0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-11-27 19:56:28 +00:00
OI-codes/LibreOJ/2130/data/manager3.out

100001 lines
195 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
5
2
2
2
7
4
6
6
5
2
9
8
12
5
5
8
8
9
5
5
3
4
7
8
12
2
7
7
6
7
8
13
6
8
11
2
6
7
5
7
8
8
12
6
5
5
12
1
4
3
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
6
7
5
3
10
6
4
1
6
5
5
1
10
4
7
6
5
2
5
4
8
4
8
7
3
4
3
8
2
2
6
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
2
5
9
3
6
1
6
2
7
6
6
4
5
5
10
7
7
5
6
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
5
7
7
7
3
8
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
7
7
3
6
4
5
4
3
4
1
6
4
7
5
4
3
0
6
9
2
5
6
5
3
4
2
8
7
6
3
6
1
4
1
8
8
2
5
4
1
5
5
4
7
1
4
5
11
9
7
1
5
1
8
4
2
2
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
5
3
3
4
5
1
3
6
5
4
5
4
4
0
7
1
4
3
5
3
7
3
4
9
2
6
4
2
3
6
7
7
7
3
6
3
4
5
0
4
5
4
2
2
4
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
7
10
5
6
2
4
3
8
2
0
7
9
10
5
6
4
2
3
8
6
5
2
8
8
7
8
4
5
1
10
4
4
4
3
2
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
6
6
6
2
2
6
5
3
5
6
4
5
4
7
1
4
4
3
3
8
5
1
7
3
3
3
2
8
1
5
2
4
5
2
5
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
2
5
5
2
8
1
6
1
1
6
2
1
7
5
5
2
1
4
5
3
6
4
6
5
5
9
4
2
2
6
7
1
4
4
1
6
4
2
6
4
7
4
3
10
4
4
3
4
6
2
2
6
3
5
3
4
0
0
5
7
7
7
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
1
2
2
2
4
5
6
6
5
2
10
2
2
5
6
4
7
6
5
2
7
6
5
5
4
3
3
4
5
5
5
6
7
3
3
1
5
3
4
7
4
8
5
2
2
7
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
3
2
7
4
4
1
4
2
3
6
1
2
3
4
5
2
3
6
4
5
3
5
7
6
6
7
6
3
3
2
2
6
4
4
6
1
1
1
4
2
4
4
1
5
4
4
5
2
4
8
3
6
4
3
4
0
7
4
3
3
1
4
1
4
1
3
4
2
4
4
4
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
5
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
2
5
5
0
3
5
0
5
6
7
4
7
0
4
2
3
3
2
2
3
4
3
7
4
5
2
3
1
11
4
3
3
6
5
2
4
3
4
4
2
4
3
0
2
1
4
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
6
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
0
2
3
6
3
2
7
2
8
4
3
0
4
0
6
12
6
1
1
4
4
1
6
1
8
5
5
2
6
3
4
0
1
3
6
0
7
2
6
4
1
2
7
4
7
5
3
1
3
3
7
1
0
2
5
4
5
1
2
4
5
4
8
4
4
5
3
2
7
0
2
6
3
4
3
3
4
6
3
4
9
0
4
1
6
3
4
3
2
9
4
7
4
3
2
4
7
5
8
3
4
4
3
6
5
3
2
1
2
8
3
1
2
3
4
3
3
7
3
6
3
3
4
3
3
3
2
10
6
4
3
6
3
4
6
4
4
0
2
3
4
4
8
3
5
4
1
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
4
4
3
5
2
2
5
1
5
3
0
2
1
6
3
6
2
5
2
3
3
5
2
2
5
6
4
3
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
3
3
3
6
1
4
7
4
5
1
3
4
3
2
2
1
5
6
1
3
4
5
7
4
1
1
6
4
1
3
4
4
4
4
3
4
6
5
5
3
4
2
3
4
6
5
4
3
2
1
4
3
7
2
2
0
3
4
3
7
0
1
4
4
2
0
1
5
1
1
2
1
3
3
3
3
10
1
5
1
1
7
3
1
6
3
2
8
0
1
2
4
5
5
1
4
2
2
3
3
3
1
2
6
6
6
4
1
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
3
7
4
3
2
2
4
3
1
0
6
3
3
2
3
6
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
3
3
8
1
3
3
4
4
2
5
0
1
8
7
4
4
0
1
4
5
2
5
3
1
2
1
2
2
4
7
4
4
2
5
3
1
2
3
4
3
2
1
2
1
4
4
0
2
1
2
3
0
3
3
0
1
4
7
0
4
5
4
1
1
2
0
0
5
2
5
3
0
1
1
2
4
4
2
3
0
7
2
2
1
4
6
6
1
4
4
6
1
5
4
2
6
3
3
5
2
3
4
6
6
5
5
4
3
4
2
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
5
1
7
1
1
2
8
2
2
2
6
3
6
6
2
4
7
7
1
3
4
3
4
2
1
5
3
3
0
5
3
3
3
4
3
8
2
6
0
5
3
0
4
3
6
4
2
6
3
5
3
7
3
4
3
9
3
2
7
3
4
5
3
5
1
1
5
0
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
3
1
2
3
3
3
4
6
1
5
2
2
5
3
3
2
4
4
6
2
1
1
5
0
4
0
3
1
2
2
3
2
4
0
1
3
2
5
8
3
2
0
2
0
4
7
5
0
2
3
2
3
2
2
2
10
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
5
9
1
2
7
1
1
2
2
3
3
1
4
3
3
1
2
2
4
4
1
1
6
3
1
2
4
1
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
0
4
2
3
3
4
3
3
0
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
3
5
1
3
5
4
1
3
3
2
0
4
2
3
5
1
1
1
3
3
1
4
0
3
4
6
3
0
3
6
2
0
3
1
7
2
2
6
8
4
3
3
8
2
2
2
2
4
3
7
3
3
5
2
5
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
2
2
4
5
3
5
2
0
0
5
3
2
4
4
4
2
2
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
4
4
3
0
1
0
2
4
2
5
3
7
1
5
2
8
1
1
6
6
3
0
4
5
2
2
2
7
1
1
7
4
3
4
2
4
3
3
2
3
2
3
4
4
2
5
0
3
3
4
4
0
5
2
4
2
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
1
2
4
6
1
3
3
2
4
5
4
0
0
5
3
4
3
6
5
7
2
5
3
3
3
4
2
3
5
0
2
6
4
0
2
0
4
2
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
2
2
1
6
0
1
6
4
0
3
1
3
1
1
4
1
3
6
0
5
3
2
0
5
2
0
1
2
5
5
1
2
2
0
3
5
1
3
3
2
1
7
5
4
2
7
4
1
5
3
1
0
5
2
3
2
3
2
0
3
3
0
5
1
2
3
0
3
2
2
4
2
7
0
4
3
1
3
4
3
1
2
3
2
7
3
4
6
3
2
7
3
1
5
1
5
4
2
1
3
3
3
2
1
0
3
2
4
1
4
0
7
0
5
2
1
4
1
4
1
3
3
0
4
1
2
3
2
1
1
2
0
4
6
0
0
3
2
1
3
1
4
5
1
2
5
5
1
5
2
1
1
1
5
2
0
1
1
2
0
7
2
4
3
4
4
3
1
6
1
3
7
2
2
0
4
0
1
3
6
4
4
0
6
2
4
2
2
4
4
2
1
1
3
5
1
1
4
2
2
5
2
1
4
3
3
2
3
2
2
2
2
4
5
3
5
0
5
3
6
3
3
4
2
5
2
0
4
1
1
2
3
5
3
2
2
2
5
2
0
8
3
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
5
2
4
3
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
4
1
3
3
3
0
5
2
3
3
0
0
3
2
5
1
5
2
2
4
8
2
2
4
3
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
2
1
1
4
2
3
3
2
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
3
8
2
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
2
5
0
3
4
3
3
5
0
4
2
2
2
2
1
0
3
1
2
2
1
0
3
2
0
0
3
3
2
5
0
1
1
6
2
3
5
0
4
1
2
3
3
2
2
3
0
2
1
1
1
0
3
1
1
4
1
2
1
1
1
3
2
4
4
3
0
1
5
1
2
2
0
3
5
1
3
2
6
4
1
3
2
2
1
4
2
2
3
1
1
1
4
2
1
2
2
1
3
1
1
4
2
3
2
5
1
4
2
2
2
2
1
2
3
2
6
2
1
5
1
1
3
4
1
4
4
2
5
4
0
7
2
1
1
2
6
2
6
1
2
1
1
3
5
2
3
1
7
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
0
1
6
5
6
3
0
1
2
3
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
1
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
2
3
3
2
4
2
4
0
3
2
2
3
4
2
2
4
2
2
4
0
4
7
2
3
3
1
2
3
2
2
1
4
3
2
3
2
3
1
5
6
4
3
1
1
7
2
5
3
2
1
1
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
3
1
1
3
1
1
4
0
7
0
1
5
0
5
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
5
2
2
5
2
4
1
5
2
4
0
0
5
6
2
0
3
2
2
4
4
4
3
3
2
1
3
3
2
3
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
1
2
3
2
2
2
2
3
5
2
0
2
2
6
4
6
1
0
0
4
3
3
2
2
4
1
0
6
0
3
8
2
0
4
4
4
1
1
6
0
2
3
3
4
4
2
4
3
3
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
3
5
4
3
3
3
2
3
2
1
0
0
4
2
0
0
0
1
1
7
3
5
4
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
1
2
0
5
2
3
1
1
3
3
2
1
6
1
3
3
4
3
0
1
1
4
0
2
3
4
1
4
5
2
1
1
3
0
1
4
0
4
4
0
1
1
2
0
1
3
3
2
3
2
5
5
2
2
0
6
6
2
2
4
3
2
6
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
3
1
1
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
0
2
5
4
1
0
2
3
2
2
3
3
3
2
4
1
7
1
1
3
2
4
3
4
2
1
2
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
0
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
1
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
5
5
4
1
5
2
3
3
1
4
2
2
4
2
2
2
5
0
8
3
2
1
0
1
3
2
2
3
3
1
2
2
2
3
10
6
3
1
2
5
3
0
5
1
2
2
1
3
3
3
3
0
3
4
1
4
0
3
2
0
1
1
0
0
1
2
0
2
3
2
2
4
4
0
0
4
1
2
2
4
0
5
1
4
0
1
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
0
1
0
1
4
3
2
4
5
1
2
5
3
5
6
2
2
6
3
5
2
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
2
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
0
0
3
1
4
5
6
4
1
3
2
2
2
2
4
0
5
3
4
2
5
2
2
3
2
4
4
4
3
4
4
0
1
6
2
1
4
2
0
0
4
4
4
1
4
1
2
2
3
4
1
3
3
0
6
4
1
3
3
0
4
2
3
1
2
2
1
0
0
0
2
7
5
0
1
5
4
5
0
2
5
5
1
1
2
4
2
4
1
0
0
0
3
0
2
3
2
1
3
3
2
1
1
3
2
2
3
2
1
1
5
0
0
4
2
3
2
6
2
1
1
2
3
4
1
2
1
1
1
7
2
1
6
3
2
1
1
2
0
3
0
3
1
2
3
5
3
4
1
0
2
0
0
4
1
1
3
3
1
3
4
3
1
2
2
1
2
0
4
4
4
3
3
1
4
4
3
1
4
3
3
2
1
1
0
3
2
2
1
1
1
5
4
3
1
3
0
1
0
1
3
1
2
1
4
5
6
1
4
3
5
0
4
2
0
6
5
3
0
5
3
2
1
4
2
5
2
1
2
2
8
2
1
8
3
0
4
1
4
3
3
3
0
0
0
2
4
2
1
3
1
2
2
7
0
0
3
2
0
4
0
0
6
2
3
2
4
4
5
0
4
1
5
9
2
0
1
2
6
0
4
2
2
5
2
3
5
2
3
4
1
0
1
1
3
2
1
1
1
2
5
2
1
1
2
1
2
0
3
3
4
0
1
1
4
6
1
2
2
0
3
3
3
6
1
1
4
2
0
4
2
2
2
0
1
1
3
1
6
6
0
5
3
2
0
2
1
2
3
6
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
4
1
2
5
3
6
3
3
2
1
4
2
1
3
4
5
3
2
1
1
1
3
1
0
2
1
0
2
4
2
1
6
1
3
1
3
2
2
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
2
2
4
1
1
4
0
1
2
0
4
2
4
5
1
2
5
5
1
3
2
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
0
2
3
1
1
5
4
3
0
1
1
5
5
3
5
1
3
2
6
3
1
2
1
3
1
2
3
1
3
1
4
4
3
1
0
1
2
2
5
0
2
1
3
3
0
1
6
2
4
1
0
5
5
4
2
2
3
3
0
4
3
3
2
1
2
0
2
2
1
2
0
2
3
3
1
0
2
3
2
1
1
1
3
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
1
1
4
1
3
3
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
0
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
7
1
5
2
3
1
2
2
3
4
2
2
6
3
2
2
2
4
1
6
1
0
0
3
2
0
3
1
2
3
1
0
2
4
3
7
5
2
1
0
3
2
0
2
2
3
4
2
2
2
5
3
1
7
5
5
3
1
1
2
2
3
2
0
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
0
3
3
0
1
1
1
0
1
3
0
2
3
3
0
1
2
2
2
1
1
2
0
2
2
2
3
0
1
3
1
2
0
1
2
4
4
5
3
3
3
4
3
1
2
2
1
5
0
1
3
3
3
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
2
1
1
1
1
3
1
0
3
5
3
2
4
0
3
0
0
5
4
1
6
3
4
0
1
1
1
2
6
2
4
4
0
5
2
0
1
1
2
4
2
3
2
1
1
2
3
4
3
4
2
3
1
3
2
1
2
2
1
0
6
2
2
0
1
4
1
1
3
0
1
1
1
3
1
3
3
1
1
3
4
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
0
2
1
0
4
1
0
2
4
2
1
4
1
0
2
2
4
0
4
1
6
5
2
1
2
1
1
0
2
5
0
1
0
5
3
2
3
1
5
6
0
0
0
3
0
3
1
1
1
2
3
3
3
3
2
2
1
2
3
3
3
0
5
3
0
0
1
0
1
1
1
1
1
2
1
2
3
2
2
3
1
0
2
1
2
1
2
3
4
1
2
5
1
1
0
2
0
1
1
3
1
6
1
1
0
1
3
2
3
0
0
2
4
3
0
2
7
0
2
0
1
1
0
0
3
2
2
1
1
0
2
2
0
2
1
3
5
2
1
0
5
3
2
2
3
1
3
3
4
4
1
2
0
2
4
2
2
0
0
3
3
3
0
4
0
1
3
4
3
1
5
3
1
2
4
2
3
0
3
1
3
2
2
2
1
1
2
3
0
2
5
3
0
1
1
0
1
1
0
2
2
1
2
2
4
1
1
1
2
6
2
4
3
2
0
1
2
0
1
0
5
1
1
0
3
1
3
1
3
4
4
4
1
2
0
3
1
6
1
2
0
2
4
0
3
3
2
0
4
2
4
3
1
6
4
0
5
0
0
0
5
0
3
1
1
1
2
2
0
2
6
0
1
4
0
0
6
1
0
4
2
2
0
3
1
1
3
0
1
2
3
4
2
4
1
1
1
4
1
4
3
5
1
3
4
4
1
2
5
1
5
2
0
2
1
1
2
0
4
1
2
2
5
3
1
2
2
5
1
0
0
5
1
3
0
3
1
1
3
3
2
3
2
3
0
2
3
2
5
5
4
1
1
3
2
0
2
0
0
5
2
4
5
2
0
0
2
0
0
0
2
1
0
0
1
0
1
1
6
1
2
1
3
1
0
4
7
2
3
2
1
0
3
2
1
1
3
3
4
1
0
1
3
3
1
0
1
1
1
1
4
2
2
4
4
4
0
0
1
2
1
0
0
1
1
1
2
2
1
1
3
3
1
2
1
5
1
3
4
0
3
3
0
1
1
3
1
2
1
4
1
2
3
2
2
5
2
3
0
1
1
3
3
0
1
4
4
0
1
3
3
1
5
2
3
1
1
1
2
0
1
6
2
1
5
1
4
1
1
3
3
0
1
2
1
2
6
0
1
1
1
4
2
3
2
3
1
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
5
1
4
1
0
4
1
0
0
3
3
4
1
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
2
1
1
4
0
1
1
2
0
2
1
2
1
0
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
1
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
3
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
4
1
0
3
2
0
4
3
4
2
4
5
1
0
3
2
1
8
3
1
2
3
0
4
2
7
3
1
7
1
3
1
0
0
5
2
4
7
2
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
0
2
1
3
0
5
0
4
4
2
4
0
0
4
0
0
1
6
3
1
2
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
0
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
2
1
3
3
3
2
3
3
1
4
3
7
2
1
2
0
2
1
5
0
4
2
1
5
1
3
0
0
1
2
3
1
0
3
1
1
1
0
1
1
0
4
3
5
1
1
3
1
1
3
1
3
1
2
1
3
0
1
0
3
4
4
1
3
1
4
1
2
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
4
1
1
0
0
5
1
3
3
0
2
1
0
1
0
1
5
2
1
0
0
2
1
0
3
1
2
0
3
6
4
5
1
5
0
3
3
5
4
0
4
0
3
6
1
3
2
3
0
3
1
1
1
1
0
2
0
1
3
2
1
1
1
3
2
0
3
0
1
4
5
1
0
3
1
6
5
0
2
2
4
5
6
5
1
2
2
1
3
1
1
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
0
1
2
4
2
2
2
4
1
0
2
3
4
3
3
3
0
3
1
1
0
2
3
3
0
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
1
1
1
6
3
1
4
2
3
3
1
3
2
1
2
3
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
2
0
3
2
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
4
1
4
2
0
4
1
2
2
0
0
2
0
3
1
0
2
2
2
2
4
3
2
1
3
0
4
0
5
4
2
0
0
1
5
1
3
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
0
0
3
2
2
0
1
9
4
4
8
3
0
3
4
1
5
2
2
3
1
1
2
0
2
1
2
1
0
1
1
6
1
3
3
1
2
1
2
2
2
4
4
2
2
3
3
2
2
1
1
1
2
2
1
1
1
0
0
1
2
3
2
2
2
3
2
2
5
1
1
3
3
2
0
4
3
2
2
1
1
0
1
1
2
1
1
3
5
2
0
1
1
2
1
2
4
1
0
0
6
1
2
1
3
1
2
2
0
2
0
1
1
0
1
2
2
2
3
2
5
1
5
3
6
0
4
5
0
0
1
0
4
5
2
5
3
0
4
3
5
0
5
3
0
4
2
1
1
2
4
1
3
2
2
2
0
0
2
4
1
5
2
2
2
6
1
0
1
3
1
3
2
1
3
0
1
1
0
1
2
7
1
1
6
0
5
1
2
4
0
2
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
1
3
1
4
1
3
2
1
0
3
1
2
3
1
4
5
4
2
2
0
1
0
1
0
5
1
1
3
4
1
1
2
1
1
3
6
1
5
1
2
1
4
1
3
3
4
1
0
1
0
3
1
0
3
2
0
1
3
3
0
3
4
0
2
0
0
1
0
0
0
2
1
1
1
1
2
0
1
7
3
2
4
2
2
2
5
3
2
1
1
1
2
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
1
1
5
1
3
2
1
2
1
1
3
4
1
0
1
2
0
3
0
1
2
1
0
3
0
3
1
0
1
2
1
3
5
2
4
1
4
1
0
3
2
4
3
1
2
5
1
0
0
4
0
1
0
4
0
1
3
3
3
3
1
4
1
1
0
1
2
3
0
0
3
2
4
0
4
1
1
1
1
3
3
3
1
0
6
2
0
2
2
1
3
3
3
0
1
5
2
1
1
3
0
0
5
4
0
0
1
1
0
0
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
3
1
3
4
1
0
1
1
3
3
4
1
2
1
1
0
1
1
2
3
5
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
0
1
2
0
0
4
2
2
5
3
2
1
1
1
1
4
4
1
5
2
0
0
2
0
1
2
2
1
1
1
3
1
3
1
2
1
0
2
1
1
1
0
1
4
1
1
2
5
2
2
2
3
1
1
3
1
0
2
2
1
3
0
0
0
3
0
1
0
3
1
1
2
1
2
3
2
0
2
3
3
1
3
2
1
3
3
0
0
2
3
1
1
1
4
1
2
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
4
5
4
2
1
1
0
0
2
0
3
6
3
2
2
1
1
1
3
0
3
1
2
1
3
3
0
0
5
0
4
2
2
1
1
3
3
5
1
4
3
0
2
0
3
2
2
0
3
1
1
2
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
1
0
1
0
1
2
4
1
1
0
3
0
3
0
2
0
4
1
0
0
3
4
4
0
1
4
4
4
1
1
3
1
1
3
2
4
3
7
2
2
1
1
1
2
3
5
1
3
2
2
2
2
2
2
4
1
0
3
4
3
1
2
1
1
2
4
2
1
3
0
3
1
0
3
5
3
3
2
1
1
3
0
3
1
3
3
2
0
1
1
0
1
0
0
4
2
2
2
0
0
4
4
5
2
0
2
0
1
2
1
3
0
2
3
3
1
3
1
2
3
0
1
4
0
3
3
1
2
2
0
2
4
4
1
0
1
0
0
4
4
1
6
3
5
1
0
3
1
0
1
2
5
4
2
0
2
0
3
2
4
1
3
2
1
2
3
3
1
5
0
1
2
4
0
1
0
0
1
3
0
2
0
1
1
6
1
1
4
2
1
3
5
3
2
3
0
0
3
0
3
4
0
3
1
0
1
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
0
0
3
3
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
2
2
1
1
0
4
2
1
1
3
2
1
1
0
1
0
3
2
0
3
2
2
3
2
1
1
0
3
1
2
1
2
5
0
3
0
0
0
1
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
3
2
2
2
0
3
0
0
1
1
3
3
0
7
5
1
2
3
1
3
0
1
0
0
4
0
2
3
2
1
1
4
3
3
2
2
0
4
1
1
1
1
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
2
4
1
1
1
2
3
1
1
0
2
1
9
2
1
3
1
2
1
0
1
6
1
2
0
1
0
2
0
3
4
0
2
1
0
1
1
3
1
2
4
2
2
3
2
1
3
0
0
0
2
1
3
1
1
2
1
2
1
2
1
2
0
0
3
1
3
4
0
1
2
3
3
1
2
1
3
1
2
6
2
1
1
1
4
0
2
1
2
1
0
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
0
0
1
2
0
1
2
6
0
1
6
2
4
0
1
0
2
2
6
4
4
1
3
0
2
1
3
1
0
1
2
2
2
3
3
4
2
2
3
6
4
4
1
2
2
1
0
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
2
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
0
3
1
2
7
1
0
1
2
0
2
2
3
4
1
1
1
2
0
1
2
2
3
2
0
2
2
0
2
2
2
4
0
1
2
0
5
0
2
0
1
0
0
0
2
0
4
1
2
4
4
0
0
1
1
1
1
2
0
2
1
1
3
1
0
0
2
3
4
3
2
0
0
2
1
2
3
0
6
3
1
1
1
1
3
1
1
0
4
2
4
2
3
5
3
2
1
0
5
2
0
0
0
3
1
3
3
10
2
1
3
0
0
1
1
2
2
5
1
3
3
2
3
0
0
2
2
1
0
1
2
1
2
5
2
0
2
4
1
2
4
0
0
0
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
0
3
1
0
2
1
2
3
3
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
2
0
1
0
0
1
3
4
2
2
2
0
1
1
0
0
5
3
5
1
2
2
1
4
0
2
3
1
0
2
0
2
0
0
2
1
0
1
3
4
4
2
4
1
3
2
2
3
1
4
0
0
6
2
0
1
2
1
1
2
1
0
0
1
4
2
1
0
8
2
2
0
3
2
1
0
3
4
1
3
2
0
3
1
3
3
3
3
1
2
1
0
1
1
1
0
2
6
2
1
1
2
0
0
3
2
1
2
5
1
2
3
2
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
2
3
3
3
3
0
1
2
3
3
0
0
0
0
1
0
2
1
0
1
0
2
3
1
2
5
1
1
2
0
0
3
1
2
3
5
3
1
3
2
2
4
0
1
1
1
1
0
2
4
0
0
0
2
1
2
1
2
2
0
2
4
1
0
0
0
5
1
2
3
2
1
1
2
0
0
1
5
3
0
5
1
1
4
3
2
5
0
0
1
2
2
1
0
0
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
0
3
4
1
3
2
1
2
0
1
2
2
3
3
0
3
2
0
0
1
1
0
0
0
3
1
1
1
2
0
0
6
2
1
1
3
2
4
3
0
0
1
2
1
2
2
1
1
0
2
1
2
0
1
1
7
4
0
1
5
0
3
2
1
1
2
3
0
2
4
0
3
1
3
2
1
1
0
2
1
1
6
2
1
1
1
2
4
2
0
3
2
1
1
4
5
3
1
2
1
1
1
4
2
2
3
2
3
2
3
3
2
1
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
0
0
2
2
3
0
1
3
4
4
2
2
1
4
1
2
3
3
1
3
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
5
1
1
3
2
0
2
0
2
0
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
3
2
2
0
4
3
3
2
1
2
1
2
2
2
3
1
2
1
1
3
1
0
0
3
2
2
1
3
0
2
2
1
2
3
3
4
0
1
1
0
3
0
4
1
2
3
2
2
1
3
1
0
1
3
3
0
1
0
0
0
1
2
2
2
0
0
4
1
2
0
3
1
2
0
0
2
1
2
4
2
0
1
2
4
3
2
2
4
4
1
1
2
1
1
2
0
2
0
2
4
0
4
0
2
2
1
4
2
1
4
2
3
0
1
1
1
2
4
6
2
6
1
2
0
1
2
2
0
0
3
2
0
4
1
4
0
0
2
2
4
2
1
2
1
0
2
3
3
1
2
0
1
0
3
2
3
3
3
3
3
2
4
0
2
4
2
1
0
3
1
2
3
1
2
0
0
2
2
2
2
0
2
4
3
0
3
5
3
2
6
2
0
3
3
3
0
1
1
1
1
1
3
2
1
0
1
1
3
1
0
1
5
2
2
1
0
5
2
3
4
0
1
4
3
1
1
1
0
2
0
4
4
1
0
3
3
1
2
4
3
2
2
0
4
2
2
0
2
1
1
2
2
0
4
4
1
1
0
2
2
0
3
1
2
3
1
3
2
1
0
3
2
0
0
2
2
0
0
5
8
2
0
2
1
0
0
2
4
3
1
3
0
0
3
4
2
8
3
3
1
1
2
0
1
4
1
1
0
2
3
1
3
1
1
1
0
2
0
0
0
3
3
3
3
0
4
2
1
1
0
2
0
2
1
3
1
2
4
1
0
1
1
2
1
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
0
2
3
3
1
1
0
0
0
6
0
2
1
1
4
7
5
1
5
2
2
2
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
1
1
2
2
0
0
3
1
1
2
4
1
0
2
0
0
1
4
1
1
1
1
2
3
0
5
1
1
1
2
2
5
1
0
1
1
0
2
3
3
3
2
2
1
3
3
3
3
3
2
0
1
1
2
3
0
0
3
3
5
1
2
0
1
0
1
0
0
2
2
1
0
3
1
3
0
1
3
2
0
1
0
2
1
1
1
1
1
5
0
4
0
3
2
2
1
2
3
0
0
3
1
2
1
2
0
0
0
0
2
1
1
0
1
2
0
2
2
0
1
1
2
0
0
1
0
1
1
1
2
0
1
1
1
2
2
0
1
5
0
0
2
2
3
2
2
1
2
0
1
2
0
0
2
0
2
2
3
2
0
2
5
1
1
1
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
0
1
1
2
4
3
1
1
1
1
3
0
5
1
1
4
1
1
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
0
0
1
2
3
0
1
2
3
4
3
0
1
4
1
2
1
1
0
2
2
2
1
1
2
5
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
1
2
6
4
2
1
0
0
1
2
1
2
1
1
1
3
2
0
2
1
3
0
0
0
3
1
1
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
4
0
0
1
0
3
1
1
3
1
2
3
0
1
1
1
2
2
4
3
0
4
2
1
2
1
5
1
1
3
2
4
3
0
3
0
2
0
2
4
1
1
2
0
1
3
2
1
5
3
2
0
0
5
2
3
0
0
0
1
2
4
0
0
0
1
3
3
0
2
1
1
0
4
3
3
4
0
1
1
3
1
0
2
0
2
1
1
1
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
1
1
0
2
1
1
1
1
3
2
0
0
0
1
2
2
0
2
2
0
2
1
0
2
1
3
0
3
0
2
1
1
2
2
1
0
2
2
2
3
2
2
1
1
3
0
1
2
0
0
2
2
1
3
0
1
2
4
4
0
0
0
1
2
3
0
0
2
0
0
4
4
1
1
1
5
1
1
2
0
1
1
3
2
2
3
3
1
1
2
2
0
1
0
6
2
2
0
0
0
1
2
4
2
1
1
1
3
0
1
3
1
0
2
1
0
2
0
1
1
6
4
2
0
1
2
1
4
2
0
2
1
1
2
4
1
3
1
5
2
0
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
3
0
1
2
0
3
1
2
2
1
1
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
4
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
2
2
0
0
0
0
3
4
3
4
3
4
0
3
5
1
1
4
3
1
0
0
7
0
6
0
2
6
0
1
2
2
3
1
0
2
2
3
3
4
1
2
0
0
1
1
0
2
2
2
2
1
1
2
2
3
0
1
2
0
2
0
3
2
3
4
2
0
3
1
0
2
1
3
0
3
0
2
1
2
0
0
3
2
2
1
2
0
0
0
0
1
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
0
3
6
0
3
0
0
3
0
2
1
3
1
0
1
1
0
3
3
0
1
2
2
2
2
1
2
0
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
0
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
2
3
0
0
1
5
2
5
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
5
2
3
0
1
1
2
2
1
3
1
1
1
3
1
0
0
0
1
1
2
2
4
5
2
2
3
1
1
5
2
2
2
0
1
1
1
0
2
2
1
2
3
1
0
2
4
2
1
3
1
4
5
0
4
0
1
4
3
1
1
1
2
0
1
1
2
2
2
2
0
1
4
0
1
1
7
0
2
0
6
0
0
3
1
2
2
0
0
0
2
2
2
2
0
1
4
2
2
2
0
0
1
2
1
1
2
2
0
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
3
1
3
5
2
0
0
5
1
0
0
1
3
1
4
0
1
1
1
1
4
1
0
1
2
3
1
1
4
0
3
0
1
0
1
2
4
1
6
0
0
2
1
3
1
4
3
5
1
1
2
3
0
4
1
1
2
2
2
3
2
1
1
7
3
1
0
2
1
3
2
2
2
1
1
1
2
0
4
3
5
4
3
2
0
1
0
1
3
1
0
3
2
2
2
0
1
1
1
1
0
7
1
0
1
1
1
2
0
1
1
2
2
1
1
2
0
0
3
2
3
1
0
1
2
1
2
1
4
5
1
1
0
2
0
1
0
3
1
0
0
2
1
0
1
1
5
4
3
3
1
2
0
3
4
0
4
2
4
0
0
0
0
0
1
0
0
1
0
1
5
0
0
1
2
3
0
0
1
0
2
1
0
0
5
1
2
4
2
1
0
0
1
0
3
2
0
0
2
0
1
4
0
3
1
0
1
2
2
3
1
2
0
1
1
1
1
1
1
1
1
2
0
3
3
2
0
1
1
0
1
1
0
0
1
1
2
0
0
1
0
2
1
1
0
1
1
0
0
6
1
0
6
1
3
1
0
3
0
1
2
1
2
4
3
0
0
1
2
0
1
2
1
1
1
3
5
1
0
5
2
1
1
3
0
3
2
3
4
0
3
1
2
2
1
0
4
2
1
1
1
3
1
2
1
3
2
0
0
1
1
2
0
0
5
2
0
1
1
1
0
0
0
3
1
0
5
2
2
2
4
0
0
1
2
1
0
5
1
1
1
0
2
1
0
1
0
2
1
0
1
3
4
0
2
1
0
1
2
1
0
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
2
5
1
0
1
1
0
4
1
0
0
2
1
2
0
5
1
1
1
3
1
1
2
0
0
3
3
2
0
0
3
3
4
2
1
3
1
2
1
0
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
1
1
3
2
1
4
2
3
0
1
1
2
0
1
1
3
1
2
1
0
0
2
0
4
2
2
0
5
1
1
0
0
2
3
0
3
4
2
3
2
2
1
1
0
3
1
1
2
3
0
1
2
0
2
2
1
4
2
2
2
2
1
1
2
1
2
1
1
5
3
0
0
3
1
1
4
3
0
4
1
3
4
1
3
1
2
0
1
2
5
2
3
0
0
1
1
2
1
1
4
0
1
0
0
1
1
2
3
1
0
1
1
1
0
1
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
1
1
1
2
2
1
2
0
3
0
1
3
0
1
4
3
0
0
0
1
3
0
0
2
2
1
2
2
2
0
2
0
2
0
3
2
1
1
0
2
1
0
1
3
2
2
3
0
4
4
4
1
4
2
3
2
1
0
0
1
6
1
3
0
0
0
2
1
3
2
2
1
2
1
1
0
0
3
0
2
0
0
1
1
3
0
1
2
2
0
2
2
0
2
1
1
1
1
5
1
2
2
1
3
5
1
0
0
2
1
1
3
0
3
0
1
1
4
2
5
0
3
0
1
1
3
1
1
1
3
2
3
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
1
2
0
3
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
1
4
2
1
0
1
1
4
1
2
0
4
2
4
2
3
0
1
4
2
1
2
1
1
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
2
1
5
7
1
1
1
1
2
0
2
2
3
2
1
1
1
1
1
0
3
1
0
1
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
0
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
1
2
1
1
2
1
3
2
7
2
2
1
0
4
2
2
1
7
2
1
2
4
0
2
1
2
1
6
3
0
0
0
2
1
1
4
0
1
3
4
5
0
2
2
4
2
2
1
1
1
2
3
0
2
0
2
1
1
2
3
2
3
1
0
5
2
1
0
2
2
3
1
4
1
5
0
1
2
2
0
3
1
4
1
1
2
2
1
4
2
1
0
0
1
3
3
3
1
3
1
2
2
2
4
4
3
5
3
3
0
1
3
7
3
3
1
2
1
0
1
1
4
3
3
3
1
1
2
3
2
3
1
3
3
0
3
3
0
1
0
1
7
1
4
3
0
2
3
1
2
2
1
2
1
2
0
1
1
1
2
4
0
1
0
1
0
2
1
0
3
2
2
0
3
2
2
2
5
2
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
7
1
1
1
1
5
3
2
0
2
2
1
1
0
1
0
4
2
1
1
1
4
0
1
1
1
4
2
2
1
0
4
5
1
1
1
3
0
3
3
1
0
3
1
6
0
2
2
2
3
2
0
0
2
0
2
2
0
0
3
1
1
2
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
2
1
0
3
2
3
1
1
1
3
2
1
1
0
2
3
2
0
3
2
3
2
3
4
0
0
3
0
1
1
2
1
3
2
4
0
2
0
2
2
2
1
2
1
1
3
2
0
2
0
0
3
1
1
1
3
0
2
0
2
3
2
0
0
2
2
1
8
3
0
2
1
2
0
1
1
4
0
0
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
1
2
1
1
3
2
4
1
1
0
0
4
3
0
3
0
5
2
2
1
0
2
0
1
0
2
0
3
4
1
1
1
5
4
1
1
4
1
2
0
4
1
1
1
4
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
2
0
1
1
1
1
1
2
2
0
1
3
2
1
2
2
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
0
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
2
2
2
2
1
0
0
2
2
2
3
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
1
0
1
1
2
0
1
1
4
3
1
2
2
1
0
4
1
3
0
2
0
3
2
1
2
1
2
1
2
0
2
0
3
3
2
0
1
4
0
1
2
2
1
2
2
1
1
1
3
0
2
1
2
1
0
3
0
2
0
3
3
0
0
1
2
3
0
0
0
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
1
0
5
1
1
1
1
2
1
5
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
2
1
1
0
1
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
0
0
1
0
1
3
0
2
2
3
1
3
0
1
2
1
4
0
2
0
0
2
1
0
4
0
3
0
0
1
0
3
3
0
1
1
2
2
3
1
2
1
1
0
0
3
0
0
1
1
1
1
3
1
1
0
0
1
0
0
0
1
0
1
2
1
2
1
0
0
1
1
1
2
4
1
3
0
1
2
5
0
1
3
1
4
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
1
1
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
1
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
1
1
1
0
1
0
0
0
2
2
0
2
0
0
0
3
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
0
1
2
1
2
1
1
3
0
2
0
2
2
0
1
3
0
1
2
2
0
3
2
0
1
0
2
4
1
0
3
3
0
0
1
3
1
3
0
0
2
1
2
5
1
1
0
3
3
0
3
3
0
1
3
2
5
0
1
1
0
3
2
0
0
0
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
0
2
4
0
0
2
2
1
2
3
5
2
1
1
3
0
2
2
3
3
3
1
6
1
0
3
1
1
1
1
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
2
1
2
0
1
2
1
1
1
2
1
3
1
0
0
2
2
2
1
2
3
1
0
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
2
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
5
3
0
2
1
3
2
2
2
0
4
0
1
1
1
3
1
2
2
1
2
0
2
3
1
0
2
2
1
0
2
2
0
2
0
1
0
2
2
0
0
2
1
1
1
2
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
2
1
0
1
3
0
0
0
0
1
3
4
2
3
2
3
0
2
2
7
1
1
1
2
1
3
0
0
1
1
1
1
0
0
2
1
1
0
2
0
2
2
1
0
1
1
4
1
0
2
1
2
1
1
2
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
1
1
0
3
2
2
0
0
0
0
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
1
1
1
1
3
1
0
1
2
1
0
1
1
0
0
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
2
4
0
2
6
1
2
2
2
3
1
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
1
1
0
1
0
1
0
1
0
3
3
0
2
1
2
2
3
0
2
3
0
0
1
2
1
2
2
2
1
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
0
0
2
2
2
2
3
2
1
3
3
0
3
0
3
0
2
0
1
2
0
5
1
1
3
1
0
0
1
0
3
4
4
0
3
0
4
0
3
0
1
2
0
4
0
1
0
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
2
1
2
1
3
2
1
0
1
4
3
2
2
2
2
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
3
1
1
2
1
0
3
2
0
0
3
0
2
0
0
0
2
2
5
1
2
0
0
1
2
2
2
1
2
2
0
1
0
0
1
1
4
0
3
3
3
3
0
0
0
5
0
2
1
0
3
2
3
1
0
1
2
0
2
0
1
3
3
7
1
1
0
3
0
2
2
0
2
3
0
1
2
0
1
0
2
1
0
2
4
1
1
2
2
2
3
4
1
1
0
1
1
2
1
3
0
3
2
1
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
0
3
2
2
1
2
1
1
0
2
4
0
1
0
3
1
1
2
1
0
0
1
1
3
0
1
2
2
0
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
0
1
0
1
0
0
0
0
1
1
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
1
1
1
1
0
2
2
1
3
3
3
0
0
0
1
7
1
0
1
0
0
1
3
0
0
1
1
1
1
0
0
2
4
1
2
3
0
0
2
1
0
1
1
2
4
0
2
0
1
1
2
1
0
0
4
1
2
4
4
3
1
3
2
0
0
1
3
1
2
0
0
1
1
1
3
3
2
0
1
2
3
1
1
3
4
1
0
1
2
3
2
0
2
2
0
1
0
0
3
2
2
3
0
2
1
0
2
1
1
0
0
2
2
3
0
3
3
1
0
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
1
1
1
1
2
2
1
2
4
2
1
1
1
1
2
2
1
3
0
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
1
0
2
2
2
1
0
3
2
2
1
1
2
0
0
0
4
1
0
1
3
2
2
2
0
1
0
2
2
1
2
0
3
1
3
1
3
2
0
1
2
2
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
0
0
0
0
2
2
0
1
2
0
0
3
1
2
1
2
2
0
1
0
0
1
2
0
3
0
1
1
1
1
1
0
0
3
0
0
2
4
2
1
1
1
2
1
4
1
1
1
1
1
1
0
2
1
2
2
1
1
0
2
1
2
3
0
0
1
3
1
0
2
3
1
0
2
0
3
2
2
2
3
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
4
0
1
1
2
1
0
3
4
1
0
2
4
1
2
1
2
2
0
2
2
0
0
0
2
1
0
1
1
1
3
0
1
2
0
4
0
1
4
0
0
1
1
3
2
2
0
2
0
2
2
3
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
2
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
0
1
2
3
3
2
1
1
1
0
0
2
0
1
4
1
2
0
1
3
2
2
0
3
1
5
2
0
0
2
0
3
1
1
1
0
1
3
0
0
2
1
0
0
3
0
2
0
0
1
1
0
0
1
3
0
0
1
0
2
2
0
0
4
1
2
1
0
1
1
0
0
2
0
3
3
0
1
1
2
2
4
3
2
1
0
6
0
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
3
2
3
1
4
3
2
0
0
2
0
1
2
1
1
0
0
3
1
1
3
2
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
2
2
0
1
0
0
4
1
3
2
2
1
1
0
3
0
0
0
1
2
0
2
1
0
2
1
0
0
2
1
2
1
2
0
0
1
0
0
0
2
1
3
0
2
2
2
0
1
1
0
2
3
0
0
0
1
0
0
1
3
0
1
1
1
2
2
0
3
2
1
2
1
0
2
2
3
0
1
3
1
0
0
0
3
1
1
1
0
3
2
1
1
0
1
4
4
3
2
0
0
0
0
3
1
0
0
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
0
0
1
1
1
2
0
4
0
0
3
3
4
3
1
4
4
1
0
0
0
2
0
0
0
2
2
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
1
0
2
1
0
3
4
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
0
3
3
1
3
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
1
0
3
3
3
6
1
1
0
0
0
1
2
1
0
2
1
1
2
1
3
0
2
0
0
0
1
4
3
0
1
3
1
1
0
1
0
1
0
1
1
4
3
2
0
0
4
3
1
0
0
1
0
0
1
2
1
3
1
3
2
2
1
1
3
2
1
1
1
3
0
0
2
2
2
0
0
1
2
1
1
2
0
2
3
0
3
1
3
3
0
1
1
0
2
1
1
2
0
2
3
0
1
0
0
1
1
2
0
1
1
0
0
0
1
3
2
2
0
0
1
2
1
1
3
1
0
2
0
0
4
1
0
0
0
0
2
1
3
2
3
2
0
3
1
1
2
1
1
1
0
0
1
0
3
1
1
1
0
0
3
1
4
2
2
4
1
1
0
0
0
0
1
0
6
2
1
2
3
5
0
2
3
3
2
0
1
1
1
2
2
1
2
1
2
0
1
1
0
0
0
3
2
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
2
0
0
0
0
2
2
1
1
0
1
1
1
2
0
0
0
2
0
1
0
1
3
3
2
3
0
1
1
0
0
2
2
4
1
2
1
2
0
3
2
1
3
1
0
0
3
1
1
3
3
4
0
0
1
2
3
0
0
2
2
2
0
2
0
1
0
3
0
4
1
0
3
1
2
1
0
2
1
1
1
0
1
0
2
0
4
2
2
1
2
1
0
3
1
2
2
3
0
6
0
4
6
2
1
0
1
1
2
4
0
0
1
2
1
2
0
1
0
1
1
1
1
4
4
1
3
2
2
2
1
2
0
0
1
3
1
0
2
1
1
0
1
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
2
1
1
4
2
0
4
3
2
1
3
0
0
0
2
1
0
2
0
3
3
0
0
0
1
0
1
2
0
6
1
3
4
4
1
3
1
3
2
2
2
0
1
0
0
1
1
1
0
0
3
3
3
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
3
1
1
1
2
0
1
1
2
1
0
1
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
2
0
4
1
2
1
0
1
1
0
1
0
0
0
1
1
0
3
2
3
2
0
0
1
0
0
1
1
0
0
1
1
1
0
2
1
0
3
1
2
1
0
4
1
0
0
0
4
2
0
0
2
4
1
2
2
2
1
0
4
1
1
1
0
1
1
0
1
2
2
3
1
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
0
6
0
4
1
2
1
0
0
2
2
1
0
2
1
3
2
1
2
0
1
1
1
0
1
2
3
1
0
2
0
1
1
1
2
0
0
0
2
1
2
0
1
0
0
1
1
2
3
0
2
1
1
0
1
3
1
3
4
5
4
2
1
2
1
0
1
0
2
1
2
0
0
2
3
1
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
0
1
1
1
1
0
1
0
1
3
2
0
4
0
1
0
2
2
2
2
1
1
2
3
4
4
1
2
1
0
2
2
0
3
0
1
2
1
0
4
3
0
1
0
0
1
2
0
1
0
1
2
2
1
1
1
1
0
2
2
0
0
2
1
3
4
3
4
3
1
1
0
1
0
1
2
1
2
0
1
2
1
4
0
1
2
2
3
2
2
0
0
1
2
0
1
5
4
0
2
1
1
0
1
3
1
2
2
0
2
1
1
1
1
1
4
1
0
1
2
3
5
1
0
0
1
2
1
4
5
1
2
0
0
1
0
1
1
2
0
1
1
1
2
2
2
4
6
0
2
1
3
0
0
0
1
0
2
0
1
2
5
0
3
5
1
1
0
2
1
1
0
4
2
1
0
0
1
2
0
1
1
2
1
1
4
2
1
1
0
1
2
0
3
2
2
1
0
2
1
3
1
2
4
0
1
1
0
0
1
0
2
0
2
1
0
2
3
2
2
3
0
1
1
1
0
0
3
0
0
2
1
0
0
2
1
3
2
1
1
0
0
2
4
1
0
0
1
2
2
3
5
2
2
2
0
2
1
2
0
0
3
0
0
0
0
0
2
3
2
1
1
1
1
2
1
2
1
0
2
1
4
0
1
2
3
0
0
3
3
0
1
1
0
2
1
1
1
1
1
1
0
2
0
0
4
1
1
2
4
3
2
2
1
0
2
0
0
0
0
0
2
0
3
3
0
3
1
6
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
4
0
3
2
1
1
2
2
0
1
1
1
1
1
1
0
2
1
0
0
0
2
2
2
1
0
1
2
2
3
0
0
1
2
0
0
3
0
0
0
1
1
5
0
5
4
2
1
2
3
0
3
1
1
2
1
0
0
0
4
1
3
1
1
0
1
1
3
2
1
1
2
3
1
2
1
2
5
0
3
1
1
0
1
0
0
3
1
0
3
0
1
0
5
2
1
2
0
2
2
0
3
1
0
1
1
0
1
3
0
0
0
2
1
0
2
2
0
0
0
0
2
5
0
0
3
4
1
1
0
0
2
2
0
2
1
1
2
0
1
3
4
0
2
0
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
2
0
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
2
3
0
0
0
1
1
3
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
0
1
0
1
0
1
1
0
1
2
1
0
1
3
1
3
1
2
0
0
2
1
0
0
0
1
1
1
1
4
0
1
2
1
0
0
4
0
1
0
1
2
0
0
1
0
2
4
2
0
2
2
3
3
0
1
1
0
0
0
2
1
0
2
0
0
2
1
0
2
3
4
1
1
3
5
1
0
1
0
0
1
0
3
1
1
0
1
4
0
2
0
0
1
2
1
3
0
0
3
2
2
1
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
0
1
1
0
0
1
0
1
0
1
4
1
0
0
2
1
0
2
1
1
0
1
2
1
2
2
1
0
1
3
1
1
0
1
2
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
0
3
3
1
1
2
2
1
0
2
0
2
2
1
1
1
0
1
3
0
3
1
1
1
0
2
2
0
0
0
2
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
1
0
2
0
0
2
2
2
1
0
2
0
1
2
1
0
1
2
0
1
0
0
2
1
4
1
1
0
5
2
1
6
0
2
0
1
0
1
1
1
3
0
1
1
2
0
1
1
0
0
0
0
0
3
0
0
4
3
4
0
1
4
1
0
1
0
3
2
0
0
0
2
2
1
1
1
4
0
3
2
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
2
1
1
0
1
0
2
0
1
1
2
3
2
1
0
2
5
1
1
0
1
1
1
0
0
0
1
1
2
0
2
1
0
2
2
4
0
1
3
2
3
0
1
2
0
0
1
0
4
1
2
0
0
1
0
0
2
0
0
0
1
1
3
0
1
2
0
1
5
0
1
0
0
0
1
0
1
3
0
0
3
2
3
0
2
1
1
2
2
3
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
1
2
1
3
2
1
0
0
1
1
1
2
1
1
1
2
0
2
3
5
1
1
0
2
0
3
0
1
1
1
2
1
0
3
0
2
0
0
1
0
0
0
2
2
0
3
0
1
0
2
1
1
3
0
0
2
2
1
2
2
1
1
0
3
3
3
0
3
3
0
1
0
2
0
1
1
4
0
1
0
2
0
0
1
2
3
3
2
1
2
0
1
1
1
1
1
0
1
2
5
0
2
4
1
2
2
1
1
0
2
0
0
2
2
3
0
1
2
3
2
0
1
1
5
1
1
0
1
2
1
1
1
1
0
1
2
0
0
0
0
2
4
0
3
1
4
2
3
0
2
0
2
2
0
1
3
3
1
2
0
0
0
0
3
4
0
4
0
1
3
4
1
2
0
1
1
2
2
0
1
0
1
1
2
0
2
0
1
3
3
4
0
2
0
2
1
0
3
1
3
1
1
1
1
1
1
3
3
0
0
2
1
4
2
2
0
0
4
2
2
0
2
1
3
2
1
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
2
2
2
0
1
3
0
0
1
2
3
2
1
1
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
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
0
2
1
0
1
4
2
3
3
0
1
0
0
1
1
3
2
1
0
1
1
1
1
0
3
6
4
1
4
1
1
3
1
3
5
1
0
2
2
0
0
1
0
2
1
0
1
0
0
1
0
2
2
0
0
0
3
2
0
1
0
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
2
1
1
0
0
0
1
0
0
4
2
1
4
0
0
0
1
1
1
1
2
3
0
2
1
0
0
1
4
0
2
0
2
3
1
2
1
4
0
0
0
1
3
0
1
2
2
0
0
2
4
1
1
0
1
1
1
0
0
1
1
2
3
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
2
1
3
1
1
0
0
0
1
0
5
0
0
2
0
3
0
1
2
4
0
1
0
1
0
0
2
2
2
4
1
7
4
2
0
2
0
1
1
3
0
2
1
0
2
1
1
1
2
3
2
1
3
1
2
0
1
3
2
0
2
2
1
1
1
1
3
0
1
3
0
2
1
1
3
3
1
0
1
2
0
0
1
2
0
0
3
1
3
0
1
1
0
2
1
0
1
1
3
3
2
0
2
0
1
4
2
3
2
0
4
1
2
2
3
2
3
1
0
0
2
1
1
1
1
1
4
0
2
2
2
1
2
2
1
2
4
2
0
1
1
1
1
4
1
1
0
1
1
2
2
0
1
0
2
1
3
1
1
2
1
2
2
1
1
1
0
2
0
2
2
0
3
1
2
0
1
0
0
1
1
0
1
0
3
0
1
3
2
1
2
1
0
0
0
0
3
0
0
1
4
1
0
0
4
0
0
1
0
1
0
0
0
3
5
1
1
1
1
2
1
1
2
0
0
0
1
4
0
2
3
1
1
1
0
1
0
2
0
2
1
1
1
0
3
2
1
1
2
0
0
0
1
4
2
3
0
0
0
1
3
2
0
2
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
1
1
2
4
0
0
1
3
2
5
2
1
0
5
0
0
0
1
2
0
1
0
0
1
0
1
1
0
2
3
1
1
1
2
2
1
0
1
0
2
2
0
0
2
4
1
1
1
0
1
0
1
1
0
2
0
0
0
0
2
3
1
1
4
4
0
2
1
3
0
0
0
1
0
3
1
0
1
2
2
3
1
0
2
0
1
2
1
0
2
1
0
2
3
1
3
0
1
3
0
1
0
1
0
0
4
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
0
1
3
3
1
1
2
0
2
2
0
3
2
0
0
2
0
1
0
0
1
2
0
1
1
3
0
1
0
0
2
0
1
1
0
5
1
0
5
0
3
1
0
0
1
1
0
3
1
1
0
1
2
0
2
1
2
5
0
0
1
0
2
1
2
0
1
1
2
2
1
1
1
2
3
1
4
0
1
0
1
2
0
3
0
1
0
1
2
3
0
2
1
0
0
3
1
1
1
0
0
0
1
0
5
3
0
1
1
1
0
2
1
2
2
0
1
0
1
1
0
0
0
1
1
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
3
0
2
0
1
1
1
1
2
1
3
1
1
1
2
1
2
1
0
2
2
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
3
1
1
2
1
0
0
0
2
2
1
1
0
1
1
1
0
1
3
0
0
1
3
3
3
1
0
1
2
1
3
1
2
0
0
1
0
1
0
0
3
0
2
2
1
2
1
2
0
0
0
0
1
3
2
3
2
0
0
1
0
1
2
2
4
1
0
2
0
1
3
1
0
2
0
1
2
1
0
1
1
1
2
0
2
0
0
1
2
1
1
1
0
0
0
0
0
2
0
1
5
0
0
0
0
0
3
1
0
0
2
2
2
1
0
0
0
1
0
1
1
4
1
2
2
2
1
1
4
0
0
2
0
2
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
1
1
2
1
0
2
1
5
1
0
0
1
4
0
4
0
1
1
0
1
0
0
1
0
1
2
2
1
3
0
1
1
0
1
3
1
0
0
1
0
1
1
0
0
1
0
0
0
1
2
2
1
0
2
2
2
3
1
0
1
0
4
0
0
0
1
1
0
1
2
5
2
4
1
6
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
3
1
2
0
0
0
0
0
1
1
1
1
3
1
2
4
2
3
1
2
0
1
0
0
0
0
0
1
1
3
2
2
2
1
1
1
1
0
1
3
2
0
3
4
1
0
2
0
0
2
0
0
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
0
1
3
0
0
1
0
2
3
1
0
2
0
1
4
1
1
1
0
3
1
0
0
2
0
0
2
0
2
1
1
2
3
1
2
2
0
1
1
0
2
0
1
2
3
1
3
3
1
4
0
1
0
2
2
0
1
1
0
1
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
0
3
1
1
0
2
2
1
2
3
1
1
1
0
0
1
0
2
0
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
4
1
1
1
3
6
0
4
1
1
3
0
1
0
1
1
1
2
0
2
3
0
5
2
0
1
2
1
1
0
1
1
4
0
2
3
2
0
0
2
2
1
2
2
1
1
2
1
0
0
0
2
1
2
0
2
3
1
1
1
2
2
2
1
1
0
2
1
0
1
0
1
0
2
1
1
3
2
0
3
3
0
0
1
0
1
1
2
0
3
0
0
1
1
0
2
0
2
0
3
0
3
1
0
2
2
2
2
3
1
0
1
0
1
0
2
0
4
1
1
1
5
1
0
1
0
2
0
3
2
0
1
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
0
0
5
0
0
2
1
3
2
1
0
2
1
0
1
2
1
2
1
0
1
3
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
4
2
2
0
0
1
0
0
1
1
1
1
0
0
2
2
0
2
2
0
1
0
2
0
1
0
1
0
2
0
0
2
2
2
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
0
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
2
4
1
4
0
1
2
0
1
2
1
1
1
1
2
0
0
0
2
2
3
2
1
3
3
2
4
0
2
0
0
3
3
0
0
2
1
1
1
2
0
1
0
0
0
3
2
2
1
2
2
1
0
0
4
1
2
0
0
1
0
1
4
3
0
2
1
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
1
1
0
1
1
2
1
0
0
0
2
1
0
1
1
2
0
2
1
1
0
0
3
0
0
0
1
2
0
0
2
2
1
0
2
2
3
1
1
1
3
1
0
1
2
1
0
0
0
4
1
0
2
5
0
1
3
0
0
0
3
0
1
3
0
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
1
1
0
0
1
1
0
0
2
0
0
0
1
2
1
4
1
1
3
2
2
1
1
1
0
2
0
1
2
2
2
1
1
0
2
1
0
1
0
2
2
0
2
2
1
1
0
2
0
2
1
2
0
0
1
1
2
1
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
1
1
2
0
0
0
0
2
0
4
1
2
3
2
0
1
2
1
0
0
4
0
4
3
2
2
1
2
0
4
1
0
0
2
1
3
0
3
3
2
4
1
2
0
2
1
0
1
1
1
0
2
0
0
3
1
0
2
1
3
1
3
0
1
1
1
2
1
0
1
0
0
1
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
5
1
1
2
0
2
1
3
1
2
0
2
1
0
1
0
3
0
2
1
2
0
2
2
1
0
1
0
2
0
1
3
4
3
1
1
0
0
1
1
0
3
0
2
1
1
0
0
1
1
0
0
3
0
0
2
0
1
1
1
1
3
0
0
3
3
2
1
2
2
0
0
2
1
0
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
0
1
1
3
1
4
1
2
0
0
0
1
1
0
1
4
2
0
0
0
0
2
2
0
1
0
2
0
2
0
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
2
0
0
0
4
2
0
0
1
0
0
2
4
3
1
2
0
5
0
0
4
2
1
3
1
0
0
1
2
1
1
1
2
0
1
0
0
2
2
1
1
3
0
1
3
0
1
0
0
4
3
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
4
1
0
1
1
3
2
0
2
4
1
1
0
2
2
0
1
1
0
0
2
1
1
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
0
0
0
0
0
0
0
5
4
0
2
2
2
1
3
0
1
0
2
0
2
1
6
2
1
1
0
2
3
4
1
0
0
0
0
0
1
7
2
1
3
0
2
0
2
2
0
0
1
1
0
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
2
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
1
1
0
0
4
3
0
0
3
0
0
2
3
1
1
2
2
1
2
0
0
0
1
0
0
0
0
1
0
1
2
3
1
0
0
0
4
1
0
0
1
0
0
2
1
1
1
1
2
6
0
5
2
0
0
1
0
1
1
2
3
2
0
3
0
0
1
2
2
0
2
0
1
2
0
2
0
2
1
0
0
0
4
0
3
1
1
1
1
1
0
0
1
3
0
1
0
0
2
1
1
0
0
5
0
1
1
0
2
0
0
2
2
3
1
3
0
2
0
2
0
1
1
3
1
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
2
0
0
1
0
2
2
2
2
3
1
1
0
0
1
0
0
3
0
2
0
0
2
0
0
0
1
3
0
0
0
2
1
1
0
1
0
0
0
0
1
1
2
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
1
0
2
3
3
3
0
2
0
2
2
2
1
3
4
0
0
3
0
0
1
1
2
2
0
0
2
1
2
1
1
0
1
3
0
3
2
1
0
0
1
0
0
5
0
2
1
0
2
2
3
1
2
1
1
1
2
3
2
1
0
0
0
1
0
2
1
1
0
2
0
0
0
1
0
3
0
0
1
1
0
1
0
3
1
0
0
2
1
2
0
2
2
0
2
1
3
1
1
1
0
0
1
0
0
4
0
0
2
2
1
3
1
3
0
1
3
3
1
1
1
1
0
5
0
0
1
0
1
0
3
0
1
2
2
0
1
0
1
0
4
0
1
1
2
0
0
0
0
2
3
0
1
2
0
0
1
1
1
1
3
0
2
2
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
3
0
1
0
2
1
0
1
2
0
0
3
2
0
0
2
1
0
2
1
2
2
1
0
1
2
1
1
0
1
0
1
3
4
1
2
0
2
3
0
0
2
0
0
0
1
1
2
1
0
1
0
3
0
1
0
1
4
1
2
3
0
1
1
2
1
1
2
1
1
3
0
2
0
1
2
2
2
1
1
1
1
0
0
3
0
1
2
2
2
1
4
2
1
1
1
0
2
5
0
2
0
0
2
0
3
0
0
2
1
1
2
2
1
2
2
0
0
3
1
4
0
2
1
0
1
0
1
2
2
2
0
1
0
2
0
1
0
0
4
1
0
1
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
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
1
0
1
0
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
0
0
0
2
2
0
0
0
2
0
0
2
1
1
0
2
1
0
3
0
2
1
3
0
1
3
1
0
3
4
0
0
3
1
0
0
0
0
1
1
2
0
3
0
0
4
2
1
1
2
1
0
1
2
2
1
1
2
1
1
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
1
1
0
0
2
3
1
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
0
0
1
4
1
1
3
0
0
1
0
1
3
0
0
1
2
0
1
1
1
0
0
0
1
0
2
1
4
2
0
1
0
2
0
2
1
0
0
2
0
2
0
4
2
0
0
1
0
0
2
0
1
1
4
0
0
4
0
3
2
2
0
1
0
0
0
3
0
1
2
0
2
1
2
1
2
2
2
3
1
1
0
0
1
0
0
1
2
2
2
4
1
2
3
1
2
3
2
2
1
2
3
0
3
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
1
2
0
1
0
0
0
0
1
2
1
2
1
2
3
1
1
2
3
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
0
1
2
2
2
0
0
0
2
1
0
1
0
1
0
2
0
0
3
5
2
1
0
1
1
0
2
2
0
3
1
1
1
0
2
0
0
0
2
3
0
3
2
2
0
1
2
0
2
3
1
0
3
0
2
3
1
2
5
4
5
1
1
0
4
0
0
2
0
1
1
0
1
0
1
2
2
3
1
1
3
2
2
4
0
1
1
0
3
2
2
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
2
1
1
2
1
2
1
1
0
1
1
2
0
1
0
0
0
2
0
0
1
2
1
1
1
1
0
1
1
1
0
0
1
3
1
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
3
1
0
0
1
0
1
3
1
0
0
1
1
0
1
2
0
0
3
1
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
3
1
2
1
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
4
0
4
0
0
4
0
1
0
2
1
2
1
0
1
0
1
0
0
1
0
4
0
3
2
1
0
1
0
1
3
2
4
3
1
0
2
2
0
1
1
0
1
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
0
0
1
1
1
3
0
0
1
0
2
1
2
0
2
0
0
0
2
1
1
4
2
1
0
0
3
2
1
0
1
0
0
3
0
0
1
2
0
0
1
2
0
6
1
2
1
0
1
0
3
1
2
0
2
2
4
0
2
1
1
1
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
1
0
3
2
3
0
2
0
1
0
0
0
2
0
1
2
0
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
1
0
3
0
0
1
0
2
1
0
2
2
2
0
1
0
1
0
1
0
0
0
0
1
4
1
0
0
1
1
1
3
1
1
2
2
1
0
0
1
1
0
0
1
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
4
1
1
0
1
1
1
4
0
2
1
2
4
0
0
1
0
4
0
1
3
0
0
1
1
2
1
2
0
1
1
0
0
1
3
0
0
1
3
0
0
1
1
3
0
1
2
0
2
0
0
1
2
0
1
0
2
1
0
2
1
2
1
0
0
0
1
1
1
4
0
1
1
2
0
0
1
0
0
0
5
1
0
0
0
1
2
0
0
0
0
0
1
3
0
0
1
2
1
1
1
1
0
3
1
4
1
0
2
0
0
1
0
1
0
3
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
5
0
1
1
1
2
0
3
1
0
2
2
3
0
0
1
1
1
1
0
1
2
0
0
2
1
2
1
0
0
0
3
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
1
2
3
1
1
0
1
2
1
0
2
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
0
0
1
3
2
1
1
0
0
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
3
2
1
0
4
0
0
0
2
2
0
1
0
2
0
3
3
1
0
0
1
1
0
1
0
2
0
1
0
0
0
6
1
0
3
2
1
0
0
1
2
1
1
1
1
1
3
1
0
1
0
0
3
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
2
0
1
0
1
3
1
2
2
0
2
1
0
0
3
0
0
1
0
1
1
1
1
0
0
1
0
0
3
3
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
3
1
0
0
1
1
2
2
0
0
0
0
1
0
1
5
0
1
3
0
1
1
0
0
1
2
2
1
2
1
4
0
0
0
0
2
3
0
1
0
1
3
2
2
1
1
1
0
1
1
4
0
2
0
2
1
0
1
0
2
2
3
0
0
1
0
1
0
2
1
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
3
2
1
3
2
0
0
2
0
0
0
1
3
0
4
1
0
0
0
2
3
3
0
2
1
0
1
0
0
3
0
2
3
1
1
2
2
1
2
2
0
0
0
0
1
1
0
1
2
1
4
1
1
0
0
0
0
4
2
0
1
2
1
0
0
0
1
4
2
1
0
0
1
2
2
1
0
1
2
1
0
1
1
2
2
1
1
1
0
0
1
2
2
0
1
3
0
1
1
0
1
0
1
1
2
1
3
1
0
3
0
1
0
0
2
0
3
1
2
1
1
1
1
1
0
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
0
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
1
0
0
1
1
0
0
0
1
0
1
2
1
1
0
4
0
4
2
0
1
0
2
1
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
0
0
0
0
1
3
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
1
2
0
1
0
1
1
3
2
2
2
0
4
1
0
1
2
2
0
0
0
1
2
3
0
1
1
0
1
3
0
0
3
3
0
1
0
0
1
1
2
2
0
1
1
2
3
1
0
0
1
3
5
0
2
0
1
0
0
2
0
1
4
0
1
0
1
1
1
1
3
0
1
1
2
3
2
1
2
1
0
1
3
2
1
3
0
1
1
2
0
0
1
0
0
0
0
2
1
0
1
3
0
3
0
2
1
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
3
4
0
2
3
0
1
2
3
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
0
3
2
1
0
0
0
2
0
0
0
0
2
0
4
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
2
1
2
1
2
1
1
3
2
1
0
2
0
1
1
4
0
0
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
0
0
1
0
0
3
1
2
1
3
1
0
0
0
1
0
1
0
1
1
1
0
1
2
2
0
0
0
2
0
0
2
1
2
1
0
1
0
0
1
3
1
0
2
2
0
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
4
0
0
1
1
0
2
1
1
1
1
3
0
0
1
0
1
1
1
0
0
0
2
1
0
1
1
0
3
1
1
2
0
2
0
0
0
1
1
4
1
0
0
0
4
0
2
1
3
1
1
2
0
0
0
1
1
0
1
1
1
0
2
0
5
1
2
1
1
0
1
1
0
0
1
1
2
0
1
0
2
0
1
0
2
0
1
2
2
1
1
0
0
2
3
3
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
1
2
0
1
2
1
1
0
0
0
2
2
1
0
2
0
1
2
2
1
0
3
0
1
1
1
1
1
0
0
3
0
2
0
1
1
1
4
1
0
3
1
4
0
3
0
0
1
1
0
1
0
3
0
1
0
0
3
0
1
2
4
3
3
0
1
0
1
2
1
0
0
0
1
0
3
0
3
3
2
0
2
1
0
0
0
0
1
1
0
2
2
2
2
1
1
1
0
1
1
4
0
1
0
1
2
0
2
0
0
1
0
2
0
2
4
0
0
0
0
0
0
1
2
1
1
1
0
0
3
2
0
0
1
1
0
2
1
2
1
0
2
2
0
1
0
2
1
2
1
0
0
1
3
0
3
0
2
1
1
1
2
1
0
2
2
1
1
1
0
2
1
0
0
2
1
1
1
3
3
1
1
1
0
2
1
3
1
2
4
0
0
0
0
3
2
3
1
1
2
1
0
5
0
1
2
2
1
3
2
1
0
0
0
0
0
2
1
1
4
1
1
2
0
1
0
0
0
4
0
0
0
1
2
1
2
2
0
0
2
0
1
0
3
0
1
0
3
0
3
0
0
2
0
2
1
2
2
3
2
4
1
0
3
2
1
0
0
2
2
3
2
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
2
3
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
3
1
1
0
1
0
0
0
1
2
0
1
1
4
2
1
1
2
3
0
1
0
0
1
1
0
0
0
2
2
0
4
1
0
1
4
0
1
1
1
1
1
2
0
1
1
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
2
0
0
1
0
2
1
0
4
2
3
0
1
0
1
1
0
2
3
0
2
1
0
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
4
3
0
1
1
4
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
1
3
2
2
2
0
0
1
0
0
2
1
0
1
1
0
1
4
0
2
0
0
4
2
1
0
0
1
0
1
3
1
1
1
0
1
0
1
0
2
2
0
0
0
3
4
1
1
1
0
0
0
1
1
2
0
1
2
1
3
0
1
2
1
1
0
2
1
2
1
1
1
0
1
0
0
0
2
0
0
1
1
1
2
1
4
0
2
0
0
1
1
1
0
0
0
1
0
3
0
1
0
1
1
2
2
2
0
2
2
3
0
2
2
0
0
1
1
0
0
2
0
1
1
1
0
0
3
2
1
0
3
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
1
0
1
1
2
0
0
5
0
0
1
2
1
2
0
0
0
0
3
0
1
2
2
1
2
2
2
1
0
0
0
4
1
0
6
1
0
1
1
2
2
1
2
1
0
1
0
5
3
2
0
3
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
2
0
2
3
1
0
2
1
2
0
0
2
0
2
1
1
3
2
3
0
4
1
1
0
2
0
1
0
3
2
0
0
0
2
2
2
1
4
1
2
2
1
2
3
1
1
1
0
0
2
0
1
0
0
1
4
0
0
2
1
0
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
1
0
1
3
1
1
2
0
0
0
1
3
2
0
1
0
3
0
1
1
0
0
0
0
2
1
0
1
1
1
1
0
1
0
1
1
1
3
0
1
1
2
2
0
3
5
0
4
0
1
0
2
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
6
1
3
1
0
1
2
2
1
3
0
1
0
2
1
0
3
0
0
0
2
0
0
0
1
2
2
1
1
4
0
4
2
0
0
1
0
1
0
1
1
1
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
3
2
1
0
2
1
0
2
1
0
2
1
0
2
0
2
1
1
0
1
4
1
1
0
0
2
1
0
1
0
3
1
0
2
0
4
0
1
0
0
3
0
0
0
0
1
1
0
2
0
2
1
2
3
0
1
1
0
1
2
0
0
0
1
2
0
0
1
3
0
3
2
5
1
1
2
1
4
0
3
1
0
1
1
0
0
1
0
1
0
0
0
0
2
3
0
0
0
1
2
0
0
2
2
2
2
0
0
2
0
2
1
3
1
1
2
1
0
0
0
3
0
4
1
0
1
3
0
0
0
0
0
0
0
1
1
2
1
0
1
2
1
0
1
2
1
1
1
3
0
1
1
2
1
1
2
2
0
1
0
0
2
0
1
1
0
3
1
0
2
1
1
3
1
0
1
1
1
2
1
0
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
2
0
2
0
1
4
1
0
0
1
1
0
1
1
1
2
1
2
4
3
1
0
2
0
1
1
1
1
0
2
0
0
0
0
1
2
0
0
1
2
1
3
1
0
1
0
1
0
0
1
1
1
2
0
2
2
2
2
0
2
0
1
1
1
0
1
3
1
2
2
0
0
1
0
0
3
2
1
1
1
1
2
1
1
0
0
0
1
0
1
1
0
2
0
0
3
2
0
0
3
1
0
3
2
0
2
2
0
0
1
0
0
3
1
0
1
1
1
0
1
3
0
0
0
0
0
0
1
0
0
2
1
2
1
2
1
2
2
0
0
1
2
0
2
4
0
2
2
0
0
0
0
1
0
2
0
1
3
1
0
0
0
2
2
1
0
0
1
1
1
0
2
0
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
1
3
1
2
0
1
0
1
2
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
1
1
0
4
1
1
0
2
1
3
1
1
2
3
3
1
1
0
1
0
1
0
2
1
2
0
0
4
0
1
0
4
0
0
1
0
2
0
0
1
1
3
0
0
0
2
0
1
1
1
0
2
1
1
1
0
0
1
1
0
1
0
0
4
1
2
1
0
2
0
2
0
2
1
0
0
2
2
1
0
2
0
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
0
1
0
0
3
3
0
1
2
6
3
1
3
3
0
2
2
1
1
1
0
1
0
0
1
3
1
2
1
0
3
3
0
1
0
2
2
5
2
0
0
1
0
0
3
1
1
1
1
0
0
1
0
0
1
0
1
1
1
2
0
2
1
0
0
1
3
1
2
1
0
1
0
1
1
1
0
0
4
1
0
0
1
1
0
1
2
0
1
2
1
0
1
2
0
0
3
3
1
1
1
0
0
1
1
2
0
1
3
1
0
1
1
0
1
0
2
1
3
0
0
3
0
3
0
2
0
0
0
0
0
1
1
3
1
1
2
0
3
0
0
1
4
2
0
0
1
1
0
0
0
4
2
2
1
0
2
5
1
2
1
3
1
3
0
0
1
1
0
0
4
0
2
0
1
0
2
2
1
2
1
1
3
2
1
0
1
1
0
2
1
0
2
1
3
1
2
0
0
2
2
1
2
1
1
2
0
1
2
0
1
1
0
0
1
1
3
1
0
1
1
1
0
0
0
1
2
1
2
3
0
0
2
1
1
0
2
3
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
2
0
1
2
3
2
1
0
1
0
0
0
3
0
3
0
2
3
3
1
0
2
0
1
0
0
0
3
1
2
2
2
4
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
2
1
0
0
1
1
0
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
0
0
2
2
2
1
2
0
0
0
0
2
0
3
0
0
2
1
0
2
0
1
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
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
1
2
0
1
2
1
0
1
2
0
2
1
0
2
1
1
1
0
1
1
2
5
2
2
2
3
2
1
0
1
0
1
1
0
1
1
4
0
0
0
0
0
1
0
1
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
1
1
0
0
1
1
2
1
0
1
3
1
1
3
0
0
1
1
2
0
1
3
0
0
3
1
4
1
0
0
4
2
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
2
1
1
1
0
0
1
0
2
0
2
1
2
0
1
1
6
2
0
0
2
2
0
2
1
0
0
0
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
1
1
0
0
1
1
2
0
2
1
1
1
0
0
2
0
2
1
0
2
0
3
0
1
1
2
0
2
1
1
0
0
2
0
2
1
0
2
3
1
1
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
5
1
1
3
0
4
0
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
1
1
2
2
1
2
1
1
0
1
1
3
1
0
0
1
1
0
3
2
1
1
1
1
1
2
2
2
1
3
1
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
1
4
0
2
1
0
2
2
2
0
0
1
0
1
0
4
3
0
3
0
2
0
1
1
1
0
3
0
1
1
2
2
0
0
2
0
0
1
0
0
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
3
0
0
0
1
2
1
0
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
2
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
1
0
1
2
1
3
1
2
3
0
1
2
0
0
2
2
0
4
3
0
0
0
0
1
2
0
0
2
1
1
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
3
3
1
0
1
2
3
0
1
2
3
2
1
3
1
0
0
0
4
1
2
0
0
2
0
2
0
0
1
0
2
2
2
0
0
0
1
1
0
3
1
0
0
3
0
0
1
0
1
1
0
0
0
0
1
3
2
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
3
2
1
0
0
0
0
0
0
0
1
1
3
1
0
1
2
0
0
1
2
0
0
1
0
0
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
0
2
2
1
1
0
0
0
2
0
4
0
0
3
3
0
1
4
2
0
0
1
0
0
2
0
1
1
0
1
4
2
1
0
1
3
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
0
1
0
0
1
1
1
0
2
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
0
1
0
1
3
0
3
0
0
4
0
0
0
0
0
1
0
0
2
1
3
2
0
2
2
0
2
0
0
0
5
0
1
0
0
1
0
0
1
1
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
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
0
1
2
0
0
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
0
2
3
1
4
2
1
0
0
2
0
1
1
1
1
1
3
0
0
0
0
0
0
2
2
0
0
0
1
0
2
4
0
0
2
2
3
0
0
2
2
0
2
3
0
0
0
1
0
1
0
0
1
3
2
0
1
2
1
0
0
1
0
2
0
0
2
0
0
2
0
2
1
0
1
1
1
1
1
0
2
0
3
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
1
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
0
2
1
3
0
1
1
0
2
1
0
0
3
1
0
0
0
3
4
2
0
1
2
2
3
1
0
0
0
0
0
1
1
1
2
2
1
2
1
3
1
0
0
2
3
3
1
0
0
1
0
2
0
3
1
2
1
1
1
1
1
1
2
2
0
3
0
0
0
2
0
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
1
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
1
0
3
1
1
2
5
2
1
3
2
1
0
3
1
4
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
3
1
1
1
0
1
2
0
3
1
0
0
1
1
1
1
0
3
2
2
0
0
2
1
1
2
0
4
4
4
1
0
0
2
0
1
1
1
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
3
1
2
1
1
1
1
0
1
0
1
0
1
3
0
1
0
1
1
2
1
1
0
2
2
1
1
2
0
0
0
1
0
0
2
3
2
1
0
2
0
0
2
1
4
2
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
1
1
3
2
0
1
0
0
1
2
1
0
3
0
2
1
1
0
1
1
0
1
0
0
2
0
1
2
1
4
1
5
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
2
0
0
1
1
1
2
3
0
1
1
1
0
0
0
4
1
1
2
0
2
0
0
1
1
3
1
1
2
0
1
2
1
0
1
1
1
2
1
0
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
0
2
1
0
0
1
0
0
2
4
1
3
0
0
2
1
3
2
1
1
0
0
0
3
0
0
1
1
0
1
1
1
4
0
1
0
3
0
0
1
1
0
2
2
1
0
0
0
1
1
2
3
0
1
0
0
2
0
0
0
3
0
1
1
2
1
0
0
1
0
0
0
4
4
1
2
2
1
2
0
3
0
2
0
2
2
1
2
3
0
2
0
1
3
1
0
3
1
0
0
1
0
1
2
1
2
2
1
0
1
0
0
2
0
0
1
1
1
1
1
0
0
0
1
0
1
2
3
0
0
3
1
0
0
2
1
0
2
0
1
0
1
1
0
0
1
1
1
0
0
1
2
1
4
3
0
1
0
1
0
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
0
1
1
0
2
1
0
0
0
1
2
0
2
2
2
0
3
1
1
0
0
0
1
0
1
0
3
2
0
1
1
1
0
0
1
2
3
2
0
2
2
1
0
2
1
0
2
1
3
1
0
0
1
1
1
1
1
0
1
1
3
2
1
0
1
0
0
1
0
1
0
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
0
1
0
3
1
1
3
1
0
1
0
2
1
1
2
2
1
4
2
1
0
0
0
3
0
1
1
1
0
0
1
2
0
0
0
4
2
0
1
0
1
0
0
0
0
3
0
1
1
0
1
1
0
1
4
0
2
1
1
1
0
1
1
2
1
0
1
0
2
0
0
0
0
1
2
2
1
0
1
2
2
1
2
1
0
2
1
0
0
2
1
1
2
1
0
3
3
2
3
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
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
1
0
0
1
0
0
0
0
1
2
2
2
0
2
0
2
0
0
1
0
1
1
0
3
1
1
2
2
0
0
0
0
0
0
1
3
0
0
3
2
1
1
1
3
2
0
1
2
2
0
1
0
0
3
1
0
2
1
0
0
1
0
2
1
2
2
1
1
0
1
1
1
0
0
1
0
6
0
1
1
0
2
0
0
0
2
1
0
1
1
0
1
0
1
3
1
0
0
0
0
4
6
1
1
0
2
1
0
2
1
2
2
0
1
2
0
3
0
0
1
3
0
2
2
1
0
3
3
0
1
2
0
1
0
4
0
0
0
0
2
2
0
0
2
1
2
1
0
1
1
1
2
0
0
1
1
5
0
3
0
1
2
2
0
1
0
0
2
0
2
0
0
1
2
1
2
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
2
0
1
0
1
2
1
2
2
1
1
0
0
0
0
0
0
1
1
1
0
1
3
1
2
0
1
1
1
0
2
0
0
2
0
2
3
2
0
0
2
1
1
1
1
0
0
1
0
3
2
1
0
1
1
0
3
1
0
1
2
1
2
0
1
2
0
1
1
0
0
2
1
0
1
1
3
1
1
0
1
0
2
0
2
1
1
2
2
0
1
4
1
0
1
2
2
1
0
1
1
2
1
1
0
0
1
2
0
1
0
2
1
0
1
0
1
0
0
0
1
0
2
0
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
0
0
0
0
0
0
1
1
0
1
1
1
1
0
3
3
2
1
0
0
1
1
0
1
0
1
0
2
4
4
0
1
0
0
1
0
1
1
1
0
0
0
1
3
0
0
0
1
0
1
1
0
0
1
2
1
0
2
0
0
0
1
0
4
2
0
0
0
1
1
1
1
1
1
0
2
0
2
2
3
1
1
3
1
0
2
0
0
0
0
2
2
1
0
0
1
3
0
3
0
0
4
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
3
2
1
0
1
0
2
0
1
1
2
1
2
0
0
2
3
0
1
3
1
0
0
0
0
0
2
1
0
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
0
0
0
1
0
0
0
0
5
1
3
1
3
2
0
0
2
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
1
1
1
1
0
0
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
1
0
0
1
2
0
1
0
2
1
1
0
3
2
1
0
1
0
3
2
4
2
0
0
0
1
1
1
3
1
0
2
1
0
0
1
0
4
0
0
0
4
1
2
2
0
1
3
0
2
0
2
0
0
1
1
1
4
1
3
4
1
0
0
1
2
0
1
1
1
1
1
2
1
2
2
0
3
0
2
1
0
1
1
1
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
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
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
3
1
0
3
0
0
2
0
1
1
2
0
3
3
1
1
0
1
1
2
3
1
0
1
1
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
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
2
1
2
1
2
1
1
0
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
2
1
1
4
0
2
1
5
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
0
1
1
0
0
0
0
1
1
0
1
0
4
1
0
0
0
2
0
0
0
0
3
0
1
2
0
2
0
0
2
0
1
0
0
0
0
3
0
1
2
1
1
1
1
2
1
0
3
0
0
2
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
1
0
3
1
1
2
4
1
1
1
1
0
0
4
1
1
1
2
1
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
2
1
0
3
1
2
0
1
0
0
2
6
1
0
1
0
1
1
1
1
1
2
3
2
0
2
2
0
0
2
1
1
2
0
3
2
0
0
2
0
0
0
1
2
0
2
0
2
0
2
1
1
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
2
2
2
0
1
0
2
2
0
2
2
2
0
0
2
0
1
1
2
0
0
3
0
0
0
1
2
2
2
2
1
0
3
2
0
0
0
0
2
0
3
0
2
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
2
0
0
2
1
1
0
1
2
2
1
3
2
4
1
1
1
1
1
1
0
1
1
4
1
1
2
3
0
1
0
0
0
0
0
2
3
0
1
2
0
0
0
2
0
0
5
0
5
0
0
1
1
0
1
1
1
2
1
0
4
1
0
1
2
4
1
0
3
2
1
0
0
0
0
1
0
3
1
0
1
1
1
2
2
0
0
1
2
1
3
0
1
1
0
1
2
0
1
1
1
3
1
2
0
0
1
0
1
1
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
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
3
2
0
0
1
0
1
1
1
5
0
0
2
2
1
0
1
1
0
0
1
1
0
2
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
2
1
0
1
1
0
0
1
0
2
1
2
0
0
1
0
2
2
1
0
0
0
2
1
3
0
2
0
5
0
1
2
1
2
0
0
0
0
0
3
2
0
2
0
2
0
1
0
0
2
1
3
1
5
0
0
1
2
2
0
1
0
0
3
2
0
0
1
0
0
1
1
0
2
1
0
0
1
1
1
0
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
1
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
0
1
0
1
2
1
1
3
0
3
5
2
1
1
0
1
1
0
0
0
2
0
0
1
2
2
0
1
2
0
2
0
1
1
1
3
0
2
0
1
0
0
1
2
0
1
0
1
0
1
0
1
2
2
1
1
0
0
0
0
3
3
0
1
2
3
1
1
0
0
0
2
0
0
1
1
1
1
3
2
0
1
1
2
0
5
0
0
0
0
1
2
0
0
1
1
0
1
1
0
1
2
3
0
2
0
1
3
2
0
0
0
0
1
2
1
0
0
1
0
4
0
0
0
1
1
1
0
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
2
0
1
0
0
1
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
2
5
1
2
0
0
2
1
1
1
3
2
0
1
0
4
1
1
2
0
2
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
3
0
2
1
0
1
1
0
1
1
0
0
4
2
0
2
0
2
1
0
2
1
2
2
0
0
0
0
1
0
3
1
2
0
3
1
2
1
1
0
2
0
1
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
3
0
0
0
1
1
0
0
1
1
3
0
0
0
1
0
1
1
0
4
1
0
2
2
0
0
0
0
0
1
0
3
2
0
1
1
1
1
1
1
2
0
3
1
2
1
0
2
0
0
1
2
1
0
0
1
1
0
5
1
0
0
2
2
0
3
0
0
0
1
0
1
0
2
1
1
0
1
0
2
0
0
0
1
1
2
2
1
0
0
0
0
0
2
1
2
2
1
2
0
1
1
1
1
0
1
4
1
0
1
0
1
3
0
0
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
2
0
0
2
2
2
1
1
2
2
0
0
1
0
1
0
2
0
1
0
0
1
1
0
2
0
3
0
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
4
0
0
1
2
0
1
1
4
2
1
1
3
0
0
1
4
2
3
1
2
2
0
1
0
1
0
0
0
0
0
2
1
2
1
2
1
0
1
2
2
0
1
2
0
2
3
2
0
0
1
0
1
3
3
1
0
1
1
0
0
1
0
0
0
0
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
1
2
0
2
0
1
1
0
1
0
1
1
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
1
0
1
0
0
0
1
2
0
0
2
0
0
2
1
2
0
4
2
0
0
0
2
0
2
0
1
0
1
1
3
0
0
0
2
0
1
0
2
1
1
1
1
1
0
0
3
2
0
1
1
2
0
0
0
1
0
1
0
4
1
3
2
1
2
2
0
0
0
0
0
0
0
0
4
1
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
0
0
2
1
1
0
0
0
0
1
1
0
3
2
0
1
0
1
0
0
1
0
1
1
1
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
4
0
0
0
1
0
2
0
0
1
1
2
1
0
3
0
1
1
2
0
0
0
0
2
0
0
1
2
0
1
2
1
0
1
2
3
0
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
5
1
0
4
1
0
1
0
2
0
0
2
0
2
0
2
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
1
1
2
1
1
1
2
0
0
1
0
0
0
0
2
3
1
0
0
1
2
0
1
0
1
1
0
0
2
1
3
0
2
2
1
0
0
1
1
0
0
2
1
1
1
0
1
1
4
2
1
1
0
2
1
2
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
0
5
0
1
0
1
0
0
1
2
1
0
2
3
0
1
0
0
1
0
1
0
0
1
0
0
3
1
0
0
1
0
0
1
1
0
0
1
0
0
1
2
1
0
3
2
1
1
2
0
1
0
1
1
2
0
2
2
3
2
0
0
4
0
0
1
1
3
0
0
1
0
0
2
1
0
3
2
4
1
1
1
1
0
2
2
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
0
0
3
1
1
1
0
1
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
3
1
0
0
1
0
2
0
1
0
0
4
1
0
0
0
1
1
0
0
0
3
0
1
2
1
0
5
0
0
2
4
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
0
1
2
1
2
0
1
0
0
3
2
1
3
0
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
1
2
2
0
0
3
0
1
0
2
1
1
1
0
0
2
0
3
5
2
2
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
3
2
0
1
1
1
0
2
0
0
3
2
1
0
0
0
0
4
1
2
0
1
0
0
2
0
1
0
3
2
6
0
0
0
2
1
3
0
0
2
0
1
3
1
0
1
2
0
0
0
1
3
2
2
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
1
0
0
0
1
0
0
2
0
1
0
3
1
4
0
3
2
1
1
2
2
1
1
1
0
2
0
3
1
0
1
0
2
2
0
0
1
1
0
1
2
0
0
1
2
0
2
1
3
0
2
0
1
3
1
0
0
0
2
1
0
0
0
0
1
4
0
0
0
2
0
1
1
0
2
0
1
2
0
2
0
0
1
1
0
1
3
2
1
3
0
0
1
1
0
0
1
1
0
2
0
2
0
1
2
0
0
0
1
0
3
1
1
2
2
0
1
2
2
0
2
4
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
0
0
1
2
1
3
3
0
1
5
0
0
0
1
0
2
0
0
0
3
0
1
0
1
3
0
1
1
1
0
0
1
3
1
0
1
1
1
1
0
3
0
0
1
3
0
0
1
1
3
1
4
0
1
0
1
0
1
1
2
1
2
0
0
0
0
1
0
1
4
0
3
2
2
1
0
0
3
1
1
1
1
1
2
1
2
2
1
0
1
0
0
0
2
1
1
0
0
1
3
0
0
1
0
0
1
1
4
0
2
0
2
0
4
0
0
0
1
0
1
0
1
5
1
0
1
1
2
2
2
0
0
1
1
0
1
1
0
0
1
1
2
0
3
0
2
2
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
0
1
2
1
2
1
0
1
0
2
0
0
2
0
1
0
1
0
1
3
1
1
3
1
2
1
0
2
0
3
0
2
1
0
0
0
0
0
3
0
0
1
1
0
0
2
1
1
0
0
1
0
3
0
3
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
0
1
4
1
1
0
0
1
1
3
0
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
2
1
0
2
0
1
2
2
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
2
0
0
2
0
1
0
0
0
4
2
1
1
0
3
0
1
0
0
1
0
0
0
1
2
0
4
2
1
2
1
3
0
0
1
1
0
2
1
2
1
1
0
0
0
3
4
0
2
3
0
2
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
2
1
3
1
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
4
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
2
1
0
0
3
1
0
2
0
1
0
0
1
0
0
3
0
3
0
0
1
2
1
1
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
3
1
1
2
0
1
2
1
0
1
1
1
1
0
2
1
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
2
1
0
2
0
0
1
1
0
2
3
1
1
1
1
1
0
2
0
3
2
0
1
1
1
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
3
3
2
0
2
1
2
2
1
2
0
1
0
0
1
0
3
2
3
0
0
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
0
2
1
1
0
3
0
0
0
2
3
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
3
0
0
2
0
2
3
0
1
1
1
1
0
3
0
2
3
0
0
1
1
0
4
1
1
1
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
1
0
3
0
0
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
1
2
0
2
0
2
4
0
1
2
0
0
2
0
0
1
1
0
1
0
3
0
1
1
1
1
0
0
1
0
1
1
0
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
1
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
0
0
1
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
0
0
0
1
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
2
1
0
0
0
1
0
1
3
0
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
4
3
1
4
0
0
2
0
1
1
1
0
3
0
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
0
0
0
0
1
0
0
1
0
3
3
0
0
0
1
0
3
0
0
1
1
2
0
1
1
0
1
2
1
0
2
1
1
0
2
2
0
0
2
3
0
2
1
2
0
1
1
1
0
0
1
0
0
0
1
3
1
1
0
0
0
0
0
1
1
2
0
0
3
3
0
2
1
0
3
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
0
0
0
3
1
1
3
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
1
1
0
3
1
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
2
1
2
2
1
0
0
0
1
0
0
1
4
0
0
1
3
0
2
3
1
0
0
1
0
4
2
0
3
2
0
0
0
1
0
0
0
1
0
0
2
3
0
2
1
0
0
0
2
1
1
1
1
3
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
4
0
1
0
2
2
0
0
3
0
0
2
2
0
1
1
0
1
3
0
0
4
0
0
2
2
1
0
0
0
2
1
0
2
3
2
0
1
1
0
1
1
0
1
0
0
0
2
1
1
0
1
2
1
4
1
1
1
1
1
3
1
0
0
0
0
0
1
2
0
1
3
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
1
3
0
3
1
0
1
0
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
3
1
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
0
2
0
0
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
1
1
2
0
1
0
2
1
2
1
1
0
0
1
2
2
0
2
1
0
1
1
1
0
0
0
2
1
0
2
0
1
1
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
2
3
1
2
0
0
0
1
1
0
0
0
3
3
1
1
0
1
1
1
0
1
4
0
1
0
0
4
0
0
2
1
0
0
0
1
1
0
2
2
1
0
1
0
0
1
0
2
0
2
0
0
3
0
2
1
2
1
0
1
1
0
0
0
1
1
1
0
0
2
1
0
1
1
2
2
1
0
2
1
1
2
1
0
2
0
1
2
0
0
2
0
0
0
1
1
0
0
2
2
1
1
1
0
2
3
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
2
1
0
0
1
1
0
0
0
3
1
0
1
0
2
0
0
2
1
1
0
2
1
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
3
0
1
0
2
0
2
3
0
1
2
0
0
1
0
0
2
0
0
1
2
2
1
0
0
1
0
1
0
2
0
1
1
1
1
0
0
2
3
1
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
1
1
3
3
0
0
0
0
0
2
1
0
1
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
3
1
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
3
0
3
3
2
1
1
1
0
1
1
1
4
1
0
2
1
1
3
2
2
0
1
1
0
1
1
1
0
0
0
2
1
1
0
1
0
1
2
0
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
3
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
3
0
1
1
0
1
0
0
0
0
0
1
0
0
1
3
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
4
2
0
2
1
2
0
2
1
0
0
1
2
2
0
1
0
0
0
0
3
0
0
2
0
2
1
1
2
2
2
0
0
2
0
0
1
0
0
1
0
0
2
2
1
3
5
0
2
0
1
0
2
5
3
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
0
2
1
0
0
0
1
1
0
0
1
2
1
0
0
2
1
2
1
0
0
0
0
0
1
1
1
2
1
2
2
0
2
0
2
0
1
0
0
0
1
0
0
2
1
1
1
2
0
1
1
2
0
1
2
0
1
0
0
1
0
1
4
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
1
1
2
0
0
0
1
1
0
2
1
3
2
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
2
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
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
2
1
1
0
0
3
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
5
0
3
0
3
1
2
1
0
4
0
0
0
0
1
1
2
1
0
2
0
0
1
2
2
1
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
1
0
0
4
4
1
1
3
2
2
1
3
1
0
0
2
1
0
2
0
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
0
0
3
1
0
0
1
1
0
0
0
0
0
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
1
1
2
0
1
1
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
2
1
2
0
3
2
2
0
1
0
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
1
0
3
1
2
1
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
0
3
1
2
1
1
0
1
0
0
2
2
1
1
1
1
2
2
1
0
2
1
0
2
2
0
0
0
0
0
1
1
1
2
0
2
1
2
0
1
1
0
0
2
0
1
1
0
1
0
0
2
1
1
1
0
3
1
1
0
1
2
0
1
1
0
2
1
0
1
1
1
0
1
1
2
1
0
2
2
0
0
0
0
1
1
4
0
1
0
2
3
0
0
0
1
0
1
1
1
1
0
1
3
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
2
1
2
1
1
1
1
0
1
1
0
2
0
0
0
0
2
1
1
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
3
2
0
1
0
0
2
3
2
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
2
2
0
3
0
0
2
1
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
0
2
1
0
1
0
2
1
1
1
0
2
0
2
0
0
3
1
0
3
0
0
0
1
0
0
2
1
2
0
2
0
0
0
1
1
4
1
1
2
0
1
2
1
1
0
1
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
2
0
3
0
0
0
2
1
2
2
0
0
0
3
0
0
0
1
1
0
4
4
0
1
6
0
0
1
0
0
1
1
0
1
1
0
1
0
0
3
2
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
3
2
2
0
1
1
0
0
0
0
1
0
0
2
1
3
1
0
1
3
1
1
0
0
1
0
1
1
1
0
2
2
2
1
1
1
2
0
0
1
1
3
2
0
1
0
1
2
2
0
4
0
1
0
1
1
1
0
3
1
0
0
1
0
0
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
1
2
3
0
0
1
2
1
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
0
1
0
1
0
1
1
0
0
0
4
0
0
0
2
0
0
1
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
0
1
1
1
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
3
1
0
1
1
0
0
0
1
0
1
0
1
0
3
0
1
1
1
0
0
1
0
1
3
4
1
2
2
0
0
1
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
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
1
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
1
1
1
0
1
0
3
2
1
1
0
3
0
1
1
0
0
2
0
2
1
2
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
3
2
1
0
0
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
2
1
0
1
1
1
0
1
0
4
2
0
0
0
0
2
3
1
0
1
1
1
0
0
3
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
0
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
1
0
0
2
1
1
0
0
1
3
0
0
0
0
1
1
0
1
1
3
0
1
2
0
0
0
0
0
0
0
1
2
0
0
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
1
0
2
2
1
0
0
1
3
1
0
2
1
1
1
1
0
1
1
1
0
1
3
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
2
2
0
3
1
2
1
1
1
4
2
2
1
0
1
1
0
0
3
1
2
1
1
0
0
1
0
1
0
0
5
2
0
1
3
3
0
1
2
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
2
0
2
2
2
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
3
1
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
2
0
1
0
2
0
3
0
0
1
1
2
1
1
1
3
1
0
2
0
0
3
2
0
0
0
1
1
2
0
0
0
2
0
3
1
2
2
0
0
1
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
3
0
2
0
0
0
3
1
0
0
0
0
2
0
0
3
1
0
4
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
2
0
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
1
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
1
0
0
2
0
1
2
1
1
0
2
1
1
1
2
1
2
0
1
4
2
1
2
0
1
0
2
2
1
1
2
0
1
2
2
0
0
0
1
0
0
0
2
3
1
3
1
1
1
0
0
0
0
1
1
1
3
1
0
3
1
0
0
1
0
1
0
0
4
1
0
1
1
1
1
2
2
3
1
0
5
1
1
1
0
0
3
2
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
2
1
1
3
2
0
0
1
0
0
2
2
1
4
2
1
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
0
0
0
3
0
2
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
2
4
1
1
2
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
3
1
2
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
3
2
1
0
0
2
2
0
0
0
0
2
4
0
2
0
0
2
1
3
1
1
1
1
2
1
2
1
0
0
0
0
2
2
1
0
0
4
1
4
0
3
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
4
0
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
2
1
3
1
1
1
2
0
0
0
1
4
1
0
1
1
0
0
3
1
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
2
0
1
0
0
2
1
0
1
0
1
1
2
0
3
0
2
4
0
0
0
1
1
0
0
0
1
2
1
1
1
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
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
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
2
1
0
1
2
0
0
1
0
2
1
2
2
1
0
0
0
0
1
1
2
2
0
0
1
0
4
4
0
1
0
1
1
0
1
1
2
2
2
1
1
0
0
0
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
0
0
0
2
0
2
1
0
2
0
3
1
0
0
1
1
0
2
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
3
0
1
1
2
4
0
0
0
1
1
2
0
2
0
2
0
0
0
1
2
0
0
0
1
0
1
3
0
0
3
0
0
0
2
1
1
1
1
0
0
0
0
3
0
0
0
0
1
1
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
0
1
1
1
0
1
3
0
1
3
1
0
1
2
0
0
1
1
2
2
0
1
1
1
2
0
0
1
0
1
0
0
0
1
2
0
3
3
0
1
4
1
2
0
1
0
1
0
1
0
1
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
3
3
2
3
1
1
0
2
1
0
3
0
1
2
3
0
2
1
0
3
1
1
0
0
2
1
0
2
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
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
0
1
0
3
1
1
2
0
1
2
3
2
0
1
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
0
0
2
1
1
1
1
0
0
0
0
2
0
1
1
0
3
0
0
2
2
0
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
1
1
1
0
0
1
2
1
0
1
0
3
0
1
0
1
3
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
4
0
0
1
0
1
2
1
0
1
0
1
0
0
1
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
0
1
0
0
0
2
0
0
0
2
0
3
2
0
0
0
1
1
1
1
1
0
1
1
0
0
0
3
0
1
0
0
2
0
0
1
1
0
1
2
1
3
1
0
0
0
3
1
0
0
0
0
1
0
0
2
1
0
3
2
1
2
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
0
2
2
1
1
0
0
0
3
0
0
2
1
0
1
0
1
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
4
0
0
0
1
0
1
1
0
1
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
0
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
0
0
2
1
0
2
1
2
1
0
0
2
1
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
2
1
1
0
1
4
1
2
1
0
0
1
0
1
0
1
3
2
2
2
1
1
0
1
2
1
0
0
1
1
0
0
2
1
1
3
3
0
1
1
0
0
0
0
0
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
0
1
1
0
0
0
1
1
0
2
3
2
0
0
1
2
1
0
1
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
4
0
0
1
2
1
3
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
1
2
2
2
1
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
0
0
1
0
1
0
2
0
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
0
1
0
3
1
1
3
0
0
2
0
2
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
4
1
1
0
0
1
0
2
3
0
1
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
2
0
1
1
0
3
3
0
0
1
2
0
0
0
0
1
2
5
2
0
0
0
1
0
1
3
0
1
1
2
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
3
1
1
0
1
1
2
0
1
3
1
0
3
1
0
1
1
0
1
1
1
2
1
1
0
0
0
0
0
0
1
2
3
1
1
1
2
0
1
0
2
0
1
1
2
0
1
1
0
0
0
1
0
1
0
2
4
1
0
0
4
0
1
0
3
2
1
0
0
0
3
0
0
2
0
1
0
1
0
0
2
4
0
0
0
2
1
0
3
0
0
2
1
1
0
2
0
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
0
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
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
4
0
1
0
3
1
1
0
2
4
0
0
0
1
1
2
2
0
0
1
2
1
0
3
0
0
0
0
0
0
0
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
0
2
1
1
0
1
1
2
0
1
5
0
1
0
4
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
2
2
2
1
0
0
0
2
0
0
0
1
0
1
2
0
2
0
2
2
0
0
2
1
0
0
0
0
0
3
1
2
1
0
0
3
2
1
4
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
4
0
1
1
0
0
0
1
0
2
1
1
1
0
1
0
2
1
3
2
0
2
0
1
0
3
0
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
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
2
0
4
0
1
0
1
0
0
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
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
4
0
2
0
1
0
0
0
5
0
0
2
1
0
2
1
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
4
0
0
3
1
0
1
0
0
1
2
2
0
1
1
1
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
2
0
2
1
1
1
0
2
1
2
2
1
1
0
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
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
3
0
2
1
0
2
1
0
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
3
2
0
0
1
1
0
0
1
1
0
2
1
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
3
0
1
2
1
0
0
0
1
0
1
0
3
2
2
1
0
0
0
0
2
0
0
3
1
2
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
2
1
0
2
0
2
2
0
0
1
0
0
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
0
0
0
2
2
0
1
0
3
0
3
0
0
1
0
1
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
4
1
1
1
0
1
1
1
0
0
0
3
1
0
1
3
1
0
0
0
0
1
4
2
0
1
0
1
1
0
1
1
0
0
0
1
0
2
0
3
0
0
2
1
1
0
1
1
0
0
1
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
1
1
1
2
3
2
1
0
0
0
1
1
0
1
0
1
0
1
2
1
1
2
2
1
1
0
1
0
1
1
0
0
3
1
1
0
4
1
1
1
1
3
3
0
1
0
3
2
2
0
1
2
2
0
1
1
1
2
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
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
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
3
0
3
2
1
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
1
1
0
2
2
1
1
2
1
1
0
1
0
0
1
0
0
0
1
1
3
1
0
1
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
1
0
4
2
0
0
1
1
1
1
0
0
0
2
3
0
3
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
1
2
1
1
2
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
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
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
1
1
1
1
2
3
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
2
1
1
0
0
0
0
0
3
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
0
1
0
0
2
0
1
1
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
0
0
1
2
2
2
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
7
0
0
0
0
1
0
0
0
3
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
5
1
0
3
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
1
1
1
2
1
1
0
0
1
1
0
2
3
0
0
0
0
1
1
2
1
0
2
1
0
2
0
3
2
0
0
1
0
1
2
2
0
0
0
1
0
1
2
0
2
2
0
0
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
1
0
0
2
1
4
0
1
1
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
2
2
1
1
0
1
0
0
3
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
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
1
0
0
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
1
0
1
1
6
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
1
4
2
1
1
3
0
1
0
0
2
1
2
1
2
2
1
1
0
1
1
2
3
0
0
1
1
1
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
3
1
0
1
0
0
0
0
2
1
1
1
2
2
0
1
1
1
1
0
1
2
2
0
1
0
1
3
1
0
1
1
1
1
1
1
0
1
0
0
3
1
0
2
2
1
0
1
0
4
0
0
1
0
0
0
1
0
0
0
2
0
3
2
1
0
1
0
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
1
0
0
1
0
1
0
0
1
4
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
0
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
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
4
1
0
0
0
1
0
1
0
0
0
1
3
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
1
1
0
1
0
3
1
0
0
1
1
2
1
1
1
0
1
1
0
0
1
0
0
3
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
0
0
0
0
2
1
2
0
0
0
1
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
1
1
2
0
0
0
0
1
0
4
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
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
0
1
0
1
0
0
3
0
0
0
1
2
2
2
1
3
0
0
1
0
0
2
3
1
4
2
1
1
0
0
0
0
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
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
1
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
2
1
1
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
3
1
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
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
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
1
2
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
1
0
3
2
1
2
0
2
0
0
2
0
1
0
0
2
0
1
0
1
1
0
3
3
1
1
1
1
3
0
1
0
2
0
3
1
1
1
0
1
1
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
2
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
2
1
1
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
0
0
0
0
1
1
1
0
0
1
0
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
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
3
3
1
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
1
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
2
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
2
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
1
1
0
0
4
0
1
2
1
0
0
0
0
1
0
0
0
2
0
3
0
0
1
1
1
0
4
0
0
1
1
1
0
0
2
1
0
0
1
4
2
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
0
2
0
1
0
1
0
1
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
2
2
1
0
0
0
1
0
1
2
2
2
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
3
2
1
0
1
0
2
1
0
1
2
0
1
1
0
0
0
1
1
2
2
1
1
2
0
1
0
0
0
2
0
0
1
2
1
1
1
2
0
2
2
1
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
3
3
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
4
0
2
3
2
0
0
1
2
0
0
0
2
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
3
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
3
0
2
0
4
0
0
0
4
0
0
1
0
0
2
1
0
0
2
2
1
1
1
2
0
1
0
3
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
4
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
3
1
0
2
0
0
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
1
0
1
0
0
1
2
0
2
1
0
2
1
1
1
0
1
0
1
1
0
2
3
1
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
3
3
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
3
0
0
0
0
2
1
0
1
0
1
0
1
0
4
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
2
0
0
3
2
0
0
2
1
0
1
2
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
1
0
0
0
3
1
2
2
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
0
1
0
1
4
0
0
1
1
2
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
1
0
0
1
2
3
3
1
2
0
2
1
0
1
0
1
0
0
1
1
0
1
2
0
2
1
0
2
4
0
0
1
1
0
1
1
2
0
2
1
3
0
2
0
0
1
0
2
1
1
2
2
0
0
1
1
3
0
0
0
3
0
0
0
3
1
0
2
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
2
1
3
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
3
2
1
2
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
3
3
1
0
1
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
0
1
0
1
0
0
3
0
1
4
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
1
2
0
2
2
1
2
0
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
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
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
0
1
1
0
1
0
1
0
4
0
1
3
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
0
4
0
0
1
0
0
1
2
1
0
0
3
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
3
0
2
0
2
1
0
3
1
2
0
0
2
0
0
0
2
0
0
0
3
1
2
0
0
0
2
1
0
0
1
1
1
2
0
1
2
0
0
0
1
2
0
2
1
1
1
0
2
0
1
1
0
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
4
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
1
1
2
1
1
0
0
0
0
0
2
1
0
2
0
2
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
1
1
0
2
2
1
3
0
0
0
0
0
2
1
0
1
0
0
0
0
3
2
0
0
1
1
0
0
1
1
0
2
0
3
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
0
1
2
0
1
0
1
1
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
2
0
1
0
1
0
1
0
0
3
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
3
1
0
0
2
0
0
0
0
0
1
1
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
2
0
0
1
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
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
0
0
0
3
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
3
3
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
1
1
1
0
0
2
1
0
2
1
0
1
0
0
0
0
1
4
4
1
1
2
0
1
5
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
2
0
1
0
0
1
1
0
1
2
0
0
0
1
2
2
1
0
0
1
1
1
0
2
2
0
0
1
1
1
1
1
0
1
0
0
0
1
0
3
0
1
4
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
4
0
0
1
0
3
1
0
2
1
0
0
0
4
0
0
0
1
0
0
0
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
1
2
2
2
0
0
0
1
0
0
1
1
1
2
0
0
1
1
0
1
0
2
3
1
1
0
0
0
2
0
2
1
1
0
2
0
1
0
1
1
2
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
2
2
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
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
2
0
0
1
1
0
0
0
2
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
2
2
2
0
0
1
2
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
3
1
1
0
2
3
0
0
0
2
2
1
1
0
0
1
2
0
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
1
1
1
2
0
2
1
0
0
0
1
3
1
1
1
5
1
1
0
3
1
0
1
0
0
0
0
1
1
2
2
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
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
0
1
2
1
2
0
1
2
0
2
1
1
2
0
1
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
2
1
0
1
0
1
2
0
0
1
1
1
0
0
1
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
1
2
1
0
0
0
1
1
0
0
1
0
1
3
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
3
2
1
1
0
1
2
1
1
2
0
5
0
0
1
1
1
0
0
2
2
4
0
1
4
1
0
0
1
0
0
0
0
1
0
0
3
1
0
1
0
1
1
3
2
1
3
0
0
0
1
2
2
0
1
1
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
2
0
1
2
0
1
0
2
0
0
1
1
1
1
0
1
0
0
0
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
1
0
3
2
1
0
2
3
6
0
0
1
4
0
0
1
2
0
0
1
3
0
0
1
0
1
0
0
1
0
0
2
1
1
0
1
0
1
1
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
1
0
0
0
0
0
1
1
1
0
0
0
3
0
1
0
0
6
1
0
0
0
1
1
1
2
0
0
0
2
1
1
0
0
0
0
0
3
1
1
1
2
1
1
2
2
0
1
0
0
1
0
0
4
0
1
1
4
0
0
0
2
0
1
0
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
1
0
0
1
1
1
3
0
1
0
0
3
1
1
1
1
0
0
2
3
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
3
3
1
0
0
0
0
1
1
0
2
0
1
1
2
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
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
0
0
1
0
1
1
1
1
2
2
0
1
0
0
1
1
2
1
2
0
0
1
2
0
4
1
0
1
0
2
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
3
2
0
1
0
1
0
1
1
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
2
0
0
1
0
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
4
1
1
0
3
0
0
0
1
2
2
0
1
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
3
1
0
2
1
0
1
0
0
5
1
1
2
1
0
1
0
1
1
1
1
0
2
2
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
1
1
0
2
1
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
1
2
1
1
0
0
2
0
2
0
1
0
0
3
0
0
2
4
0
0
1
0
2
1
0
2
1
1
0
1
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
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
0
1
0
1
0
2
0
0
1
1
1
1
2
1
3
0
0
0
0
3
0
2
0
1
0
0
1
0
1
2
0
1
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
0
0
1
1
1
1
0
3
0
3
3
0
1
0
0
2
1
0
0
2
2
0
0
4
1
1
1
2
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
3
0
2
0
0
0
1
1
1
0
1
2
1
2
0
1
2
2
0
0
4
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
2
3
2
0
0
1
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
0
1
0
3
1
0
2
2
0
1
1
0
0
3
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
3
0
2
1
0
1
1
0
1
2
0
2
0
3
0
1
1
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
0
2
1
1
1
0
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
0
1
0
1
2
0
2
0
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
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
2
1
0
1
0
0
0
2
1
2
0
1
1
1
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
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
1
2
1
0
0
1
2
0
0
3
0
1
0
0
2
0
0
2
0
0
2
0
1
0
1
2
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
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
1
0
2
1
1
2
0
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
1
1
4
0
1
2
2
0
2
0
0
0
0
1
2
2
1
0
0
0
2
1
1
1
1
1
0
1
0
2
0
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
3
1
3
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
2
1
0
0
0
2
0
1
1
0
1
1
1
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
3
1
2
0
0
1
0
2
1
1
1
1
2
1
1
3
0
0
0
0
0
1
0
2
1
0
0
3
0
0
2
1
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
0
0
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
1
1
4
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
0
0
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
0
2
0
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
3
0
4
0
1
1
0
0
2
0
1
2
0
0
0
0
1
2
0
1
0
3
1
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
3
1
1
1
1
0
0
3
1
0
2
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
1
0
1
3
0
3
2
1
0
1
2
0
0
1
0
0
0
4
0
1
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
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
1
0
0
3
0
0
0
1
2
0
0
1
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
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
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
0
1
3
5
2
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
2
3
3
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
3
0
1
0
0
0
1
3
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
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
0
1
1
0
0
2
0
0
3
1
1
0
1
2
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
4
2
1
0
2
0
1
0
1
0
3
0
3
0
1
1
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
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
1
0
0
1
0
0
2
1
0
0
2
0
1
0
1
1
1
0
0
0
2
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
1
0
0
0
2
0
2
1
0
3
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
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
1
0
1
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
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
1
2
2
0
1
0
1
2
0
0
0
3
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
2
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
3
0
1
0
2
0
0
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
3
1
0
0
0
1
1
0
1
3
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
2
3
1
0
0
0
0
1
0
2
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
0
0
0
0
3
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
0
1
1
0
1
1
0
2
4
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
1
2
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
1
5
1
1
0
1
0
0
0
1
1
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
1
0
1
0
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
5
0
0
0
1
0
1
1
1
1
0
1
4
2
0
0
0
0
0
0
1
1
1
0
3
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
1
1
1
0
2
1
1
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
3
0
1
1
0
1
2
1
1
0
0
0
0
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
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
1
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
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
0
0
0
2
0
1
1
0
0
0
0
1
0
3
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
2
0
2
0
0
2
0
1
1
0
2
1
2
0
0
1
1
1
0
0
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
1
2
0
1
1
0
1
1
3
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
3
0
1
3
3
1
1
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
2
1
2
1
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
4
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
2
0
1
0
1
0
3
2
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
0
0
0
0
2
0
1
1
0
1
0
1
1
2
2
2
1
0
0
2
1
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
0
1
1
3
1
1
0
0
1
0
0
1
0
4
0
1
0
2
0
0
1
0
1
1
0
1
0
1
1
2
3
1
0
0
1
1
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
1
2
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
3
1
0
0
2
0
4
1
0
2
1
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
2
1
1
1
1
0
0
1
1
2
1
0
0
2
1
0
2
0
0
0
2
0
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
0
0
2
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
2
0
1
0
0
1
2
0
1
0
1
0
1
1
2
0
2
3
1
0
0
4
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
1
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
3
0
2
0
0
2
2
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
2
1
2
2
1
0
0
3
1
1
1
0
1
1
0
0
2
0
0
2
0
0
0
1
4
0
0
1
2
0
1
1
0
2
2
0
3
2
2
0
1
0
2
1
0
2
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
2
1
0
1
1
0
1
2
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
1
1
1
1
2
2
0
0
0
2
0
1
1
1
2
1
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
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
3
0
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
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
4
2
0
0
0
1
0
0
0
0
1
1
2
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
3
1
2
0
0
1
0
0
0
2
1
1
1
2
0
1
2
0
2
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
0
2
1
1
1
3
0
0
0
2
2
0
0
1
0
0
1
1
0
1
1
1
2
3
1
2
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
2
1
1
1
0
1
0
0
1
1
2
2
0
0
1
3
0
1
1
2
1
0
0
2
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
2
2
2
1
2
1
2
3
0
0
0
2
1
0
0
1
1
1
0
0
2
4
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
1
1
1
3
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
3
1
1
1
1
1
0
2
2
0
0
2
1
0
1
1
1
1
0
3
1
0
2
1
1
2
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
0
1
1
0
2
0
0
1
3
0
0
1
2
0
0
0
1
1
0
1
4
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
5
3
0
0
2
0
2
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
3
0
2
2
0
1
0
1
0
0
2
1
1
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
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
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
4
0
0
2
0
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
1
0
3
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
3
1
1
0
0
3
0
3
0
0
0
1
0
0
1
0
0
1
0
3
1
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
2
4
0
1
2
0
1
1
3
3
0
0
0
0
0
0
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
1
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
1
0
2
1
0
2
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
0
2
4
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
2
1
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
4
2
3
2
0
1
0
0
2
4
0
1
0
1
1
1
1
4
0
0
2
0
0
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
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
0
2
0
0
0
1
1
1
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
2
3
0
0
1
0
0
0
1
0
4
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
1
1
0
3
1
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
1
0
0
0
1
0
0
1
2
1
1
1
2
0
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
4
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
1
3
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
1
0
2
1
0
1
1
0
2
0
0
3
0
1
0
0
0
1
2
0
0
0
3
0
0
0
1
0
3
1
1
0
1
1
2
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
3
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
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
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
2
0
5
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
2
0
1
1
1
1
0
0
1
1
0
3
2
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
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
0
0
0
0
0
2
1
3
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
1
3
0
1
1
0
0
1
3
2
0
1
1
0
2
0
0
1
1
0
0
3
1
2
1
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
1
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
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
0
0
1
0
2
1
1
0
1
0
0
0
3
1
0
2
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
5
2
0
1
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
1
1
0
2
1
0
2
0
1
0
0
1
1
0
0
1
0
1
3
0
0
1
0
1
0
3
2
0
1
1
2
1
0
0
0
0
0
1
3
0
0
0
0
3
1
0
0
1
0
0
1
1
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
2
0
1
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
3
3
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
2
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
3
1
1
1
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
2
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
3
0
0
2
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
2
0
1
1
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
1
1
2
2
2
1
0
0
0
1
1
2
0
0
1
1
0
0
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
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
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
0
0
1
1
0
0
1
2
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
0
1
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
1
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
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
3
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
3
3
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
1
1
0
0
1
1
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
1
0
2
1
0
0
0
1
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
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
2
0
2
2
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
0
2
2
2
1
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
1
4
1
0
1
2
1
2
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
2
1
1
2
0
0
3
0
0
1
0
0
1
1
0
1
0
1
0
1
3
0
0
1
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
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
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
1
0
2
3
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
2
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
1
0
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
3
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
3
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
1
1
0
0
4
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
2
1
1
1
1
0
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
3
2
1
1
0
1
2
1
1
3
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
3
0
0
2
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
2
0
0
1
1
2
1
6
1
0
2
0
0
1
0
1
3
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
2
1
1
1
0
0
0
1
3
0
1
2
2
0
0
1
0
0
1
1
2
0
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
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
1
0
2
0
1
0
0
1
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
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
0
1
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
1
0
2
1
3
0
0
1
0
1
3
0
1
0
3
0
0
2
1
0
0
0
2
1
0
1
0
0
3
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
3
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
2
1
0
1
2
3
1
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
3
0
1
0
3
0
0
0
0
2
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
1
1
3
2
1
0
0
0
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
1
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
3
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
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
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
4
1
0
2
1
0
1
2
0
0
1
1
0
4
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
3
3
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
2
2
0
1
0
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
0
2
0
0
0
2
0
0
0
1
1
1
2
0
0
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
1
1
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
0
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
3
1
1
0
2
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
4
0
0
0
1
0
2
1
0
1
1
3
1
4
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
1
0
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
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
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
2
2
1
0
1
0
2
0
1
0
0
0
1
0
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
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
1
1
0
3
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
3
2
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
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
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
1
0
5
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
0
4
1
0
4
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
3
0
0
1
1
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
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
0
0
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
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
0
0
0
1
0
0
4
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
1
0
2
1
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
3
0
1
1
0
2
0
0
1
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
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
2
3
2
0
2
1
0
1
1
1
0
2
0
2
1
0
1
1
0
2
0
1
0
0
0
1
0
0
2
1
1
1
0
2
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
1
2
0
1
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
1
2
2
0
3
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
3
0
1
0
1
3
1
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
3
1
2
0
0
0
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
2
0
1
0
1
1
0
2
3
0
1
0
1
1
1
4
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
3
2
0
0
1
1
0
0
0
1
1
2
0
3
0
3
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
3
0
1
4
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
1
0
1
0
0
1
1
0
1
1
0
2
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
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
3
0
0
1
0
1
0
0
1
4
1
1
0
0
0
0
0
1
0
1
0
2
0
3
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
1
2
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
4
0
1
1
0
2
0
1
0
0
1
0
6
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
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
0
3
0
1
0
0
4
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
2
3
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
3
0
0
0
1
0
1
1
1
1
0
1
0
0
3
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
3
0
2
0
1
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
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
0
1
1
0
1
0
2
0
1
0
1
3
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
5
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
3
0
1
1
0
0
3
0
0
0
1
1
0
1
1
0
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
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
2
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
3
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
1
1
0
1
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
0
2
3
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
2
1
0
1
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
0
0
3
4
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
3
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
1
0
1
0
4
0
1
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
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
1
1
0
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
4
0
1
1
0
0
1
0
1
0
0
0
3
0
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
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
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
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
3
3
0
0
3
1
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
0
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
1
0
0
0
1
1
2
2
0
0
1
0
4
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
3
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
3
0
3
0
0
2
0
2
0
0
2
4
0
1
0
0
1
1
0
0
0
3
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
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
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
2
0
2
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
4
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
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
1
0
1
0
2
0
0
1
0
2
0
1
2
0
3
0
0
1
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
1
0
0
2
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
3
1
0
0
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
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
2
1
2
0
0
1
0
0
1
1
1
0
0
1
0
2
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
2
0
0
2
1
0
1
3
0
0
0
0
0
0
0
3
0
1
1
2
1
0
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
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
1
1
1
1
1
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
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
3
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
3
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
1
1
2
2
0
0
2
0
1
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
3
0
2
2
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
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
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
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
0
3
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
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
2
1
1
2
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
2
0
0
1
0
1
0
3
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
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
1
0
1
0
1
1
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
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
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
4
0
1
1
1
0
0
1
1
0
2
0
4
1
1
1
0
1
0
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
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
2
1
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
2
1
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
3
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
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
0
0
1
0
0
0
0
0
1
1
3
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
3
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
2
3
0
0
1
1
1
1
0
2
0
0
3
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
1
1
1
0
0
1
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
0
0
1
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
1
0
2
0
1
1
0
1
0
2
2
3
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
3
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
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
1
1
1
0
2
2
2
0
3
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
3
2
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
3
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
3
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
1
2
0
1
1
0
0
2
0
4
0
3
1
0
1
1
0
1
1
2
0
1
0
0
1
3
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
3
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
1
1
0
0
0
3
0
0
0
1
1
0
2
1
0
1
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
3
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
2
2
0
1
0
2
1
2
0
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
1
3
1
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
3
2
0
0
3
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
2
0
2
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
2
0
2
1
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
1
4
0
1
0
1
0
0
0
0
1
2
2
0
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
2
0
4
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
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
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
0
1
2
0
1
1
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
2
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
5
0
1
0
1
0
1
0
2
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
2
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
2
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
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
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
4
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
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
0
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
3
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
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
0
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
0
1
1
1
1
1
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
0
0
1
3
1
0
0
1
0
2
0
0
0
1
1
1
0
0
1
1
1
0
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
0
4
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
2
1
1
2
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
2
0
1
0
0
1
3
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
2
2
1
2
0
0
0
0
0
1
3
2
1
0
1
1
1
1
0
1
0
1
0
2
0
0
0
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
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
3
2
2
3
0
0
1
1
2
1
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
3
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
1
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
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
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
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
1
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
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
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
0
1
1
0
3
0
1
2
2
0
0
1
0
0
0
0
2
1
1
1
0
2
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
0
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
0
3
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
1
1
0
0
0
1
1
2
2
3
0
0
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
1
1
0
0
0
0
1
3
2
0
4
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
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
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
3
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
3
0
1
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
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
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
2
0
0
0
1
3
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
1
0
2
3
0
0
0
2
0
1
0
0
0
2
1
0
1
2
1
0
3
0
1
0
0
0
0
0
1
1
1
0
3
0
1
0
1
1
1
0
0
2
1
3
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
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
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
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
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
3
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
2
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
3
1
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
3
0
1
0
0
0
1
0
0
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
3
1
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
3
1
0
3
0
0
1
0
0
0
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
3
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
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
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
2
0
2
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
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
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
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
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
2
1
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
2
1
0
0
0
2
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
1
2
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
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
0
2
1
0
2
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
1
1
0
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
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
1
1
1
2
1
0
1
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
3
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
1
3
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
1
1
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
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
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
1
1
0
1
3
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
1
0
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
2
3
1
0
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
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
2
2
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
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
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
3
0
1
2
0
0
0
3
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
3
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
1
1
1
0
0
1
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
3
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
3
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
1
0
4
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
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
3
1
0
0
0
0
0
2
0
2
2
1
0
1
0
2
1
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
2
5
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
3
2
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
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
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
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
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
2
0
1
0
2
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
1
0
0
1
3
2
1
0
2
0
2
1
0
5
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
3
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
3
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
4
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
5
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
1
2
1
2
2
1
0
0
0
2
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
1
3
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
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
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
3
1
0
0
2
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
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
3
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
1
0
2
1
3
0
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
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
2
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
4
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
3
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
4
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
3
2
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
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
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
3
0
1
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
3
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
1
1
1
1
2
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
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
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
2
2
0
1
0
1
3
0
0
0
1
1
0
0
3
1
0
0
0
1
0
1
0
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
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
1
1
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
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
3
1
0
0
2
0
0
1
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
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
0
0
1
1
2
1
0
0
0
2
0
2
0
2
0
0
0
1
1
0
3
0
0
0
0
2
3
0
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
1
1
1
0
4
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
2
1
0
0
1
2
1
1
0
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
1
0
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
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
0
2
1
2
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
3
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
3
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
2
0
3
0
0
1
2
2
0
1
4
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
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
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
1
0
1
2
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
2
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
3
0
1
3
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
3
3
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
4
0
0
1
3
1
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
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
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
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
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
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
0
0
1
1
1
2
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
5
1
1
0
0
1
1
3
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
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
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
1
2
1
3
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
0
1
0
0
1
1
1
1
0
1
0
2
0
2
0
1
0
0
1
0
1
0
2
2
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
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
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
1
3
1
1
0
0
1
0
1
2
0
1
0
0
4
0
0
0
1
0
0
0
0
1
1
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
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
1
0
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
1
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
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
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
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
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
1
0
1
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
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
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
4
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
4
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
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
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
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
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
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
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
4
1
0
0
0
2
1
0
0
0
0
2
0
1
2
3
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
0
1
1
2
0
0
0
3
0
1
0
0
1
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
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
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
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
0
0
3
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
3
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
4
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
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
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
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
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
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
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
3
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
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
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
1
0
0
0
3
2
0
0
0
0
2
1
2
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
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
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
1
1
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
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
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
3
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
3
0
0
1
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
0
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
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
1
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
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
1
0
0
1
0
0
1
0
1
0
1
0
1
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
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
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
0
0
1
0
1
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
3
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
3
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
3
0
0
1
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
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
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
3
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
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
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
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
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
1
2
0
0
3
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
1
0
0
1
0
1
0
1
1
2
0
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
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
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
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
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
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
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
2
3
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
3
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
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
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
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
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
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
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
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
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
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
0
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
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
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
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
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
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
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
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
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
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
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
2
1
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
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
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
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
0
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
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
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
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
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
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
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
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
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
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0