
1
0
2
1
3
3
2
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
1
1
1
2
0
4
0
1
1
1
0
0
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
6
1
0
0
0
1
4
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
3
1
3
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
4
0
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
1
0
0
1
0
2
1
3
1
1
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
3
0
1
3
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
3
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
3
0
0
3
2
0
0
5
1
8
4
2
1
0
1
0
0
0
3
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
3
16
0
2
0
4
0
0
0
0
1
0
7
0
1
1
1
2
1
2
2
1
3
1
1
1
1
0
0
1
0
0
0
1
1
0
2
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
3
0
4
1
2
0
1
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
3
4
0
0
2
2
1
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
5
2
0
2
1
2
0
0
1
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
2
1
1
3
0
0
1
1
1
0
1
2
3
0
2
0
0
1
0
10
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
2
3
6
0
4
0
0
5
0
3
1
0
0
2
4
2
0
0
0
1
1
1
1
0
0
0
4
0
0
0
0
1
6
0
1
2
0
1
0
2
0
2
3
1
0
0
1
0
24
3
0
1
2
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
2
1
2
1
1
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
3
1
0
0
0
2
0
127
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
3
3
3
1
2
0
0
0
0
1
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
2
5
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
3
0
0
0
1
1
1
4
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
3
3
1
0
0
3
0
2
0
3
0
3
0
1
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
3
0
2
1
0
1
1
1
2
1
1
1
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
2
1
0
1
0
5
0
0
1
0
0
34
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
3
0
1
0
0
4
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
0
0
0
1
0
0
0
1
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
2
1
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
5
2
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
1
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
5
4
0
0
2
0
1
0
1
4
0
0
0
0
0
1
3
1
0
0
0
2
4
1
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
4
2
0
0
0
1
1
1
1
0
0
4
0
1
1
1
2
1
2
0
1
0
2
0
0
0
0
1
5
2
2
0
1
1
1
0
5
0
1
4
2
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
1
3
1
1
0
0
1
0
1
3
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
3
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
2
0
6
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
3
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
15
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
2
0
5
0
0
1
1
2
0
0
0
0
0
0
1
0
1
3
2
1
0
0
1
2
1
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
0
4
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
4
0
0
0
3
0
1
0
0
1
4
0
5
2
2
0
1
3
0
1
0
0
0
0
0
1
0
0
3
0
0
1
1
3
0
0
0
0
0
0
2
0
3
2
1
2
2
0
0
1
0
3
3
0
0
0
3
1
0
0
1
1
0
0
4
1
1
1
0
2
1
0
4
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
4
0
0
1
0
3
1
0
0
0
0
0
1
6
0
0
0
0
1
1
0
0
1
1
1
0
1
3
1
0
1
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
1
0
0
4
1
0
0
0
1
3
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
47
0
1
1
2
0
3
2
0
0
1
2
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
2
0
2
0
1
0
0
1
0
1
1
1
1
1
2
2
3
0
0
1
2
0
1
0
0
1
2
2
1
0
0
0
0
1
2
1
3
0
0
2
0
0
2
0
1
1
0
2
1
1
3
0
0
3
0
2
1
0
0
1
1
0
1
2
2
0
0
1
0
2
1
0
1
1
2
6
1
7
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
5
2
0
1
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
3
2
2
0
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
2
0
1
0
1
3
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
1
1
2
0
0
0
1
11
0
0
2
0
2
0
1
0
1
0
1
0
1
4
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
2
0
0
1
2
2
3
1
0
1
3
0
0
0
1
0
0
0
3
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
4
0
2
1
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
1
1
2
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
3
0
1
1
0
1
1
2
0
0
0
1
0
1
0
2
0
1
1
1
4
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
3
0
2
1
1
0
1
0
1
1
1
0
0
0
4
0
0
0
3
2
0
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
3
1
0
0
0
1
0
31
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
1
1
2
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
1
5
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
1
0
5
0
1
2
1
0
1
4
0
0
1
4
2
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
3
0
0
0
0
2
3
0
0
3
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
5
3
1
0
1
1
2
0
0
0
0
0
1
2
1
2
3
0
1
1
0
2
0
1
1
2
0
2
0
4
1
0
1
1
1
0
1
0
0
2
6
2
1
1
1
0
1
0
3
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
19
0
0
0
0
0
2
0
1
1
4
1
0
2
2
2
0
2
0
0
0
1
1
0
0
0
1
2
1
2
0
1
0
0
0
1
0
0
0
1
1
1
0
4
0
0
0
1
0
1
0
0
2
1
2
1
1
4
1
0
1
0
0
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
8
0
0
1
0
0
2
1
1
0
0
3
1
0
1
2
1
1
0
1
2
1
1
0
1
0
0
0
2
0
0
0
0
4
2
1
2
0
0
4
0
0
1
0
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
3
0
8
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
3
1
1
3
1
0
0
1
0
1
1
5
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
3
0
0
3
0
0
3
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
1
1
2
0
0
1
0
0
0
1
1
0
0
0
1
1
5
2
0
0
0
1
1
1
0
2
0
1
0
2
1
0
1
2
0
1
0
0
1
2
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
1
1
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
3
0
1
1
0
5
2
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
16
7
0
0
3
0
0
0
1
0
0
1
1
3
3
2
3
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
4
5
0
8
2
0
0
0
1
3
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
2
1
3
1
0
4
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
9
0
1
0
0
0
0
0
1
0
1
1
2
0
4
0
2
1
5
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
12
2
2
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
4
2
0
2
0
0
0
2
3
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
3
2
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
1
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
4
0
1
1
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
3
0
0
2
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
4
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
2
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
3
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
3
3
1
1
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
1
0
51
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
5
2
1
0
1
0
1
1
1
1
1
0
0
0
2
1
2
0
2
0
1
1
1
0
0
0
1
0
0
3
0
1
1
0
1
1
0
0
0
4
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
19
6
0
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
4
1
0
2
0
1
0
0
4
2
1
0
0
1
1
0
1
0
0
0
2
1
0
8
0
0
1
0
3
3
0
1
1
1
0
0
6
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
1
2
0
0
2
15
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
4
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
8
2
0
0
0
2
2
0
1
1
0
2
1
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
8
1
1
3
0
1
4
1
0
2
0
1
0
0
1
1
3
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
3
1
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
4
0
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
6
1
0
0
4
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
1
1
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
1
0
0
3
0
0
0
2
0
0
0
1
0
2
0
4
0
0
1
0
0
4
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
3
5
0
0
3
0
0
0
0
1
2
3
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
0
0
1
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
2
1
2
4
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
7
1
1
3
1
0
1
1
1
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
2
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
1
0
4
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
1
1
1
0
0
1
9
2
1
0
0
4
1
1
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
1
2
2
2
0
0
4
0
1
0
0
2
0
3
0
0
2
2
3
1
1
4
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
1
0
3
0
0
2
1
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
8
0
2
0
0
1
1
2
1
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
5
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
2
1
1
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
7
0
0
1
1
0
0
1
0
2
0
2
3
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
3
0
1
0
1
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
5
1
1
5
1
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
23
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
3
0
0
1
3
0
0
5
1
1
1
0
1
0
0
3
1
0
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
2
1
2
1
1
1
1
0
0
0
2
1
0
0
0
1
3
1
0
0
0
0
0
3
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
2
0
0
2
1
0
1
0
1
2
0
1
0
1
2
3
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
2
1
3
0
0
0
1
0
4
3
0
0
3
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
2
2
1
2
4
1
0
5
1
0
0
0
0
0
4
1
1
0
1
0
2
0
0
0
2
0
1
4
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
1
1
0
0
1
0
0
0
1
3
1
0
2
0
2
0
0
0
6
1
0
2
0
1
0
1
0
3
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1093
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
3
0
3
3
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
3
0
0
0
0
9
1
0
0
0
0
1
1
0
1
0
6
3
0
2
0
1
0
0
0
2
2
3
2
1
2
0
0
0
2
0
1
1
0
0
0
4
2
3
0
0
7
0
0
0
0
0
2
0
1
1
0
0
0
1
0
4
0
2
0
1
1
0
1
0
2
1
1
1
1
0
2
2
0
1
3
0
0
0
0
0
2
5
0
1
0
1
2
1
0
1
0
1
1
1
2
1
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
1
0
0
2
2
3
3
1
3
0
0
0
0
2
0
0
2
1
1
0
0
3
5
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
1
1
1
1
3
0
0
0
0
2
1
3
0
2
1
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
4
0
1
0
1
1
0
0
1
1
1
1
0
0
3
0
0
1
0
0
1
0
1
0
0
0
5
0
0
0
1
0
1
1
0
1
1
0
1
0
4
1
0
1
0
0
0
0
1
0
2
0
4
3
3
2
3
0
1
2
0
0
0
5
0
1
0
1
1
2
1
0
2
0
1
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
3
1
3
1
2
0
0
0
0
0
0
0
4
0
0
2
3
1
2
0
2
0
1
0
2
1
0
1
4
0
2
0
2
1
1
0
2
1
2
0
1
0
0
1
0
0
1
2
0
3
2
1
0
1
2
1
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
2
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
4
0
0
1
0
0
0
0
2
3
0
2
0
0
1
1
1
1
1
1
1
2
2
0
0
4
1
2
0
0
0
0
0
0
3
2
0
1
2
0
0
1
0
2
0
0
1
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
2
2
1
0
2
3
0
0
0
1
1
0
1
0
1
0
0
3
0
0
2
0
3
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
2
3
0
2
3
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
2
2
0
3
0
1
0
0
1
0
0
1
0
1
1
0
1
3
1
1
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
1
0
1
1
3
0
0
1
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
10
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
3
2
1
0
0
1
2
1
0
1
0
1
0
0
0
3
0
1
1
0
3
1
0
3
0
0
0
0
1
6
0
0
0
0
0
1
1
3
1
4
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
1
0
1
0
2
1
1
6
0
0
0
2
1
0
0
0
2
1
0
2
0
2
0
1
1
0
0
0
1
2
1
1
1
1
2
0
0
1
0
0
0
1
0
0
1
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
5
2
0
2
0
1
0
1
0
4
0
2
2
0
2
2
0
0
0
1
0
0
5
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
1
2
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
3
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
5
1
1
0
0
1
1
0
0
1
0
0
0
0
0
6
1
1
1
0
0
1
4
0
0
2
0
0
1
1
0
3
0
2
15
1
0
0
2
2
5
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
6
0
0
1
0
3
1
0
0
3
1
1
0
0
1
0
3
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
5
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
2
1
1
1
0
3
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
1
2
0
0
4
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
5
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
12
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
3
0
1
2
2
0
1
3
1
2
0
1
2
0
2
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
1
3
1
1
0
0
0
1
0
1
3
2
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
2
1
1
0
0
0
0
2
1
3
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
3
1
1
0
1
1
0
0
2
0
0
0
2
5
1
0
0
1
1
1
1
3
0
0
1
1
0
0
2
0
1
0
0
0
1
0
9
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
3
1
2
0
1
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
1
2
0
4
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
1
3
1
0
0
1
1
0
0
2
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
2
0
0
5
1
1
0
1
1
1
3
1
0
0
1
1
0
4
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
4
1
0
0
2
2
0
2
3
1
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
3
11
0
0
0
0
0
0
1
0
1
5
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
1
3
0
0
0
0
2
6
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
3
2
0
0
2
0
1
1
1
0
3
5
0
0
0
0
0
0
1
0
0
5
0
0
0
4
1
2
2
0
0
1
29
1
0
0
0
1
1
1
2
1
3
0
1
1
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
1
3
0
0
0
0
1
0
3
0
0
0
0
1
2
1
2
0
3
1
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
1
1
1
0
0
0
1
1
0
1
0
3
5
0
1
0
0
1
2
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
4
0
0
1
1
55
1
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
46
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
1
0
1
2
4
0
1
0
0
1
1
0
1
2
0
1
1
0
2
8
1
0
3
1
1
2
1
0
1
1
2
4
2
0
1
0
0
1
0
1
0
2
2
0
1
1
1
3
0
1
2
1
0
5
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
3
0
2
0
0
1
2
0
2
1
0
0
0
0
2
0
3
47
0
0
0
1
176
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
2
0
0
9
0
0
0
0
0
0
2
3
3
0
2
0
2
1
0
2
0
1
0
0
1
4
0
0
1
0
2
1
0
0
0
0
2
1
0
0
10
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
3
0
4
1
0
0
0
0
0
1
1
0
1
0
4
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
2
2
2
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
1
2
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
1
25
1
0
2
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
10
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
3
0
1
4
0
1
1
1
0
1
1
0
0
1
1
2
6
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
3
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
1
2
0
1
0
4
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
3
0
2
1
0
1
2
0
0
0
1
0
0
1
3
0
1
1
0
0
0
0
1
0
3
17
2
0
2
0
1
0
1
0
0
0
0
1
0
4
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
4
5
2
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
1
1
1
0
0
1
1
0
1
1
2
0
0
1
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
7
2
0
0
3
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
4
0
0
0
0
1
2
0
19
1
4
0
0
0
1
0
0
1
0
0
0
1
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
1
3
1
1
0
1
1
0
1
2
0
1
0
0
4
0
0
0
0
1
0
0
0
1
4
1
0
1
0
3
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
14
0
2
0
1
1
1
1
0
4
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
8
0
1
0
0
1
1
0
3
3
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
4
0
10
0
0
0
1
0
0
0
0
4
0
0
1
1
0
1
0
4
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
4
0
2
0
2
0
0
1
2
0
0
0
1
0
0
3
3
0
3
1
1
1
3
1
2
0
0
2
0
4
1
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
3
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
5
0
0
3
1
1
0
1
0
1
0
1
0
0
1
0
0
0
4
0
0
1
0
5
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
3
1
0
1
1
3
0
0
1
2
1
0
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
3
0
3
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
0
1
3
0
0
0
1
4
0
1
2
1
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
3
0
3
1
0
0
0
1
0
0
0
1
2
0
1
0
0
3
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
6
0
1
3
1
0
0
0
1
0
0
1
1
1
0
0
0
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
4
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
1
1
1
1
1
0
0
0
0
2
2
0
0
1
4
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
3
0
0
0
1
3
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
1
6
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
0
1
2
0
5
6
0
1
2
0
2
1
0
0
0
1
0
4
1
0
0
0
3
0
2
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
3
1
1
0
1
0
0
1
0
2
0
0
5
0
0
2
1
0
0
1
1
0
0
1
0
1
1
3
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
0
0
0
2
0
16
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
24
0
0
3
1
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
5
0
0
0
2
0
0
1
1
6
1
0
0
1
2
0
0
1
0
0
4
0
0
0
0
3
3
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
4
1
1
2
0
0
1
4
0
0
2
0
0
1
0
2
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
2
0
1
0
1
0
2
2
0
3
1
0
1
1
0
1
3
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
3
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
2
2
0
1
0
0
11
0
0
2
1
0
0
1
0
0
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
6
0
2
0
1
1
0
0
1
0
0
1
0
1
0
1
1
7
1
0
0
3
0
0
2
1
1
0
1
1
1
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
5
1
0
0
1
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
3
1
2
0
1
3
0
1
5
1
1
1
0
0
1
0
2
0
0
0
0
2
0
5
1
0
0
0
1
3
2
0
1
1
0
0
3
2
2
3
0
0
0
2
0
1
0
0
0
1
0
3
1
0
0
1
1
1
0
0
0
2
1
1
0
1
1
1
1
3
1
1
1
0
0
1
0
0
0
2
1
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
2
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
4
1
0
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
2
0
3
1
0
2
1
0
3
0
1
3
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
4
2
1
0
1
0
0
0
0
2
0
0
0
8
2
2
0
1
1
2
0
0
0
3
0
0
1
0
0
1
1
1
0
0
5
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
2
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
2
1
0
1
1
0
0
0
0
2
0
2
2
0
1
2
0
0
0
2
0
2
2
2
1
1
0
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
6
0
1
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
2
1
0
1
3
0
0
0
1
0
4
0
0
1
0
1
1
0
0
3
1
0
1
0
1
1
0
2
3
2
0
1
0
1
2
1
0
0
1
0
0
0
1
1
2
0
1
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
21
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
5
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
2
2
0
0
0
4
1
0
0
1
0
1
0
0
2
2
3
2
0
4
1
0
1
0
0
0
0
1
1
3
0
1
0
1
0
0
0
1
2
1
3
1
0
0
0
2
1
0
1
0
5
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
1
1
0
1
0
84
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
4
1
1
0
1
0
0
2
1
2
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
3
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
3
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
1
1
1
0
0
0
1
2
1
0
1
0
1
0
1
2
0
3
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
2
1
0
4
0
1
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
1
3
0
4
0
0
3
0
1
2
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
1
3
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
4
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
3
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
3
3
1
1
0
312
0
0
2
1
0
1
1
0
1
0
3
2
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
3
0
1
0
0
1
0
0
0
0
0
1
4
5
0
0
0
3
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
3
2
1
0
0
0
3
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
2
9
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
2
0
0
0
0
0
0
1
4
1
2
0
0
5
0
0
0
0
0
0
0
1
0
0
2
1
0
4
2
0
0
0
30
1
1
0
0
0
1
0
1
0
1
0
0
0
0
11
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
5
1
1
0
0
1
1
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
4
1
1
0
2
0
2
0
3
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
3
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
6
0
2
0
0
0
3
0
0
1
2
2
0
0
0
0
0
1
0
0
0
3
1
0
0
2
5
0
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
5
0
2
0
1
0
0
2
0
0
1
0
3
0
1
1
0
0
0
3
2
0
3
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
4
0
0
0
0
1
0
1
2
0
3
1
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
4
1
0
3
1
0
0
0
3
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
3
0
2
1
1
0
0
0
1
0
1
0
0
0
3
3
0
0
0
0
5
1
0
1
0
1
0
1
0
2
0
1
2
0
0
0
0
1
3
1
2
1
2
3
0
0
6
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
4
3
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
4
1
0
1
0
0
1
2
0
0
0
4
1
0
0
1
0
0
3
0
0
0
5
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
5
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
4
5
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
1
3
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
3
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
6
0
0
1
0
0
1
3
0
0
0
0
1
1
2
0
0
0
1
1
0
1
5
2
1
2
0
1
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
1
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
0
1
2
1
0
0
37
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
11
0
1
0
0
0
1
3
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
1
0
1
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
4
2
0
1
1
1
0
1
4
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
1
1
1
0
3
0
1
2
0
2
0
5
0
0
1
3
0
0
0
0
0
1
5
1
0
0
0
2
2
0
1
0
0
2
0
1
2
3
1
0
0
1
0
1
0
0
1
2
0
0
5
0
0
0
0
1
0
0
2
2
2
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
2
23
3
4
1
0
2
1
0
1
0
3
1
1
1
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
1
2
2
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
6
0
2
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
2
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
9
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
4
1
1
0
0
1
1
3
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
1
0
1
1
0
0
0
1
0
0
1
1
2
1
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
1
2
0
2
1
0
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
3
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
1
0
1
1
2
1
0
0
3
0
1
0
0
1
2
3
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
1
2
0
1
0
0
2
4
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
0
5
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
15
0
0
2
0
0
0
1
0
1
1
0
0
1
3
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
3
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
4
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
8
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
3
1
0
1
0
1
2
0
0
1
1
3
0
3
1
0
1
1
0
11
1
0
3
0
0
0
0
0
3
0
1
2
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
5
1
0
1
1
2
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
1
2
0
0
0
1
1
1
1
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
1
1
0
0
1
2
1
1
0
1
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
3
1
0
3
0
0
4
0
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
6
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
5
0
0
1
1
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
1
1
0
3
0
0
1
0
0
1
1
0
2
0
2
0
2
2
0
1
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
1
0
1
2
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
10
0
0
0
12
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
3
1
2
1
1
0
0
0
1
2
0
0
0
3
0
1
0
0
1
2
0
2
4
77
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
4
2
1
0
3
2
0
0
0
3
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
4
0
0
6
0
1
1
0
0
0
0
1
0
1
0
0
5
0
0
0
1
0
3
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
4
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
57
0
1
8
0
0
0
1
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
2
1
1
0
2
1
0
3
0
3
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
3
1
0
1
2
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
4
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
3
0
57
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
2
0
4
0
0
0
0
1
0
0
0
0
0
1
0
7
0
1
1
0
1
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
4
0
0
0
0
1
0
1
0
0
0
0
0
2
5
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
5
1
0
0
7
0
0
0
0
1
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
5
0
1
0
0
3
0
1
4
1
2
0
0
0
2
0
0
0
1
1
0
3
0
1
0
3
0
0
1
1
0
1
0
3
4
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
68
3
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
2
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
4
0
0
0
1
0
2
2
1
0
3
0
1
1
1
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
3
1
1
0
1
0
3
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
2
1
1
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
4
0
0
1
1
2
3
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
3
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
4
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
1
2
3
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
4
0
1
1
2
0
1
0
2
1
0
0
0
9
0
1
1
0
0
0
3
1
0
2
4
0
0
1
0
3
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
3
1
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
1
0
2
3
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
1
1
1
0
0
1
2
1
1
0
0
0
60
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
1
2
3
0
1
0
0
6
2
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
4
0
0
0
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
1
5
0
0
1
4
0
0
0
1
0
0
0
2
1
1
1
1
0
1
0
1
2
1
2
0
1
0
0
0
2
1
1
1
0
0
0
28
1
0
2
0
0
2
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
4
1
0
0
1
1
1
0
1
0
0
0
2
1
0
3
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
5
1
1
1
0
0
2
0
0
0
1
1
0
5
0
1
0
1
0
0
1
0
0
0
0
1
3
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
1
0
1
5
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
5
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
2
0
2
1
1
1
2
1
1
0
0
0
7
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
5
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
3
0
2
5
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
24
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
1
1
1
0
1
1
0
0
0
3
2
0
0
0
3
3
1
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
1
3
0
6
0
0
4
1
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
3
2
0
0
0
0
1
1
5
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
4
0
0
0
1
0
0
0
4
3
1
0
3
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
23
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
2
2
3
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
1
1
2
0
0
1
1
2
1
0
0
1
2
0
1
0
2
5
0
0
1
0
0
0
9
0
1
2
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
2
1
1
2
3
1
0
0
3
3
1
3
1
10
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
3
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
1
1
0
3
1
0
0
0
0
1
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
3
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
3
2
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
2
0
4
0
0
0
3
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
1
2
3
1
0
1
0
2
0
0
0
0
1
0
1
3
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
3
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
3
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
1
2
2
1
1
0
0
0
1
0
1
0
1
0
0
0
3
2
1
0
0
0
0
4
0
1
0
0
0
0
1
1
0
7
0
1
7
0
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
1
1
0
3
1
0
0
0
4
0
2
0
1
1
1
0
0
0
0
0
1
0
3
1
1
0
1
2
0
1
0
1
0
0
1
2
0
0
0
2
3
1
0
1
3
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
7
2
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
2
0
2
0
1
3
0
2
0
2
2
0
0
0
1
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
4
0
1
1
1
0
0
1
8
2
0
0
1
0
1
1
1
3
0
1
2
0
1
0
0
4
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
5
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
33
2
2
0
0
0
2
3
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
3
0
0
0
0
0
1
4
0
3
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
1
1
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
1
13
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
4
1
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
9
1
0
0
0
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
2
1
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
1
0
1
0
1
2
1
0
3
1
0
0
0
2
1
0
1
1
2
0
1
2
2
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
3
1
1
2
0
0
1
0
1
1
0
0
1
3
3
2
1
2
1
1
0
3
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
3
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
3
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
3
0
1
1
0
0
0
0
0
4
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
1
1
0
41
0
1
1
0
2
0
0
0
0
0
28
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
0
1
0
0
11
3
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
1
4
0
1
3
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
5
0
3
0
0
1
1
0
0
1
1
0
0
0
8
0
1
0
0
1
2
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
1
1
1
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
1
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
3
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
1
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
2
1
2
0
13
0
0
0
0
0
1
0
0
0
2
0
0
7
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
6
1
2
0
0
1
0
2
0
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
2
2
0
0
1
1
0
0
0
0
6
0
0
12
0
0
2
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
3
1
0
0
0
0
0
1
4
0
0
0
1
1
0
1
3
0
0
2
1
2
4
0
2
3
2
0
0
1
1
0
0
98
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
1
0
1
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
4
1
6
0
0
1
1
2
1
0
1
1
0
0
8
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
3
3
0
4
0
2
74
2
2
0
0
0
4
0
0
2
0
0
0
0
1
1
3
1
3
1
0
0
3
1
0
1
0
0
3
1
0
2
0
0
0
2
0
0
0
1
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
1
1
1
3
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
5
1
3
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
8
0
1
3
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
1
1
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
4
0
0
1
1
1
2
1
1
0
1
0
0
1
2
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
2
0
2
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
2
1
1
1
0
3
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
4
0
0
0
0
1
0
3
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
5
0
3
2
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
1
0
0
2
1
0
0
0
1
0
0
1
3
0
0
0
1
3
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
3
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
3
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
6
0
2
3
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
6
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
4
1
1
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
2
1
1
0
0
1
1
16
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
1
1
2
5
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
3
0
0
4
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
2
0
0
0
1
0
23
0
0
1
0
0
2
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
6
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
4
0
0
4
2
1
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
0
3
0
3
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
1
0
6
0
0
1
0
1
0
0
2
3
0
0
0
0
1
0
1
1
0
0
1
4
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
6
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
21
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
3
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
36
0
0
1
1
0
1
1
3
0
1
3
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
0
3
0
1
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
1
0
4
0
0
0
1
0
16
0
0
220
0
2
1
0
30
0
0
0
0
1
0
0
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
1
0
0
1
0
1
0
0
1
0
1
0
3
0
0
0
1
1
0
1
1
0
3
1
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
2
1
1
3
0
0
1
0
0
3
2
2
1
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
1
5
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
3
0
3
1
1
1
1
2
0
2
0
1
0
0
1
5
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
4
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
1
1
2
0
1
3
0
0
12
5
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
1
1
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
4
0
0
0
1
0
1
1
0
0
0
0
0
9
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
2
0
0
5
1
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
1
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
3
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
1
0
1
0
1
1
8
5
1
0
0
0
1
0
0
1
0
1
0
0
1
0
16
0
0
0
0
2
0
0
0
1
0
1
10
0
0
0
3
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
1
0
1
2
1
0
3
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
26
0
1
0
0
0
1
0
1
0
2
2
4
0
1
1
2
1
0
3
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
3
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
1
5
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
1
1
0
2
0
2
7
0
1
0
0
4
1
0
1
3
0
0
0
0
0
0
0
1
0
0
4
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
4
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
10
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
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
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
21
0
3
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
1
4
0
0
1
4
3
1
0
1
0
0
4
1
2
1
1
4
0
0
0
1
2
1
0
2
1
0
4
1
1
0
0
3
0
1
0
0
0
0
4
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
100
4
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
1
0
2
2
2
3
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
3
1
1
0
0
0
0
0
4
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
4
1
0
2
0
4
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
0
1
0
0
1
0
1
2
2
0
0
0
1
2
2
0
1
8
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
3
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
7
1
1
0
1
3
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
1
1
0
118
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
16
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
6
1
0
2
6
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
2
0
1
9
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
3
0
1
98
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
3
1
0
0
4
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
1
4
0
0
2
0
0
0
0
0
1
3
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
3
0
0
1
8
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
6
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
4
0
0
0
0
2
0
0
0
0
0
0
11
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
2
5
1
0
1
7
1
0
0
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
3
0
3
0
1
1
1
0
0
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
5
2
0
1
2
1
4
0
0
2
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
1
0
0
30
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
1
3
1
1
0
3
1
0
3
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
3
0
0
1
1
1
9
0
1
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
3
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
7
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
1
3
2
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
2
1
0
0
0
2
3
1
0
0
0
0
2
0
0
1
0
0
4
1
0
0
0
1
0
4
0
1
0
1
3
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
49
0
0
2
0
0
0
0
5
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
1
6
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
1
0
4
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
2
1
1
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
1
0
2
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
3
5
8
0
0
0
1
1
0
15
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
3
2
3
2
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
1
1
1
0
0
1
2
1
1
0
0
1
0
0
1
0
0
1
3
1
1
1
4
0
1
1
1
0
0
0
0
0
0
0
2
0
6
0
2
3
0
1
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
8
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
3
3
0
1
0
3
0
1
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
3
3
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
1
4
0
0
0
4
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
11
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
3
1
0
4
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
1
1
0
15
0
2
2
1
1
2
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
1
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
25
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
3
2
1
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
2
0
1
2
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
1
7
1
0
0
1
8
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
3
0
0
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
1
0
0
0
0
70
10
0
0
0
7
2
2
1
0
2
0
2
0
1
1
1
0
1
0
0
0
1
1
0
1
2
1
2
0
0
0
1
0
0
0
0
3
0
1
3
0
1
4
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
10
1
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
4
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
7
0
2
14
0
0
1
0
1
2
0
2
0
23
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
2
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
3
0
2
8
0
1
1
1
5
0
0
0
0
0
0
1
1
0
1
0
2
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
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
9
3
1
1
1
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
3
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
4
0
2
0
1
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
10
0
7
3
2
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
1
2
0
3
1
1
0
3
1
1
0
2
2
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
2
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
2
0
0
0
1
0
1
1
3
1
1
1
27
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
1
1
0
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
4
1
1
0
0
2
1
0
1
0
2
1
0
0
2
5
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
2
3
0
1
1
3
0
0
0
1
1
0
0
1
4
0
1
2
1
2
3
0
0
0
1
0
1
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
2
4
0
0
0
2
1
1
0
1
1
1
0
1
0
0
1
30
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
1
30
0
0
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
5
4
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
6
0
2
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
2
3
0
0
1
1
2
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
2
0
2
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
5
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
11
0
0
1
0
0
0
4
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
8
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
6
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
4
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
4
0
3
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
5
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
5
0
1
7
0
0
0
0
0
0
20
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
3
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
5
0
0
0
0
1
3
0
1
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
3
3
0
0
0
0
2
0
7
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
3
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
5
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
11
3
0
0
0
0
1
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
119
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
14
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
4
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
4
0
0
0
1
0
0
1
0
0
3
3
8
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
5
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
4
1
1
1
1
0
0
0
1
0
1
1
0
1
1
3
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
3
0
0
2
0
1
3
0
0
0
0
1
0
2
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
5
3
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
5
14
1
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
2
0
1
0
1
0
1
0
4
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
4
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
1
0
1
0
0
2
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
2
2
0
0
1
1
1
0
0
1
1
3
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
3
0
1
0
2
0
0
2
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
1
0
1
0
1
4
1
0
1
3
1
0
3
0
0
0
0
5
1
1
1
2
1
0
1
3
0
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
2
0
3
1
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
2
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
3
0
2
3
3
0
1
0
0
0
3
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
0
2
1
0
0
3
1
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
1
1
0
0
1
0
0
4
1
0
0
0
0
0
1
0
1
1
0
1
4
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
3
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
1
2
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
2
2
0
1
0
1
1
2
0
0
0
1
1
1
0
0
6
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
4
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
25
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
1
1
0
0
2
1
0
0
2
0
2
0
2
0
4
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
1
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
5
0
2
1
5
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
11
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
1
0
6
0
0
0
0
2
0
4
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
3
2
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
3
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
1
1
2
0
1
2
0
1
1
1
0
0
1
1
6
0
0
0
1
1
0
0
0
1
0
0
1
1
2
3
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
10
3
0
0
2
0
3
0
0
0
0
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
5
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
4
0
0
0
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
2
1
0
0
1
4
0
0
0
0
0
3
0
0
1
1
0
1
2
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
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
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
3
0
0
1
3
1
0
1
0
0
0
0
6
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
1
2
1
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
1
4
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
2
1
2
0
0
1
0
0
4
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
1
1
0
0
1
1
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
2
1
0
1
1
1
2
0
5
1
1
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
22
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
2
1
1
0
1
0
2
3
0
1
0
5
0
1
3
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
4
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
1
0
1
0
0
0
0
1
0
2
3
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
85
1
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
1
0
131
0
0
0
4
2
1
0
0
0
3
1
1
0
0
0
1
0
0
0
1
2
1
0
0
2
0
3
1
0
0
0
0
2
1
0
2
4
0
2
4
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
3
1
0
0
0
0
2
2
0
1
2
1
7
1
0
1
10
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
4
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
23
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
5
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
2
0
0
0
2
0
0
1
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
11
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
6
0
0
1
0
0
0
0
0
0
34
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
1
3
0
1
2
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
4
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
6
0
1
0
0
0
1
2
1
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
2
4
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
3
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
1
0
1
0
3
0
0
1
1
1
3
0
0
0
0
5
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
6
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
90
0
1
0
0
1
1
0
0
1
1
0
0
0
2
3
0
1
0
2
1
0
0
0
0
0
4
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
5
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
3
0
2
1
0
1
4
0
0
0
0
0
4
0
0
0
0
1
1
4
0
0
0
0
0
0
1
3
4
0
0
1
2
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
0
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
4
1
0
0
0
3
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
3
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
2
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
2
1
0
0
1
0
0
0
0
1
0
0
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
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
3
2
0
1
5
4
6
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
8
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
11
0
0
0
1
1
0
0
0
4
1
0
0
4
0
1
1
0
1
1
0
0
0
0
1
4
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
3
0
0
3
0
0
1
2
0
1
1
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
1
7
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
5
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
3
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
7
0
1
0
2
0
1
0
0
0
0
3
1
1
3
3
2
0
1
0
0
0
0
0
2
1
0
0
1
0
5
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
4
0
0
0
0
3
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
3
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
1
1
1
1
0
0
1
11
1
1
1
3
0
0
0
0
0
1
0
0
3
1
2
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
2
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
4397
0
0
4
1
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
10
0
0
0
1
0
9
8
6
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
1
1
1
0
1
4
0
0
0
0
7
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
4
0
0
0
0
0
7
1
1
1
0
0
1
0
0
0
8
10
0
0
0
0
0
2
0
0
10
1
1
3
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
6
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
8
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
3
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
7
0
5
0
0
1
9
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
6
1
0
0
0
0
0
0
1
0
3
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
8
0
1
0
4
0
0
1
7
0
0
6
1
0
1
1
1
0
0
1
4
0
0
0
0
0
0
0
1
7
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
6
0
0
2
0
1
0
2
0
3
0
0
0
0
0
6
0
0
0
3
4
1
1
0
2
0
0
0
1
0
0
2
3
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
1
0
3
5
2
0
5
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
4
1
0
2
1
0
2
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
7
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
1
1
0
0
0
0
1
3
2
3
1
3
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
3
0
1
0
0
1
4
0
1
0
0
1
0
1
0
2
1
0
0
1
1
0
6
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
3
1
1
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
1
1
0
1
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
3
0
0
0
0
1
0
1
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
1
2
5
7
1
5
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
7
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
6
1
0
2
0
1
0
0
0
1
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
7
0
0
1
9
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
5
2
1
0
0
1
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
1
1
2
1
0
0
4
0
2
0
5
1
0
1
0
0
0
1
1
0
0
0
1
5
1
2
0
1
0
0
1
0
1
1
2
1
3
2
0
2
0
0
0
0
0
3
0
0
1
0
40
1
0
1
2
0
0
1
0
5
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
2
1
1
0
1
0
4
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
3
3
1
0
1
5
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
3
5
0
0
1
2
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
3
0
1
0
0
1
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
4
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
5
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
4
1
1
0
0
0
2
0
2
0
1
61
0
6
0
1
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
3
0
2
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
2
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
3
0
0
1
6
0
0
1
0
0
2
0
0
5
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
1
2
2
2
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
5
1
0
1
0
1
6
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
4
2
3
1
1
24
4
0
0
1
0
2
0
0
4
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
4
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
4
0
4
0
1
0
95
0
0
0
0
1
1
1
0
3
0
2
3
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
4
0
0
0
0
4
0
0
0
3
0
0
4
0
2
4
0
0
0
0
1
0
0
1
0
23
0
2
1
0
0
0
2
0
0
4
0
0
2
0
70
0
2
1
1
0
6
2
0
0
0
0
0
3
0
1
1
1
1
0
0
4
0
1
1
3
4
0
5
0
2
0
1
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
4
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
1
1
1
2
0
0
0
0
0
1
0
0
3
0
1
1
0
2
0
0
6
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
6
1
2
1
0
1
0
5
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
3
0
0
0
5
0
2
4
0
10
1
0
0
2
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
5
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
9
0
2
0
1
0
1
0
2
4
0
0
1
1
0
0
0
1
0
1
0
0
1
3
0
0
1
2
0
3
0
2
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
1
4
2
1
0
0
0
1
0
0
0
0
3
0
0
0
6
1
0
2
0
3
0
2
0
1
8
1
1
0
0
0
0
0
0
0
0
1
3
5
1
0
0
0
3
1
0
0
2
1
0
1
0
0
0
2
1
0
0
0