0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-12-25 18:32:00 +00:00
OI-codes/LibreOJ/2130/data/manager6.out

100001 lines
196 KiB (Stored with Git LFS)
Plaintext

18
7
7
9
11
0
8
4
15
5
7
8
1
13
7
10
8
6
3
10
8
7
7
12
1
7
12
9
8
6
0
5
0
3
6
5
4
9
3
6
6
8
3
6
6
7
6
11
9
12
12
8
0
3
8
6
7
5
4
12
16
1
7
4
4
3
11
8
7
10
8
7
5
4
11
7
7
7
3
8
8
3
7
3
7
5
5
5
3
2
8
5
10
7
3
7
6
6
4
6
3
5
6
4
10
8
6
5
6
0
3
3
6
5
9
7
4
7
7
9
5
7
5
8
7
0
6
1
13
7
9
0
3
4
0
5
7
3
6
8
5
4
6
7
0
7
5
3
6
1
10
10
0
7
3
8
6
0
11
5
5
7
4
6
3
4
3
5
7
4
10
3
6
11
5
0
7
3
4
7
4
6
1
5
9
8
0
4
6
7
0
11
2
5
7
7
4
2
3
6
5
6
2
8
3
7
6
4
7
6
3
2
8
4
3
4
4
6
5
5
6
3
7
8
3
5
9
1
6
8
6
3
9
4
4
5
1
10
1
6
5
11
5
4
9
6
8
8
5
7
8
1
2
5
6
6
4
8
3
2
0
8
6
0
4
4
8
3
6
4
5
2
8
1
3
4
2
1
7
2
1
5
5
6
1
6
3
0
5
8
2
5
0
8
8
9
8
5
10
1
7
10
0
4
5
3
9
5
4
0
2
2
3
7
5
3
3
5
5
6
10
0
3
1
8
1
2
2
6
3
0
3
3
0
2
5
7
9
9
2
0
6
3
7
4
3
6
2
4
8
5
5
2
3
1
3
9
3
4
4
8
0
0
2
2
6
7
5
7
4
4
7
6
2
6
7
7
3
5
4
6
3
3
6
7
5
0
1
0
5
10
5
3
4
9
2
6
6
3
2
2
6
5
7
12
0
7
2
3
9
0
1
6
4
3
5
7
4
8
4
4
0
7
5
4
1
3
4
6
8
5
0
7
8
3
6
5
4
0
10
4
5
6
2
3
4
3
9
3
1
0
2
7
7
8
2
0
3
5
2
1
6
4
7
7
3
2
5
7
3
2
0
7
8
4
1
2
1
7
4
2
3
6
6
8
4
5
2
3
5
7
6
4
4
4
6
1
1
5
3
5
3
5
3
3
4
3
3
6
6
7
8
4
4
6
5
0
4
2
9
5
5
9
4
6
6
4
0
10
2
1
3
2
6
2
3
0
6
10
0
2
7
6
3
9
10
6
4
4
4
7
4
0
1
2
4
4
6
12
6
8
0
3
1
6
3
3
8
5
7
5
4
2
1
9
5
4
9
6
4
0
4
7
5
4
5
4
5
1
5
4
3
7
1
3
3
5
7
2
2
3
5
6
4
4
4
6
9
3
6
5
11
2
4
6
7
5
6
3
3
3
3
0
5
0
0
3
2
4
0
3
2
3
1
3
2
7
2
2
3
2
4
5
4
5
6
4
2
5
5
1
2
2
5
4
5
2
1
8
9
6
2
2
0
3
1
7
2
5
3
3
1
3
5
4
6
7
8
7
2
6
5
4
1
5
4
5
0
2
3
3
4
5
2
1
5
5
5
4
2
7
3
3
4
6
6
3
5
3
2
9
2
1
3
3
5
4
9
4
3
5
9
8
7
6
6
7
6
4
7
3
8
5
5
4
0
2
4
4
5
5
0
12
0
8
5
5
1
6
4
2
4
2
3
6
3
2
2
3
2
3
2
5
0
4
3
3
1
3
1
5
0
8
5
9
2
4
4
7
1
4
4
1
2
6
6
4
6
4
2
3
2
9
4
3
2
5
5
3
3
9
4
6
2
4
6
6
3
2
4
2
9
8
2
3
3
2
2
5
3
0
6
4
3
3
10
0
1
3
1
0
4
4
8
2
4
1
7
8
2
8
4
0
2
0
5
4
1
4
5
4
2
4
4
2
7
2
3
3
4
3
4
7
3
5
6
0
5
2
8
2
5
0
5
1
6
5
0
5
5
4
6
0
6
2
3
0
4
1
0
7
0
1
0
2
4
0
4
2
6
6
4
2
2
4
1
5
6
3
3
6
2
3
3
4
4
8
9
3
4
2
0
7
2
1
249
4
13
4
6
6
2
2
10
5
8
1
3
5
9
2
4
4
1
3
3
3
4
6
4
0
4
4
0
3
1
0
5
12
7
5
4
9
6
1
2
1
4
0
0
5
5
2
5
4
5
3
0
0
2
4
8
0
2
5
2
5
3
4
3
2
0
6
3
3
0
8
4
3
2
0
2
6
3
1
3
7
2
5
0
1
4
1
2
7
5
4
3
1
1
4
4
3
3
2
2
0
7
5
2
8
2
4
3
3
1
1
5
5
4
2
2
9
3
5
3
0
4
0
4
1
3
5
7
3
3
5
5
0
0
3
4
5
7
6
5
6
5
4
4
4
4
6
4
4
4
0
4
2
4
0
2
5
0
2
2
5
1
7
3
5
0
1
3
3
5
3
4
2
3
3
3
4
4
2
3
1
5
1
1
1
5
5
7
3
5
3
5
5
2
0
4
0
6
8
4
2
0
3
6
4
1
3
3
5
5
3
7
5
7
2
0
7
5
11
5
2
1
5
2
3
3
0
6
8
3
1
2
5
6
0
3
7
2
1
2
1
0
6
0
3
7
4
3
2
4
3
4
1
4
2
4
4
5
0
0
4
4
7
5
4
7
6
4
6
2
5
2
0
7
0
7
2
2
0
6
2
2
0
3
1
3
11
1
1
1
3
3
5
5
7
1
2
2
6
6
7
6
3
7
1
2
3
5
4
3
1
1
7
3
4
1
5
2
2
5
0
4
5
0
0
2
4
1
1
4
5
4
3
3
1
10
5
9
1
1
2
1
3
6
1
0
4
0
7
0
3
2
0
4
1
5
8
4
3
5
5
5
3
0
3
6
3
2
2
5
0
2
7
4
2
1
3
2
0
4
2
2
2
7
5
2
4
5
3
4
3
3
1
3
0
4
1
2
2
2
2
1
1
3
3
2
2
3
3
4
5
2
3
3
5
0
2
7
7
4
0
3
2
6
4
1
4
1
3
5
2
5
2
3
3
3
4
5
4
6
5
5
7
0
1
2
9
7
7
6
3
0
3
1
6
1
3
3
2
1
3
0
5
4
0
0
1
1
1
6
7
6
3
4
2
7
6
0
4
2
3
1
3
2
4
0
1
7
4
3
5
1
3
4
2
2
2
6
3
2
5
3
3
4
1
1
4
6
4
8
2
6
3
6
3
3
3
9
2
2
1
1
6
5
4
0
1
5
4
2
7
4
2
2
5
1
4
7
5
1
3
3
1
5
2
3
4
11
4
0
1
0
3
5
2
5
8
2
3
0
1
4
3
1
1
6
6
7
5
4
2
3
2
2
6
1
2
2
5
3
2
3
4
1
5
2
4
2
7
3
5
4
4
4
4
1
6
9
3
6
7
2
7
5
1
3
1
5
2
7
0
3
4
5
1
5
4
3
4
7
5
5
3
3
3
2
2
5
2
2
3
5
2
5
0
2
4
4
4
4
4
3
0
7
3
4
8
1
3
6
7
6
2
2
0
2
5
6
1
3
2
6
1
5
8
3
5
5
1
1
6
7
8
1
2
1
4
4
4
3
6
6
3
12
3
6
3
1
0
2
1
3
6
3
1
0
2
4
1
1
2
6
5
0
0
2
4
4
3
4
2
2
0
2
5
4
2
1
3
1
4
2
1
2
4
4
8
5
6
6
1
2
0
4
3
2
4
7
4
3
2
4
2
0
3
5
2
5
2
10
4
5
6
5
5
1
4
3
2
1
0
5
7
3
4
2
4
3
3
2
8
0
6
4
7
1
2
1
2
1
4
2
4
0
5
1
7
3
2
3
2
6
4
4
2
1
3
4
0
2
4
6
7
2
0
2
4
2
1
10
3
4
1
3
2
7
4
4
4
3
3
3
2
2
3
0
0
2
2
4
4
2
8
1
6
0
2
1
2
0
4
3
3
2
2
1
3
8
1
3
4
3
6
0
7
1
0
3
4
2
7
2
2
1
4
2
2
1
4
2
1
2
7
3
8
6
3
5
3
3
2
6
6
6
3
2
9
4
3
4
3
2
2
0
1
3
3
5
5
5
6
0
0
6
0
4
5
3
1
4
5
1
4
5
1
0
0
8
4
1
4
4
6
0
2
1
3
1
5
2
0
2
3
1
4
3
5
5
5
1
4
2
3
5
7
3
7
4
0
3
6
3
5
1
3
1
5
4
1
1
1
2
7
5
9
1
5
6
5
2
5
4
2
5
3
4
5
0
2
1
3
3
0
3
0
5
4
3
1
2
3
4
4
3
6
2
6
3
4
2
2
4
0
1
0
3
2
7
1
4
4
6
2
2
1
2
5
3
1
4
4
2
2
2
1
4
6
3
8
3
5
5
3
4
1
2
2
6
6
3
0
3
0
2
2
0
1
2
1
3
4
2
2
4
3
2
3
5
2
0
3
2
6
4
0
1
4
4
0
2
2
2
1
2
3
3
5
2
5
2
3
0
2
2
4
4
1
1
1
0
3
0
1
5
2
4
1
4
0
2
4
5
3
2
4
1
0
1
7
1
1
6
3
4
4
2
2
1
8
2
0
5
3
1
0
6
5
0
4
5
4
1
2
1
3
1
2
0
2
6
4
5
2
1
2
6
1
1
3
4
6
2
0
4
3
4
2
4
5
3
1
0
3
6
3
6
9
2
4
2
4
6
2
3
4
1
5
1
5
4
0
2
4
1
3
0
3
3
3
0
0
1
4
1
2
2
5
2
4
2
2
0
5
3
4
4
5
5
2
8
4
5
5
1
1
2
0
3
1
3
1
8
2
2
4
1
5
8
3
4
3
4
3
1
1
2
6
4
2
1
4
3
4
2
3
3
7
2
1
1
0
3
2
5
4
0
5
0
4
4
2
5
6
0
4
4
2
5
4
3
4
0
2
1
0
2
0
1
0
3
4
2
5
1
4
0
4
0
2
3
2
7
1
2
1
5
7
3
3
3
1
2
3
0
5
3
8
4
5
1
5
0
0
7
6
0
3
2
2
5
8
2
1
4
4
3
4
0
4
2
1
4
1
1
2
4
1
2
4
3
4
1
0
1
2
5
2
4
5
5
1
1
3
3
3
0
4
7
2
3
2
2
2
5
4
4
2
3
3
3
5
2
5
5
6
7
1
3
4
2
3
1
5
1
0
8
9
3
0
1
2
6
8
5
0
4
3
4
2
2
2
2
1
3
2
3
0
2
3
5
1
4
0
1
1
2
5
4
4
8
4
2
0
2
1
0
4
3
1
1
3
3
6
3
3
4
0
1
1
1
0
2
0
3
4
7
1
0
3
6
5
2
0
5
2
4
2
2
5
1
0
0
2
1
2
3
7
2
4
3
6
1
2
3
2
5
6
0
9
1
0
1
3
4
5
5
3
1
5
1
0
1
6
2
0
3
2
3
3
5
1
5
5
0
3
3
1
6
1
3
1
3
1
3
3
2
0
6
1
3
4
1
0
5
1
0
5
2
1
2
2
5
5
3
2
6
1
5
0
2
6
5
6
4
4
6
3
4
4
4
5
4
1
2
2
4
3
3
5
3
4
3
4
3
4
7
2
7
2
0
2
0
3
4
5
6
3
5
1
3
5
3
3
5
1
2
2
4
6
1
5
5
2
0
3
4
3
3
5
4
5
6
1
3
4
7
1
1
5
4
5
10
1
7
0
3
4
1
3
1
2
6
3
4
5
3
6
2
4
4
3
3
1
3
0
8
5
2
3
2
4
3
0
1
2
3
2
1
0
3
6
1
4
2
1
7
5
3
1
0
3
3
0
2
1
5
0
2
6
1
0
3
4
2
3
3
0
0
0
3
3
1
1
1
5
0
0
5
1
2
4
0
5
4
4
1
1
5
0
4
4
3
3
4
5
1
0
7
3
5
0
2
4
5
1
3
5
3
7
2
1
0
2
1
3
3
2
7
1
6
2
3
4
3
6
4
2
7
1
4
6
2
2
6
8
1
0
2
3
2
2
1
7
4
1
3
3
4
2
2
3
2
2
3
3
3
3
0
3
2
0
1
3
0
2
5
2
4
0
1
1
2
5
1
5
3
3
4
6
0
2
3
1
3
4
6
2
2
3
3
6
3
4
3
1
2
1
0
2
2
0
3
3
0
6
2
0
2
3
1
5
3
2
3
2
5
2
4
6
2
2
5
6
5
3
5
1
5
5
1
2
1
0
2
0
8
1
2
1
0
2
6
0
5
0
3
1
2
4
2
1
2
4
1
6
9
3
1
0
0
5
4
7
3
5
5
2
0
3
4
4
9
4
4
2
1
2
2
3
9
2
2
1
3
6
2
2
4
1
4
3
0
4
4
4
2
1
3
2
0
5
3
3
2
3
1
2
2
2
4
3
0
2
2
0
5
2
5
0
0
3
4
3
2
4
1
2
5
2
5
0
5
6
1
4
2
5
1
2
4
3
0
2
4
5
1
3
5
2
6
4
1
2
5
6
4
0
1
3
2
5
2
1
6
1
4
3
2
2
2
4
3
5
4
8
6
4
3
0
4
4
4
0
0
5
1
0
4
3
4
7
3
4
3
0
2
1
1
2
0
4
3
1
0
2
2
2
3
8
0
5
2
9
1
2
5
8
8
3
7
2
4
0
2
2
2
0
4
1
4
3
3
2
9
2
3
3
2
0
2
4
3
2
2
8
6
0
0
2
1
0
1
6
1
3
3
3
1
1
0
0
2
5
3
2
7
2
2
1
2
3
6
2
3
3
0
4
3
2
1
2
3
4
4
4
1
3
1
3
9
0
0
5
6
3
4
2
3
7
4
2
0
0
5
3
1
5
4
2
3
2
0
4
5
3
1
3
1
3
3
3
2
0
5
4
1
6
3
2
3
4
4
3
2
4
1
0
3
4
0
0
0
3
1
0
3
4
3
7
3
0
2
1
2
0
4
6
4
2
1
5
3
5
4
1
2
0
2
2
4
2
1
1
2
7
1
3
2
4
2
0
4
6
1
0
5
3
2
5
6
0
3
2
3
1
3
1
1
3
1
0
7
3
4
4
4
4
2
3
4
2
2
6
3
0
2
2
3
3
3
2
2
0
3
0
1
3
2
2
1
2
4
0
5
4
2
1
7
0
3
4
2
3
3
1
2
4
6
3
1
1
1
2
2
1
1
1
3
2
4
1
2
4
5
4
3
1
2
2
5
2
2
2
4
1
3
5
2
5
3
0
5
3
3
1
3
2
1
2
4
2
3
3
3
2
1
4
1
5
1
1
0
2
1
1
5
4
2
1
5
2
5
2
4
1
2
0
3
1
4
7
4
2
2
5
6
2
2
7
0
0
1
0
4
2
2
2
3
2
2
1
3
1
1
5
1
1
4
4
1
3
3
0
0
5
5
3
3
0
1
1
0
0
4
2
2
2
4
2
0
0
4
3
2
5
0
1
0
4
4
3
0
3
2
3
2
1
0
3
5
3
7
3
2
1
4
0
7
1
8
1
4
4
3
0
1
4
1
3
2
1
2
4
1
0
3
2
1
4
3
4
1
1
5
4
4
2
2
1
2
0
0
2
3
2
4
1
6
0
1
2
1
3
4
0
0
0
3
0
1
2
2
2
1
2
4
4
5
1
0
2
5
3
2
7
1
0
0
3
0
1
1
3
3
1
1
5
1
0
2
1
2
5
3
1
5
3
2
4
0
1
1
2
0
3
4
6
1
1
2
3
0
2
2
2
3
5
3
4
5
0
3
1
4
4
1
3
2
2
1
1
0
3
4
1
1
2
3
5
2
5
0
2
0
2
6
0
1
5
5
2
7
0
3
4
1
2
6
2
3
4
0
6
2
0
2
1
3
5
4
6
1
2
2
0
0
2
3
0
3
2
0
2
2
3
4
2
3
0
2
5
4
1
0
2
2
3
3
1
3
2
5
3
2
3
6
2
3
0
5
1
0
0
6
3
5
1
0
6
2
3
1
3
1
4
2
0
3
8
4
0
4
7
3
2
5
6
3
3
3
0
2
6
3
1
4
4
0
4
3
1
4
3
4
1
0
1
4
1
0
0
5
2
2
0
0
1
3
3
3
3
5
3
3
0
2
2
3
4
2
4
4
4
8
0
4
1
19
5
3
3
3
0
1
3
4
6
3
3
1
3
3
1
3
0
1
3
0
1
1
0
2
2
1
4
5
5
1
1
1
3
4
0
3
2
4
3
6
6
0
3
3
0
0
5
5
6
1
2
7
4
2
1
3
1
2
4
2
4
2
1
2
0
1
3
3
2
3
0
4
2
1
3
0
4
1
4
0
3
2
3
1
4
1
5
2
5
2
4
3
1
1
1
1
0
3
0
4
9
4
3
3
1
3
7
1
4
0
3
1
0
5
1
2
1
0
6
1
4
4
7
3
1
3
1
0
3
2
8
1
1
4
1
2
11
1
1
3
1
4
1
3
2
6
5
1
2
3
1
2
2
0
2
1
3
3
2
3
1
3
0
1
3
2
5
2
3
0
3
4
1
3
3
5
5
3
0
3
7
3
0
2
4
2
2
2
3
6
4
1
0
0
3
0
3
6
0
5
2
1
0
3
1
3
0
4
4
2
2
4
1
1
0
2
4
0
4
2
0
1
5
3
1
2
3
0
0
6
1
4
2
2
4
1
0
2
2
3
6
4
7
5
8
2
0
3
1
5
3
2
1
5
2
1
2
3
2
0
2
4
1
4
0
2
3
3
2
3
0
2
1
2
5
2
0
0
2
1
2
2
1
1
0
3
5
5
1
1
5
1
2
1
0
1
0
1
1
3
4
4
2
4
3
8
1
2
3
1
5
3
1
1
2
0
0
2
1
0
0
3
3
0
1
5
5
1
0
4
2
4
4
0
1
3
2
2
2
4
1
1
2
0
2
4
0
0
7
3
6
0
4
4
4
1
2
2
0
2
0
1
0
2
3
5
4
2
3
6
3
1
0
0
1
1
2
6
2
2
4
1
3
3
2
1
5
3
10
5
1
1
3
1
3
4
2
2
2
3
0
3
4
5
4
0
2
2
5
2
4
4
1
1
5
1
3
3
3
0
7
3
5
1
0
5
2
4
3
3
2
1
3
1
1
1
4
0
4
4
3
4
4
2
7
0
1
6
3
3
0
2
1
4
3
3
3
4
1
3
4
1
5
0
4
1
3
5
3
4
1
3
2
5
1
1
1
0
2
6
2
1
3
2
1
5
3
3
2
5
0
3
2
6
1
1
4
1
2
6
3
6
2
2
0
1
2
2
4
0
1
3
2
3
2
5
5
5
3
2
0
1
3
1
2
1
3
2
2
2
2
5
2
4
1
5
4
0
3
7
3
2
2
4
1
1
0
1
5
2
2
2
6
4
2
1
2
3
4
1
2
4
2
0
3
2
1
4
4
1
2
3
1
1
1
2
0
0
3
0
1
1
1
3
4
3
5
4
3
11
3
2
2
5
0
5
2
0
2
5
5
7
2
2
1
0
0
2
1
1
4
1
0
5
0
0
3
3
3
1
1
3
4
0
1
3
0
2
1
3
8
3
2
6
5
0
1
0
5
0
3
3
0
4
3
0
3
2
1
0
2
0
3
3
3
1
2
2
2
0
1
3
0
0
3
3
4
4
0
1
3
0
0
2
2
2
5
0
1
1
2
1
1
3
4
0
0
4
5
3
1
3
3
0
4
4
3
3
1
1
0
1
2
3
3
3
2
2
7
0
0
2
2
0
5
4
2
3
2
1
1
2
4
0
2
2
4
3
0
4
1
0
1
5
2
0
3
0
2
0
1
1
3
3
2
5
0
0
3
2
3
0
1
3
2
1
0
4
0
3
5
2
2
3
0
3
1
4
2
2
1
1
2
2
0
0
1
0
1
2
2
1
3
1
3
2
6
2
0
3
4
0
6
4
2
4
5
2
4
7
2
2
0
0
4
4
3
1
3
3
4
5
4
0
4
1
3
2
2
1
1
1
0
1
1
0
0
4
0
4
4
1
0
2
2
3
0
3
3
1
1
2
3
0
1
0
3
3
1
1
4
3
2
2
1
1
5
0
1
2
1
4
3
2
2
0
1
1
1
1
0
0
0
5
1
0
0
4
5
6
2
5
5
0
6
3
3
1
3
3
0
7
2
1
5
4
2
4
0
0
10
4
1
1
3
0
1
2
4
0
2
0
4
9
2
3
0
1
5
1
4
5
3
0
1
4
6
2
3
0
0
3
0
3
3
4
2
0
1
1
0
2
1
7
5
2
0
1
0
3
3
1
3
1
0
4
2
3
3
0
0
0
3
1
2
4
2
2
1
2
2
1
1
1
3
1
2
1
7
7
2
3
3
4
0
2
0
3
2
0
2
2
3
1
2
2
4
0
4
0
2
0
5
0
1
3
1
0
4
2
5
5
2
2
1
0
1
2
0
3
5
1
4
1
4
1
3
0
0
0
0
2
0
4
0
1
5
4
0
4
0
0
3
1
0
3
4
1
2
6
3
3
2
2
5
3
0
4
0
3
3
4
2
0
0
0
5
4
1
1
6
2
6
3
1
3
0
2
1
2
10
1
2
0
4
1
5
1
3
4
5
2
1
5
1
0
3
4
4
2
5
6
2
3
1
1
2
2
1
3
2
3
1
3
2
1
5
1
1
1
5
2
1
0
0
5
3
1
3
0
1
2
3
3
2
0
4
0
1
3
5
0
2
2
6
0
0
4
3
1
6
0
0
0
1
1
3
4
0
2
3
2
2
4
2
1
3
2
2
3
1
1
1
0
0
0
4
3
0
6
0
0
2
7
3
1
4
2
3
0
1
3
3
2
1
5
2
0
1
2
5
5
3
6
2
0
1
1
0
0
4
4
2
0
1
3
2
4
2
0
4
0
1
2
2
2
3
2
0
4
5
1
0
1
2
0
3
4
1
3
0
1
3
1
0
4
4
1
1
5
1
1
3
0
1
7
0
2
0
1
3
2
4
3
2
0
3
3
0
3
1
3
2
2
3
2
5
2
0
0
1
2
1
1
0
0
5
0
0
6
1
1
2
0
3
1
4
0
2
3
1
0
1
1
2
0
5
2
1
6
2
5
3
5
1
2
0
2
5
2
1
3
4
3
1
3
2
3
4
1
2
2
0
4
1
1
1
0
4
0
1
2
0
2
2
5
2
2
3
0
3
0
0
5
0
2
1
6
0
3
3
1
4
1
0
0
2
3
4
3
2
0
1
1
1
0
1
1
5
2
1
2
2
2
2
1
0
4
1
1
1
2
2
1
5
2
1
2
5
7
0
3
1
2
2
1
0
2
2
1
1
1
3
4
1
1
3
3
2
1
0
1
0
3
1
1
4
5
1
5
7
1
1
1
2
7
3
0
0
3
1
2
0
5
4
2
1
2
3
2
1
4
1
0
1
1
2
1
1
2
4
3
2
6
2
2
2
3
0
0
2
6
1
4
1
3
4
0
2
3
5
2
2
2
2
3
2
1
4
0
3
0
4
3
1
0
3
4
0
1
0
0
4
4
1
0
1
3
4
6
4
3
2
2
1
4
2
4
0
1
0
3
4
0
4
1
4
3
5
2
2
3
3
4
5
0
5
2
3
3
3
1
0
3
0
1
5
1
5
3
2
7
0
0
1
2
1
0
6
0
2
3
1
1
5
1
2
1
3
1
2
0
2
1
2
3
3
2
1
2
2
1
5
4
0
1
2
1
0
4
0
1
2
3
3
0
2
1
2
2
3
3
3
1
0
1
2
3
4
1
1
2
1
2
3
2
2
2
4
0
3
4
4
4
1
0
0
1
0
2
2
2
4
1
3
4
0
4
2
2
2
2
2
4
1
0
0
3
6
4
2
1
3
2
1
1
0
2
3
8
0
5
2
1
1
1
3
3
0
2
2
1
3
1
0
1
4
3
1
3
3
0
1
3
0
3
1
3
2
1
2
1
1
3
1
1
0
0
0
2
0
3
2
5
1
1
1
2
3
3
3
1
2
4
3
4
1
0
0
5
0
1
6
4
1
1
3
4
3
1
2
6
1
3
0
3
0
6
0
2
3
3
1
0
0
0
1
1
0
2
3
5
0
0
4
1
1
1
0
2
1
0
1
0
6
1
1
1
0
0
4
0
3
5
1
1
3
1
1
3
4
4
1
2
2
0
0
2
2
1
0
4
2
2
1
1
4
5
0
0
2
3
1
3
2
1
2
0
0
0
1
1
1
3
1
0
3
3
3
4
1
0
2
1
1
1
4
1
2
0
2
3
3
3
3
1
1
1
2
3
0
0
3
0
4
4
5
0
3
5
2
1
1
3
1
0
2
7
2
1
1
3
2
5
2
3
4
3
4
2
1
2
3
1
2
4
1
1
4
2
2
3
1
1
4
0
2
0
1
0
2
3
0
4
3
4
4
61
2
1
0
0
3
1
3
3
4
1
1
4
2
1
2
3
1
0
4
1
4
2
5
0
0
2
5
4
4
0
3
1
4
5
0
1
0
1
0
1
3
2
2
0
1
3
4
3
1
1
2
2
2
3
1
1
3
5
4
5
2
2
5
1
2
0
4
4
3
3
4
3
0
2
1
0
3
1
3
3
2
3
0
0
3
3
0
2
4
3
3
2
2
0
1
3
3
2
0
3
1
2
0
3
1
1
1
2
3
4
2
1
1
0
0
2
4
2
3
1
2
5
5
0
4
1
3
0
1
3
1
3
0
1
4
2
2
1
0
4
2
2
2
3
2
5
0
1
2
3
1
1
1
3
0
1
2
1
3
2
2
2
0
7
1
3
2
1
1
0
1
2
0
1
2
3
8
4
0
0
4
3
4
1
4
2
0
3
3
0
2
1
2
1
2
2
4
4
3
1
3
1
3
1
2
3
5
1
3
1
0
0
8
1
5
0
2
2
4
5
3
0
2
2
2
2
2
2
0
2
7
2
3
3
5
0
1
2
5
1
4
2
2
3
3
1
0
1
1
2
1
0
2
2
1
2
0
2
5
4
3
4
1
2
2
0
1
1
0
1
1
4
5
0
0
1
0
1
5
2
2
6
1
5
6
3
1
4
0
3
3
1
2
3
2
0
4
1
0
7
3
3
1
2
3
3
0
0
3
2
0
4
2
3
0
2
2
6
1
1
1
0
1
0
3
1
1
4
3
4
0
2
1
4
2
2
1
3
6
1
1
6
1
3
1
0
0
0
2
1
4
5
0
3
3
1
5
0
3
2
2
1
3
4
0
3
0
2
3
2
0
3
0
3
2
0
1
3
2
2
2
4
1
4
0
0
6
1
3
1
5
5
0
4
3
3
1
0
5
2
5
4
3
5
4
5
0
1
1
0
2
3
8
1
3
3
0
4
2
1
5
0
3
5
1
2
4
0
3
8
4
0
0
7
1
1
3
1
0
1
1
3
2
4
0
4
2
1
0
1
1
3
4
5
1
3
2
1
0
0
5
4
0
3
1
2
1
3
0
2
3
2
2
2
3
2
1
3
1
3
0
0
4
1
3
1
5
0
3
3
3
0
2
1
0
1
3
2
4
2
3
2
1
1
5
1
2
0
0
4
3
0
4
0
4
3
1
3
0
1
0
4
1
3
1
2
1
4
4
3
2
2
2
2
1
0
0
1
2
1
0
5
3
2
3
5
2
2
0
4
1
0
2
0
1
3
3
3
4
2
3
3
3
0
1
0
2
2
2
1
3
0
0
3
1
1
3
0
0
2
0
2
0
9
2
3
5
1
2
2
6
1
1
1
3
4
0
0
1
1
2
2
1
1
2
4
6
3
2
3
2
4
2
1
2
1
7
1
3
1
2
1
5
0
1
2
0
3
0
3
3
4
1
0
3
4
0
1
2
0
5
1
0
2
2
0
3
0
1
1
2
3
2
0
2
3
0
3
5
3
2
2
0
4
1
4
2
1
1
2
1
2
1
4
2
3
0
2
0
2
3
0
2
2
0
5
0
3
3
3
0
2
0
2
3
3
2
0
2
0
1
1
1
0
1
2
5
0
0
0
2
2
2
4
3
2
2
1
1
0
0
2
2
2
0
2
0
1
3
2
0
3
3
5
4
4
7
1
2
3
5
7
2
5
2
5
1
0
3
2
1
2
3
4
3
0
2
1
3
4
1
0
0
2
5
1
2
2
0
2
4
3
3
2
3
3
2
3
2
4
3
2
0
1
4
1
0
2
3
2
2
4
5
4
2
4
0
0
1
4
2
2
0
2
3
2
1
1
2
2
3
2
3
3
5
2
1
1
3
1
1
3
4
2
1
1
5
3
4
1
3
1
2
3
3
1
2
3
1
1
1
3
0
3
1
3
4
0
1
2
1
0
0
3
2
0
1
1
2
1
3
3
1
3
1
0
1
2
0
0
0
0
4
0
3
3
3
2
3
2
1
3
3
5
4
6
1
0
0
0
2
1
2
1
3
1
0
1
2
2
3
2
3
3
1
4
1
1
3
3
1
2
0
5
0
2
3
1
0
1
2
2
0
4
2
2
3
3
3
2
1
4
0
1
3
4
0
2
3
4
1
1
1
4
0
0
1
2
3
5
1
6
1
28
6
1
2
2
1
2
3
1
2
2
0
0
1
0
3
1
2
1
1
2
3
4
2
1
2
0
1
2
0
3
1
1
3
0
1
3
0
2
2
2
2
0
3
1
2
4
0
2
2
0
0
3
1
4
2
0
5
1
1
1
1
0
0
4
4
0
2
0
2
2
4
3
1
2
2
0
2
2
1
4
2
3
0
0
3
2
6
0
2
0
0
3
3
2
1
3
2
0
1
1
2
4
1
0
1
5
0
2
0
3
1
3
3
3
3
1
0
3
3
2
3
3
3
3
0
6
4
3
1
0
3
0
4
1
2
3
4
0
2
2
3
0
3
0
5
3
3
2
1
1
4
2
3
1
3
1
3
0
1
1
2
2
6
1
1
3
1
3
2
3
2
0
0
0
2
6
1
6
1
0
1
0
2
1
0
2
3
5
3
2
6
3
3
2
4
1
3
2
0
2
3
0
2
3
3
2
3
3
1
0
1
3
3
2
4
1
5
2
2
2
4
2
1
2
1
3
1
7
2
1
4
0
1
1
2
4
3
3
6
3
4
1
0
3
0
1
1
1
3
0
4
2
0
3
4
5
1
1
2
4
3
2
0
0
1
1
1
0
1
0
2
0
1
4
2
0
0
0
2
4
2
2
5
2
2
1
4
1
1
4
0
3
2
2
4
3
0
2
0
0
0
3
0
2
1
4
1
1
2
0
2
1
4
3
2
2
0
4
3
0
0
1
0
2
1
1
3
1
0
2
1
0
3
2
0
2
2
4
2
2
0
0
1
0
3
4
3
4
0
5
1
0
0
5
1
1
1
5
4
3
2
3
1
4
4
3
0
1
1
4
5
2
0
1
2
1
2
3
2
1
2
3
2
0
0
3
2
5
4
1
4
2
6
0
0
4
2
0
1
0
4
0
0
3
3
5
3
3
1
0
3
4
3
4
3
0
4
1
2
4
1
3
2
1
0
2
2
4
0
1
2
1
2
0
2
2
1
3
1
4
2
2
0
2
0
1
3
3
0
2
2
2
1
2
2
2
3
3
4
4
2
1
0
5
0
3
1
1
2
1
1
1
1
2
4
5
0
0
1
1
2
2
2
4
3
3
2
1
3
1
1
4
1
3
3
1
5
1
1
2
4
1
1
2
4
5
4
3
1
0
0
4
1
2
4
1
2
1
7
3
3
1
4
2
2
0
1
0
0
2
3
3
0
2
3
0
1
2
1
2
1
2
0
1
4
1
3
1
4
3
1
1
3
0
0
1
4
0
2
0
3
2
2
1
0
0
1
4
0
4
0
3
1
0
1
3
2
2
3
1
1
2
0
1
1
2
1
1
0
1
3
0
1
6
0
0
2
2
4
1
4
2
0
0
1
0
1
1
0
2
2
3
3
1
1
2
0
1
0
7
0
2
1
3
2
3
0
1
4
2
2
1
2
4
3
2
4
3
1
1
4
0
1
1
0
3
1
2
5
3
2
4
2
2
1
4
1
3
0
1
2
3
0
2
2
0
1
1
0
1
3
1
2
1
4
0
0
1
0
3
2
1
1
0
1
0
3
4
2
2
0
0
3
0
0
3
2
2
4
1
2
1
5
1
3
3
4
3
1
0
2
0
3
3
1
5
2
7
4
3
0
3
1
3
2
1
1
0
0
0
2
1
4
1
1
1
1
3
2
1
2
3
2
1
3
1
0
5
5
3
5
1
2
2
3
6
1
0
1
1
4
7
3
3
4
3
1
2
3
6
0
1
3
2
2
2
5
0
1
2
0
1
3
4
4
2
1
0
2
1
0
1
2
1
2
1
1
1
2
3
1
1
2
2
3
3
1
1
3
0
1
5
0
3
0
2
5
3
0
0
2
4
1
4
3
5
1
1
3
0
4
1
3
2
2
8
2
0
5
4
2
3
2
0
5
1
1
1
1
2
0
2
1
0
3
2
3
4
3
1
1
3
5
3
2
4
0
0
1
2
0
1
0
2
3
2
2
1
4
2
3
1
0
2
0
3
0
2
0
0
1
3
2
4
2
1
0
1
1
2
1
2
1
0
1
2
3
1
4
4
0
3
2
0
5
0
2
1
3
3
3
1
4
0
2
0
5
2
1
1
0
2
1
1
4
2
0
1
1
1
5
4
3
3
6
4
2
2
3
1
1
5
3
1
1
0
0
2
5
1
4
0
1
2
2
2
3
1
0
3
0
5
0
2
1
2
3
3
2
0
2
2
2
1
3
2
0
3
2
1
3
2
1
0
1
0
1
2
1
3
0
2
1
6
1
1
3
1
0
1
1
1
6
0
3
1
0
1
5
2
3
2
2
1
3
0
0
0
6
2
0
4
1
6
2
1
3
1
0
3
2
3
2
2
0
4
5
2
2
5
0
3
1
0
3
5
3
0
0
2
2
0
1
2
4
4
2
0
3
2
0
4
0
1
2
5
2
0
2
2
3
1
4
1
2
0
2
1
1
0
1
1
2
1
0
4
2
2
1
0
1
0
2
0
2
2
4
0
0
5
1
0
2
1
6
4
2
2
3
0
2
4
3
0
0
0
0
2
1
2
0
0
6
1
6
2
1
2
0
3
1
6
3
3
0
0
2
0
0
1
1
1
2
2
0
1
3
2
6
3
2
1
2
2
2
3
2
2
3
2
3
1
2
0
0
3
0
1
7
1
2
2
2
2
0
3
1
2
1
2
3
0
2
1
3
2
1
3
1
0
1
1
0
1
1
0
4
1
4
4
2
3
5
1
3
7
1
1
0
1
2
2
0
0
6
0
1
0
3
3
3
2
6
2
1
2
1
2
1
3
2
1
2
3
1
4
2
2
2
1
3
3
2
3
1
0
0
0
3
9
1
1
4
0
0
0
4
2
2
1
0
1
1
1
3
0
1
2
2
0
5
1
2
1
0
0
0
2
3
1
0
2
2
2
2
2
3
0
3
0
1
2
1
3
0
0
3
1
1
4
4
1
1
2
2
4
1
5
3
2
2
1
0
1
3
1
1
0
4
1
1
2
2
1
4
0
1
4
2
0
1
2
3
3
2
1
3
3
1
1
1
1
0
4
1
3
2
1
0
0
2
0
1
2
2
3
1
2
2
3
1
0
0
1
0
3
1
0
1
1
3
4
3
2
0
0
0
2
3
3
1
7
2
6
0
0
0
1
4
4
2
2
0
1
5
2
0
2
2
1
4
1
3
0
2
0
4
0
3
3
3
2
2
0
1
0
2
0
2
2
0
1
2
2
2
2
2
2
3
1
1
4
0
0
0
1
0
2
1
1
3
1
0
3
0
1
2
1
2
2
3
3
0
2
1
4
0
0
3
1
2
2
1
2
1
0
4
1
2
0
2
0
2
3
3
1
0
3
1
6
2
1
1
4
1
0
2
2
1
2
0
1
0
2
2
0
0
3
2
3
0
2
0
1
0
0
1
1
1
2
2
1
2
2
3
3
2
5
1
1
1
2
1
0
4
1
1
2
0
3
1
2
5
1
0
1
2
1
2
0
3
3
4
2
1
0
3
2
0
3
0
1
3
1
1
0
2
4
0
1
1
2
0
1
0
0
6
2
13
1
1
2
1
2
1
1
3
1
2
1
2
3
0
1
0
0
4
3
3
1
0
7
2
1
3
2
4
2
1
2
1
1
3
2
1
0
3
1
2
3
4
3
2
1
0
2
1
2
0
3
2
3
3
0
0
1
4
1
3
3
0
1
0
1
1
0
2
2
1
3
4
0
0
2
0
6
1
4
0
1
1
0
3
1
3
0
2
2
0
2
0
5
1
3
2
3
2
1
1
1
2
2
2
2
0
0
1
0
2
0
2
1
2
4
0
2
3
1
2
1
2
3
0
1
4
1
3
0
4
2
2
0
2
3
1
2
5
2
1
0
1
2
0
0
1
1
2
2
0
0
0
2
2
0
3
1
5
6
3
3
0
1
0
0
0
0
0
3
1
2
0
0
2
2
0
2
0
0
6
6
5
1
2
2
3
1
0
1
0
1
0
3
2
2
3
2
2
1
1
1
2
2
0
2
4
1
1
4
1
1
3
1
3
2
4
4
3
0
5
0
2
4
3
0
1
1
0
3
2
7
2
3
5
0
6
1
3
0
0
0
2
2
0
3
2
0
1
1
4
1
7
2
0
0
1
2
0
1
4
3
1
3
1
1
1
1
1
2
0
0
4
1
2
2
0
2
1
1
5
1
0
4
4
5
3
4
5
0
0
2
2
3
1
2
1
5
0
3
4
2
2
2
3
0
0
3
5
0
4
5
6
4
0
0
2
1
2
3
1
5
1
1
2
2
6
0
0
0
2
1
1
4
0
3
2
2
0
1
1
0
0
1
2
1
4
1
3
0
2
2
1
2
0
1
4
2
1
0
1
3
2
2
2
2
0
1
3
2
0
1
5
3
4
2
4
1
1
3
1
4
0
0
2
1
5
1
1
4
0
2
0
2
2
3
2
2
0
2
1
2
1
0
0
1
3
4
2
0
4
2
0
0
3
0
5
0
4
1
3
1
1
3
2
1
1
2
0
1
0
2
3
0
0
5
0
1
0
0
1
3
7
0
5
3
4
0
1
1
6
3
1
1
1
2
4
0
0
2
0
0
1
3
0
2
1
0
2
3
2
0
1
2
0
1
2
3
1
0
3
2
0
0
1
0
0
0
3
2
3
3
2
2
2
4
0
0
0
2
5
5
1
1
2
3
2
1
2
2
2
0
0
6
4
1
5
1
2
1
1
6
1
3
3
4
0
2
1
1
1
2
2
0
0
4
2
0
2
3
3
3
3
4
2
2
0
3
1
1
2
2
3
1
0
0
1
1
4
1
1
6
1
2
6
1
3
2
2
1
0
2
0
1
0
1
4
2
4
3
3
1
0
1
4
1
3
1
2
2
0
2
0
0
0
0
1
0
0
5
3
2
3
1
1
2
1
2
2
3
2
2
6
6
1
0
5
0
6
0
3
1
2
4
0
2
2
1
4
5
0
7
2
2
4
0
0
2
0
3
4
1
2
3
0
0
2
1
4
0
0
1
0
1
1
3
4
0
0
4
0
0
3
3
0
0
4
4
1
1
4
2
5
3
0
1
0
0
1
2
1
0
2
1
1
0
3
0
2
0
1
0
3
0
3
4
0
2
2
1
1
0
2
0
0
5
1
5
0
2
0
1
9
3
3
1
2
1
0
2
3
3
1
1
6
2
3
1
1
3
2
1
0
3
6
4
4
2
2
4
0
1
1
0
2
1
1
2
2
4
3
5
5
1
1
0
0
3
1
5
0
1
3
4
3
0
1
2
4
1
1
3
0
1
0
1
3
0
5
1
1
3
1
2
5
2
0
1
1
2
0
4
1
1
0
0
0
3
4
3
3
0
1
1
2
3
4
1
2
0
0
5
0
2
0
1
0
0
2
6
0
1
0
2
3
1
1
3
2
3
1
3
3
1
2
1
0
1
2
1
3
0
3
0
2
1
1
1
2
1
6
1
2
5
1
1
0
3
2
3
3
2
2
4
1
0
0
5
2
0
2
0
1
0
1
0
1
4
1
2
0
3
0
1
0
2
1
3
3
3
2
4
2
1
0
1
3
0
0
3
0
3
2
2
0
2
1
2
4
2
1
1
1
0
4
0
1
0
2
1
3
3
1
1
0
2
5
1
5
0
2
2
1
4
1
6
3
1
2
1
1
0
3
0
1
2
2
1
0
1
2
1
0
3
0
0
0
0
1
1
1
4
2
3
4
2
0
2
2
2
2
0
2
0
2
1
3
3
2
2
2
3
5
3
1
1
3
2
0
3
0
0
1
3
2
0
6
2
0
0
0
2
0
2
2
3
1
1
0
1
0
2
2
2
6
0
1
2
3
0
4
5
1
0
0
2
2
0
1
0
3
0
1
2
1
2
0
5
0
3
0
1
4
0
3
1
2
0
0
0
2
1
0
2
0
0
0
5
1
0
0
2
0
0
1
2
1
5
2
2
2
0
1
2
5
4
0
2
2
5
3
1
3
2
1
0
2
1
0
0
0
1
4
1
3
5
6
0
2
3
0
2
3
2
2
8
3
0
2
5
0
0
1
0
3
0
2
2
3
3
0
1
0
0
3
2
0
0
0
2
2
0
0
0
0
0
2
2
4
3
1
1
1
3
3
3
1
3
2
0
3
2
0
1
1
2
1
1
1
1
5
2
0
2
0
3
0
1
1
3
3
5
1
2
0
1
0
1
1
4
1
3
2
3
2
1
1
5
1
2
3
6
2
3
3
0
2
2
0
0
0
8
0
1
1
1
1
3
1
0
1
1
0
4
0
3
2
1
1
0
4
2
0
3
3
1
2
2
2
0
4
0
0
3
1
0
1
4
0
1
1
3
0
1
2
2
2
0
0
1
2
0
0
0
0
7
3
6
0
1
2
1
3
0
2
0
5
1
0
0
0
0
1
0
5
3
1
0
0
1
2
3
3
4
1
1
1
1
0
0
0
0
2
4
4
3
2
1
0
1
0
3
0
2
0
0
2
1
1
1
0
1
1
0
0
7
3
0
1
2
0
5
1
2
2
0
3
2
2
0
3
1
1
0
3
4
2
0
1
0
0
3
3
1
2
3
1
0
1
1
0
0
2
1
1
1
0
2
0
3
3
103
2
0
1
1
1
4
0
0
1
4
0
1
1
3
1
5
2
1
0
2
3
1
3
0
1
0
4
3
0
0
0
2
1
7
0
2
3
1
0
2
0
3
0
1
2
2
3
2
2
2
2
1
3
0
1
0
2
3
3
3
3
4
1
0
1
1
1
2
1
0
0
1
0
1
2
0
5
3
2
1
2
2
2
3
2
4
0
0
2
1
0
0
0
2
0
1
0
3
0
1
2
1
2
2
0
3
1
0
1
1
7
0
0
4
2
0
1
1
0
0
0
2
2
4
3
2
4
1
5
2
4
0
1
1
4
0
0
2
2
3
2
3
3
2
1
3
3
3
3
1
1
1
1
3
0
2
2
0
0
0
1
0
0
3
1
3
0
0
4
3
2
1
3
0
0
0
1
4
1
0
1
0
0
0
1
1
3
3
0
0
1
0
2
0
1
0
6
3
0
1
0
0
1
1
3
0
2
2
1
0
0
3
2
2
0
0
2
3
0
1
0
3
1
1
3
3
2
5
1
0
1
2
1
2
2
0
3
0
2
4
1
1
1
0
3
0
3
0
0
3
1
2
6
1
2
1
3
2
1
1
3
4
0
0
2
3
1
0
1
2
2
3
0
0
1
3
2
1
1
1
0
1
0
3
1
2
0
1
2
3
2
0
1
0
2
1
1
0
0
3
1
0
1
6
1
2
4
2
0
2
0
0
2
0
2
1
1
1
0
1
0
1
2
1
1
1
2
2
2
2
2
2
1
3
3
3
1
3
2
1
2
2
1
0
2
2
1
1
3
3
2
2
1
1
2
0
0
0
1
1
0
2
1
3
0
1
0
3
1
0
1
0
2
3
2
1
0
3
3
3
4
0
1
2
3
0
2
7
1
0
1
2
2
0
1
3
1
4
1
2
0
2
4
0
0
3
0
2
2
0
1
3
1
2
1
4
3
0
1
3
2
3
4
0
0
5
0
4
4
0
3
1
1
4
0
0
0
2
1
2
0
2
0
1
2
1
9
2
0
4
0
0
0
0
9
1
1
3
1
1
0
1
4
2
0
0
2
0
2
1
0
2
4
1
2
0
1
1
4
1
1
2
3
1
1
5
4
2
3
0
1
3
5
0
0
5
4
5
0
0
2
1
2
0
0
1
2
2
3
0
2
3
3
1
0
1
0
2
2
3
2
0
1
1
2
0
1
3
3
1
0
2
2
2
2
0
0
0
2
5
5
4
4
2
1
3
4
1
3
2
2
0
4
1
1
3
0
0
4
5
1
1
0
3
2
2
2
5
3
1
3
0
2
2
4
2
0
3
0
1
1
1
0
0
1
1
2
0
4
1
2
0
2
0
3
2
3
2
3
1
2
3
0
3
1
3
0
1
2
2
1
4
4
4
0
1
0
0
1
0
0
1
2
0
2
3
0
1
0
1
1
2
1
0
1
1
3
4
0
3
1
1
2
1
0
3
3
2
5
2
1
0
3
3
2
0
2
4
3
4
2
0
2
1
0
0
1
3
1
2
2
2
0
0
0
1
1
2
0
0
2
3
1
1
1
1
2
0
1
0
4
2
0
1
3
1
2
0
3
2
3
2
2
0
2
0
3
2
1
0
2
2
4
1
3
1
0
0
0
2
1
1
0
0
1
1
2
0
1
0
1
0
1
3
2
2
0
0
1
0
1
3
3
2
4
0
1
0
3
1
0
3
1
0
3
4
4
1
0
1
0
1
3
0
0
1
3
2
1
4
1
2
0
1
0
1
0
0
0
2
1
3
3
1
0
2
0
1
2
2
0
0
2
3
3
2
4
1
0
3
2
0
3
3
2
0
1
4
1
1
1
0
4
1
0
2
2
2
0
2
0
2
3
3
0
1
1
2
3
2
2
3
3
3
0
0
3
0
1
4
4
2
2
1
0
2
2
4
2
0
1
1
1
0
0
2
1
0
0
2
3
3
0
2
3
0
2
3
4
0
5
4
0
0
5
1
0
3
0
0
1
9
2
2
0
2
1
1
2
2
0
2
0
0
0
3
0
1
2
0
1
3
1
2
0
2
1
1
3
2
0
1
3
0
0
1
2
1
2
5
0
1
0
1
0
2
4
3
1
1
1
2
3
2
0
5
2
1
1
1
3
2
0
1
1
1
1
2
0
2
0
1
1
1
1
0
2
4
1
0
3
3
1
1
0
1
4
1
3
1
3
2
3
3
0
10
1
2
3
2
2
1
2
6
2
1
4
0
1
0
3
1
2
1
1
2
2
1
1
2
1
3
0
1
3
1
2
1
2
2
3
3
1
2
1
2
0
1
1
2
0
4
0
0
0
1
2
4
0
1
2
0
0
1
2
2
2
4
3
2
3
0
2
0
2
1
0
3
2
2
4
4
3
1
2
1
0
2
2
8
0
0
1
2
1
1
0
0
0
0
1
1
2
6
2
1
0
2
3
0
0
3
2
1
3
2
1
0
2
1
0
2
4
1
0
1
5
3
0
2
2
0
0
1
0
3
0
0
0
1
1
1
2
2
0
2
0
0
2
1
0
1
1
0
0
2
0
3
0
1
0
2
1
2
0
1
3
1
0
0
1
1
6
1
1
1
0
4
1
2
4
0
1
0
0
3
2
1
2
2
5
2
2
2
2
5
0
0
0
0
1
1
3
1
2
4
1
1
4
1
3
0
0
1
2
1
0
1
3
2
0
0
1
3
4
0
0
1
3
1
0
1
2
4
1
2
3
0
2
1
1
0
2
1
4
1
2
1
0
0
6
3
0
1
0
5
2
0
3
0
3
0
1
1
3
5
3
2
2
2
1
0
0
0
3
1
1
1
0
1
4
0
0
1
3
2
0
0
2
2
2
2
1
0
3
0
3
1
0
6
3
2
0
2
2
1
3
2
0
2
1
2
5
1
2
1
0
2
2
0
0
2
0
1
1
4
1
3
0
1
4
1
1
0
1
0
1
2
0
4
1
1
2
0
0
1
0
1
4
1
1
1
3
3
2
1
3
0
2
1
2
0
4
1
3
0
0
1
3
4
0
1
2
1
1
3
0
1
0
1
2
2
3
1
3
2
1
1
0
1
3
4
4
1
3
1
1
0
3
1
1
0
3
2
2
0
2
1
1
1
1
1
3
0
0
0
1
3
1
1
2
2
0
0
0
1
4
0
1
0
0
0
4
2
0
1
3
2
4
1
1
2
1
3
1
0
4
1
5
0
0
3
0
0
3
0
0
3
1
1
6
4
0
1
0
2
3
1
1
0
0
0
0
2
0
1
2
2
2
1
0
1
2
1
1
1
2
1
0
4
2
0
2
4
1
1
2
7
5
0
2
0
4
1
3
0
0
1
2
0
1
1
1
1
4
3
2
1
20
0
2
1
3
1
1
1
4
2
1
0
3
0
2
1
1
1
2
2
1
0
0
1
0
0
1
1
2
3
0
1
3
1
1
1
2
0
2
1
3
1
1
1
0
0
0
3
2
2
2
0
2
0
2
1
2
1
2
2
3
1
3
3
3
1
0
4
1
2
6
3
0
8
2
0
1
0
1
0
0
6
0
0
3
2
1
0
1
3
0
0
2
0
0
2
1
1
2
1
0
1
1
0
1
2
2
3
0
5
1
2
0
0
1
2
2
2
1
1
1
0
5
2
1
1
4
1
6
0
1
0
1
0
4
0
1
0
0
4
0
1
0
2
1
1
0
2
3
1
1
2
2
1
0
2
1
1
1
0
0
1
1
1
4
3
0
0
2
0
3
3
0
0
1
3
1
0
1
2
1
0
2
1
2
2
4
0
3
0
0
3
1
2
1
1
0
0
2
2
1
1
0
1
0
0
2
3
3
1
1
0
4
1
2
3
1
2
2
5
2
2
2
0
0
1
1
1
3
3
1
1
2
3
0
0
0
1
0
1
0
1
1
1
4
0
0
0
3
1
0
3
0
1
0
1
7
1
3
3
2
1
2
1
0
0
0
2
1
2
3
0
4
0
3
2
2
3
4
0
2
0
1
1
0
2
0
5
3
1
1
0
2
3
0
3
2
3
1
3
3
0
0
0
3
3
0
0
6
2
1
2
9
1
2
0
5
1
0
0
1
4
4
3
0
5
1
1
1
1
5
3
2
1
0
1
1
2
0
0
2
1
6
2
0
2
0
1
0
1
1
0
1
1
0
0
0
1
0
1
3
1
1
3
1
2
2
1
2
2
1
3
0
3
3
5
1
3
2
3
1
3
5
1
5
1
1
5
2
2
2
1
0
0
5
0
0
1
1
2
5
1
2
1
2
1
1
1
3
1
0
1
2
0
5
1
1
0
2
1
0
2
0
2
2
0
0
3
0
2
1
1
1
1
0
0
0
2
2
2
1
4
2
2
1
5
1
2
2
0
0
0
0
2
5
1
0
1
1
1
1
2
0
1
0
1
1
2
0
0
1
1
2
1
5
0
1
0
0
2
0
0
7
0
3
0
0
7
2
0
1
1
1
1
0
0
3
2
1
1
1
3
1
2
1
0
3
2
0
2
1
1
1
1
1
2
0
1
0
1
3
0
0
1
3
0
3
3
0
2
0
1
5
1
3
4
0
0
0
0
1
1
2
1
3
0
3
1
0
0
1
1
0
1
0
2
1
1
0
2
5
0
1
3
0
0
3
2
4
2
1
3
0
2
4
2
1
3
0
6
0
4
0
2
1
0
0
3
10
4
2
5
1
1
2
1
1
3
0
0
1
1
1
1
0
4
1
1
2
1
5
1
0
3
1
0
1
4
1
0
0
6
2
1
0
1
1
2
2
0
3
3
1
3
2
4
2
2
3
1
1
3
3
1
2
2
4
0
4
3
0
0
1
6
0
1
0
2
0
2
1
1
8
3
1
2
2
1
0
2
0
3
4
1
1
2
1
0
3
0
0
0
4
0
2
0
0
0
2
1
0
1
0
4
1
3
6
3
2
3
0
1
0
1
0
2
3
3
5
1
1
1
0
3
3
0
0
2
2
3
0
3
4
3
1
2
3
3
0
0
2
0
2
0
1
3
0
2
0
2
0
0
1
2
3
1
0
2
1
2
2
0
2
3
1
4
0
1
2
1
1
1
0
1
5
2
0
1
1
3
1
1
2
3
3
0
1
1
4
0
3
2
0
0
5
3
4
1
1
0
3
3
4
0
2
2
0
4
1
0
2
1
0
0
3
2
1
0
1
1
4
4
1
2
0
2
0
1
1
0
0
2
0
1
0
5
3
4
1
5
2
1
5
2
2
2
1
2
2
2
0
49
4
0
3
2
2
1
1
2
3
0
1
1
4
3
0
2
2
1
0
1
0
2
1
5
1
2
1
0
1
0
3
1
2
3
2
2
2
1
3
2
4
3
0
0
2
0
4
0
0
1
1
3
2
1
3
1
4
1
3
4
2
3
2
1
2
4
2
7
0
2
2
2
2
2
3
1
0
2
0
1
0
2
1
3
2
1
3
0
2
2
0
0
0
4
3
0
2
1
2
4
0
0
0
0
1
4
1
3
2
4
0
1
0
0
6
1
1
0
1
1
0
1
0
0
1
1
2
1
2
4
3
1
2
1
0
2
4
2
2
0
1
3
3
2
0
5
2
1
2
5
5
0
2
0
0
2
0
1
2
1
2
1
1
1
2
1
1
2
2
2
2
3
0
2
4
1
0
0
2
3
1
3
2
4
0
2
1
1
3
1
0
0
0
4
3
2
1
3
3
1
2
1
0
2
1
4
2
3
4
0
0
1
2
1
1
0
0
1
0
3
4
2
0
0
4
2
1
0
2
0
1
0
1
4
0
3
1
1
1
1
0
0
2
2
0
0
2
0
1
1
1
2
0
0
3
2
0
0
3
3
2
1
1
3
1
3
1
1
5
1
3
0
4
3
1
4
0
1
1
3
0
2
3
2
0
0
0
0
0
0
1
2
0
2
4
2
6
2
1
3
1
0
1
3
2
1
1
0
2
3
0
2
1
0
1
2
3
0
0
3
1
1
2
2
3
0
0
2
1
4
1
2
0
1
1
2
0
0
2
3
1
1
10
1
0
0
5
2
2
0
1
1
2
0
1
0
0
1
0
2
1
0
2
2
1
1
0
2
1
1
2
0
1
2
0
0
1
2
1
1
0
3
2
2
2
2
0
0
1
1
2
3
0
1
1
4
0
0
2
2
3
1
1
4
0
0
2
1
3
3
3
0
1
1
1
0
0
2
1
3
1
2
0
5
0
1
0
3
1
5
2
3
1
5
1
0
2
2
0
3
1
2
1
4
0
2
3
1
0
0
2
0
0
3
2
1
1
3
2
2
1
1
0
4
2
0
5
0
1
1
2
0
1
0
1
1
4
1
0
0
1
2
3
3
1
4
2
3
3
1
3
1
1
2
1
0
0
1
1
3
1
2
4
0
1
3
4
1
0
0
0
0
5
2
2
5
0
2
0
1
3
0
0
3
1
1
3
1
0
2
2
4
2
1
1
2
1
0
1
0
4
2
0
2
0
0
0
0
3
2
1
2
0
3
1
0
0
0
2
2
0
0
1
1
2
1
3
2
2
4
0
2
2
2
0
3
0
2
1
1
2
1
1
0
0
1
3
0
1
4
2
0
2
1
1
2
1
1
1
1
6
2
2
1
3
1
1
1
0
1
2
3
5
3
2
0
0
0
1
3
0
0
1
2
2
2
2
1
0
1
1
1
3
1
2
0
0
3
0
2
0
4
7
0
2
0
2
0
0
5
1
2
2
3
1
1
1
2
2
2
9
0
0
1
0
3
1
2
1
0
0
0
3
3
5
2
1
1
2
1
2
1
1
0
0
1
2
4
5
0
1
1
1
0
2
0
1
0
1
1
1
2
1
0
1
2
0
2
3
2
1
2
0
0
5
3
2
0
0
1
1
2
3
0
0
2
2
4
2
0
0
2
0
1
3
2
2
2
3
2
0
1
3
5
0
0
0
1
4
3
1
1
3
4
0
4
0
3
2
3
1
1
0
0
3
2
0
0
1
1
0
2
4
1
1
0
1
0
0
2
1
1
0
3
0
2
0
1
0
1
1
3
0
0
2
2
2
2
2
1
1
2
5
1
0
1
3
1
1
0
1
0
2
2
0
3
0
3
4
0
2
2
2
0
2
0
2
0
2
3
1
1
1
1
0
0
2
4
1
3
0
2
3
1
1
2
3
2
0
1
1
3
5
2
3
0
1
0
3
0
2
0
1
2
1
4
0
0
1
0
1
2
0
0
3
1
2
1
0
2
4
1
2
1
0
2
1
2
0
2
5
1
0
2
3
1
0
1
0
0
2
2
3
0
5
0
1
0
0
0
0
0
1
1
2
4
1
1
2
1
0
1
0
3
0
1
4
0
2
0
0
3
2
1
0
1
0
0
3
1
1
0
0
0
1
0
0
0
1
1
0
1
1
2
1
4
3
3
0
5
0
0
1
2
1
0
3
0
3
2
1
2
2
1
1
3
0
2
1
2
0
0
3
0
3
5
0
2
0
1
4
2
2
1
1
2
1
0
2
5
2
0
0
0
3
3
0
0
0
5
4
1
2
4
2
2
0
4
0
2
2
0
4
2
1
1
1
0
0
2
1
2
3
2
4
2
2
4
1
4
0
2
1
1
0
2
1
5
4
3
2
0
3
2
5
2
1
0
2
4
2
2
0
1
3
2
3
3
1
3
3
0
0
1
0
0
2
2
1
1
2
2
2
2
2
2
1
1
0
3
0
3
3
4
5
0
1
3
0
2
0
2
2
0
2
0
0
1
4
1
2
0
1
0
1
0
1
0
1
1
1
4
2
0
4
1
2
4
0
2
2
0
3
0
0
1
1
1
0
2
3
4
2
1
2
2
2
1
4
1
1
0
2
1
1
0
1
0
0
1
2
0
0
2
3
4
0
1
0
2
5
2
1
2
2
0
4
0
3
0
1
0
4
1
0
3
3
2
2
0
0
3
0
2
1
0
4
2
0
1
1
4
1
0
0
1
0
2
1
2
1
0
2
0
2
0
5
4
2
0
2
0
1
0
0
1
0
0
2
2
2
0
0
2
2
0
4
4
0
0
0
0
5
0
0
1
1
1
0
1
0
4
1
1
0
2
1
1
1
0
2
0
1
1
1
1
0
0
1
0
0
0
1
3
2
0
0
2
2
0
2
0
3
2
0
2
3
0
4
1
0
0
0
2
0
1
1
3
2
1
3
4
0
1
0
2
1
0
3
0
5
1
0
1
0
1
0
1
1
0
2
5
6
1
0
1
1
0
0
3
1
2
1
4
0
1
0
1
1
0
1
2
1
1
5
1
1
4
0
2
1
0
3
1
2
0
4
2
7
1
0
0
2
3
0
1
0
0
1
0
1
1
1
1
4
4
2
2
0
3
1
1
0
0
0
1
0
5
0
0
0
1
0
1
3
0
0
1
1
2
2
2
0
0
0
1
1
1
3
0
1
2
1
3
4
0
4
1
0
1
0
2
0
1
1
1
2
0
4
3
4
4
0
0
5
1
3
2
0
1
2
2
1
3
0
0
2
0
2
2
3
1
0
2
1
1
5
3
1
1
0
0
0
1
1
0
2
2
2
4
0
2
3
0
1
1
2
2
3
2
0
0
2
2
1
0
3
0
1
4
1
0
1
1
3
0
0
0
1
1
1
0
1
1
4
3
1
0
1
0
5
1
0
3
2
1
0
0
0
3
0
4
1
2
0
0
2
2
2
4
4
1
0
0
0
6
1
4
2
1
2
1
0
1
0
1
2
0
4
3
0
2
0
3
3
0
5
2
0
0
1
1
4
1
1
0
1
3
0
3
2
3
1
0
1
1
0
0
0
1
0
0
1
0
2
1
0
1
2
0
4
1
1
1
0
4
1
1
0
0
0
0
6
1
0
1
1
0
0
1
3
0
1
2
1
6
2
2
1
1
1
3
3
0
2
1
3
0
0
5
2
0
1
1
1
3
0
1
2
3
4
3
3
3
3
4
1
1
3
1
3
0
2
3
0
3
4
3
0
0
0
1
4
1
2
0
0
1
0
4
0
0
1
2
2
0
1
0
0
1
1
1
3
0
2
4
1
0
2
0
0
2
0
4
1
1
2
3
3
2
1
0
2
3
0
0
3
2
1
1
1
0
2
0
0
1
1
1
1
2
1
1
2
2
1
3
1
1
1
5
0
1
3
3
1
0
0
0
2
1
3
0
2
1
1
0
0
2
0
0
1
2
0
1
3
2
0
2
1
3
6
3
0
0
1
1
1
4
0
3
4
1
1
0
1
4
0
0
3
3
3
1
3
0
0
0
0
3
2
1
0
1
3
0
2
3
3
0
1
1
1
0
1
1
2
4
3
1
0
0
1
4
2
0
1
1
0
1
0
3
2
0
0
0
4
0
1
4
0
2
2
0
0
2
1
2
2
1
1
1
0
2
0
2
2
0
2
1
1
2
1
0
2
1
0
0
3
5
0
0
2
3
0
1
0
0
3
0
1
0
2
0
4
3
3
1
1
0
0
1
0
1
1
3
0
0
0
1
0
1
0
2
2
3
2
3
2
3
0
3
1
1
3
5
3
1
1
2
2
0
3
0
0
2
0
2
3
1
0
2
1
0
1
0
0
1
1
2
1
0
1
1
4
3
3
2
1
0
4
0
0
1
1
1
1
3
1
3
4
0
2
0
2
1
0
0
1
0
1
1
0
1
2
0
2
1
2
3
3
3
1
1
1
0
1
2
1
2
3
1
2
1
2
3
4
2
1
1
1
3
2
1
1
1
1
1
2
1
2
0
0
1
3
0
0
2
1
2
2
1
4
3
2
1
3
2
6
0
1
0
2
4
1
1
2
5
1
3
1
3
4
0
4
2
5
1
0
4
1
0
0
2
1
2
0
1
0
0
3
1
5
3
0
1
2
4
2
1
3
0
3
3
0
2
0
2
1
1
1
0
1
1
0
0
2
4
1
3
3
0
2
1
3
2
1
3
3
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
2
3
4
5
0
0
1
2
0
0
0
1
0
2
0
0
0
4
1
2
1
1
1
1
0
0
0
1
1
0
2
2
1
4
2
1
2
0
2
1
0
0
4
0
0
1
2
1
1
0
0
0
3
2
2
2
2
0
1
0
1
1
1
0
1
2
1
0
0
1
0
3
1
4
1
1
0
0
2
0
2
0
0
0
1
2
2
1
1
2
0
2
2
4
0
2
2
1
1
1
0
2
0
0
3
0
2
3
4
0
2
0
2
1
20
2
2
4
5
0
1
1
0
0
1
1
1
1
0
1
1
1
0
2
3
2
0
0
5
0
1
1
4
0
1
0
3
3
0
3
0
1
0
0
3
0
3
2
3
3
1
1
1
2
1
1
2
2
1
0
0
0
0
3
1
0
3
1
0
0
0
7
1
1
2
3
1
0
3
2
0
1
0
1
0
3
0
0
0
1
0
0
3
4
0
0
0
0
4
2
2
2
3
3
1
1
0
2
1
0
0
1
0
0
0
3
1
3
2
3
3
1
1
1
0
3
1
2
1
5
0
2
0
1
1
0
1
0
4
0
1
2
1
1
0
0
3
4
1
1
1
2
1
0
0
3
2
2
1
4
4
5
3
1
0
0
1
0
0
0
1
3
0
0
0
1
1
2
1
2
2
1
0
0
0
1
2
0
0
2
1
0
0
1
1
1
2
1
5
1
1
0
2
0
0
3
0
4
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
3
1
3
2
2
2
0
0
2
0
0
1
3
3
1
2
2
1
2
0
0
5
2
2
0
1
1
5
2
0
0
1
2
2
1
2
2
0
0
2
3
0
2
5
1
1
6
1
1
0
1
1
2
7
2
2
3
4
0
0
5
0
2
2
0
0
0
1
2
0
2
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
3
3
2
0
2
2
2
0
3
3
0
4
1
1
2
1
3
3
0
0
0
1
1
0
2
0
2
0
3
0
0
2
1
2
0
1
1
0
1
2
6
1
3
0
0
2
1
0
2
3
1
4
0
0
1
0
2
1
1
0
2
2
0
1
1
0
7
0
0
3
0
0
4
2
2
1
1
2
2
0
1
0
4
4
0
3
0
1
11
1
0
1
2
2
1
0
1
2
1
2
1
0
0
1
0
0
1
1
0
1
2
1
0
0
1
1
2
1
0
2
2
3
0
0
0
2
0
0
0
0
1
0
1
0
6
1
1
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
3
0
0
1
1
1
0
2
2
3
1
2
0
2
3
2
1
0
1
4
2
1
0
1
0
2
3
2
2
3
0
2
0
0
0
2
0
0
3
2
2
2
0
1
0
0
1
2
0
0
4
1
0
0
1
2
3
1
0
1
3
3
0
1
2
2
2
0
1
3
0
3
1
2
0
2
2
4
2
4
3
3
2
0
2
2
1
1
0
0
2
1
3
3
0
1
0
1
0
1
3
2
1
0
1
1
4
0
2
2
0
2
0
0
3
1
0
0
0
2
3
2
3
1
1
3
0
1
6
0
0
0
2
0
0
2
0
3
0
1
1
2
1
1
1
0
0
4
2
0
3
0
2
0
0
2
2
1
0
1
0
0
0
2
4
0
1
1
1
2
1
1
1
1
2
2
1
3
1
3
1
0
4
1
1
5
1
1
2
2
3
4
4
1
0
0
3
0
1
2
0
0
3
1
0
1
0
0
0
1
2
2
1
0
2
1
1
2
1
0
1
0
1
0
0
2
2
1
1
1
1
0
1
3
6
0
1
0
1
0
1
0
1
0
0
1
0
3
1
1
2
0
1
3
2
1
0
0
2
0
1
2
0
1
0
0
5
3
0
0
0
2
0
1
0
0
1
0
0
1
0
1
3
0
0
2
2
1
2
1
1
2
4
2
0
2
0
1
0
0
3
3
3
3
1
0
0
1
1
1
1
3
1
1
0
0
1
0
0
1
0
0
0
0
1
2
3
0
1
0
3
1
1
3
1
0
2
1
4
3
0
1
0
1
3
0
1
1
2
2
2
0
1
1
1
0
0
0
1
0
1
2
3
1
2
0
0
1
2
3
0
1
1
0
4
3
3
2
2
0
2
1
2
4
1
0
1
2
0
3
0
0
2
1
1
2
1
0
0
2
0
0
1
0
1
1
1
4
0
2
0
1
4
1
0
1
2
0
2
0
2
1
3
3
3
0
1
3
1
2
2
0
1
0
1
0
1
2
2
2
3
0
1
1
1
2
0
3
2
0
0
0
1
0
2
1
1
2
1
0
4
4
2
1
1
1
2
2
0
0
3
2
0
4
2
3
1
3
0
3
0
2
0
0
2
2
1
1
2
0
5
1
1
1
0
0
3
3
1
2
2
0
6
0
0
2
2
2
1
2
2
2
3
3
3
3
0
0
0
6
1
0
0
0
0
2
1
0
0
3
4
2
3
1
1
0
3
0
2
0
5
2
2
2
0
0
2
1
2
2
3
3
1
0
11
1
1
3
1
3
0
1
1
0
1
3
1
2
1
2
2
2
2
1
6
1
2
1
0
3
2
0
0
2
1
2
1
1
0
0
1
2
3
0
3
1
0
0
0
0
4
1
0
2
0
2
2
0
1
4
2
5
0
1
0
1
1
2
2
0
0
0
3
4
0
1
0
1
1
4
2
2
2
0
0
1
2
3
0
0
2
0
0
4
0
2
0
0
2
0
5
2
2
4
2
0
1
0
0
1
2
0
3
1
1
1
3
2
1
3
2
2
0
0
1
3
2
3
0
2
1
2
4
1
1
0
3
0
0
3
2
1
1
1
2
0
2
1
2
0
0
1
0
1
0
2
1
2
0
0
3
0
1
1
0
2
0
1
2
1
1
0
3
1
5
1
2
3
0
4
4
2
2
2
0
1
1
1
1
0
0
0
0
0
1
3
3
0
2
2
2
2
1
4
2
1
0
0
0
2
1
1
1
0
3
2
4
0
0
3
0
0
2
1
3
1
0
1
2
0
0
2
2
4
3
0
1
0
1
0
0
1
3
2
0
2
0
0
3
0
3
5
2
1
20
0
0
4
4
0
1
2
0
1
0
0
3
1
0
2
0
0
1
1
3
1
0
2
0
2
2
1
1
1
1
3
0
3
3
0
0
3
2
2
3
3
1
3
0
3
0
2
1
2
0
0
5
0
0
0
0
2
2
0
4
2
1
0
0
0
0
1
2
1
1
0
0
2
1
0
0
4
0
3
0
1
2
1
0
1
2
1
0
1
0
0
2
0
5
2
0
3
1
3
1
3
2
1
3
1
1
1
1
1
0
0
5
3
1
0
0
1
1
0
1
1
0
2
0
1
0
1
0
0
2
0
4
0
1
3
2
2
1
3
2
0
2
1
1
2
1
1
2
1
4
4
0
1
2
0
0
3
0
0
1
1
2
0
2
2
0
1
1
0
0
2
3
0
2
1
0
2
2
3
0
2
0
3
3
1
3
2
2
0
2
0
4
0
1
2
0
2
3
2
1
1
2
0
0
1
1
2
0
2
2
2
2
4
0
0
2
2
0
0
1
2
0
0
2
0
6
2
0
0
2
0
2
1
2
1
0
0
0
2
2
5
1
1
1
0
2
2
0
1
3
1
2
2
1
0
0
2
3
0
2
4
0
0
0
3
1
2
3
1
0
3
0
0
1
1
2
1
0
2
1
2
3
3
3
2
1
0
2
0
2
2
4
1
2
0
2
0
0
4
6
1
1
2
0
1
0
0
0
4
1
2
0
2
2
0
1
1
0
4
2
4
0
1
1
0
1
0
1
1
3
1
0
2
1
1
0
2
0
0
1
2
0
3
0
4
2
1
0
1
4
5
0
5
3
0
1
1
0
0
2
1
1
0
2
2
1
1
1
0
0
3
2
1
3
0
1
0
2
0
4
0
0
2
2
1
0
3
5
0
2
1
2
1
0
0
1
2
0
0
1
1
0
0
2
1
1
1
2
4
2
2
1
0
0
1
0
0
0
2
2
0
2
0
1
3
1
0
2
0
2
3
2
2
1
0
6
2
2
8
1
0
1
0
2
0
2
1
2
0
3
1
0
1
0
0
1
0
0
3
3
0
0
0
0
0
0
0
2
4
1
4
1
0
1
2
0
2
0
1
4
2
0
0
1
4
0
0
0
1
0
3
3
3
0
3
1
2
1
0
2
2
0
0
3
1
0
3
0
1
0
2
0
1
0
0
1
2
2
2
1
0
4
0
0
0
0
0
1
1
5
0
2
1
3
2
1
2
1
0
3
3
1
6
2
3
0
1
0
0
2
0
2
1
1
4
1
0
0
3
2
2
0
3
3
0
1
1
0
2
0
2
2
3
2
2
2
0
1
0
2
2
2
0
3
4
2
0
0
2
1
2
1
1
0
4
1
3
0
2
5
0
0
0
0
2
3
2
2
2
0
1
1
2
1
1
2
1
0
0
5
0
3
0
3
1
0
2
0
0
3
3
1
0
0
0
1
0
0
3
0
0
0
3
0
2
1
1
3
4
0
3
0
1
0
0
1
1
2
1
1
1
0
0
1
3
0
2
2
4
4
2
1
3
0
2
0
2
3
2
2
3
0
0
0
4
0
2
2
3
0
1
0
0
0
0
0
2
0
1
3
4
1
0
0
3
2
0
2
2
1
0
2
0
0
2
0
2
0
0
1
0
2
1
1
0
0
1
0
0
1
3
1
2
2
3
5
1
2
3
3
0
0
2
0
2
2
0
3
0
2
1
1
1
0
0
3
0
0
2
3
2
1
5
2
0
2
2
1
0
0
1
0
1
1
0
1
0
2
0
0
2
0
1
2
1
0
4
2
1
4
6
2
0
3
1
0
1
1
2
0
0
2
0
1
0
1
1
2
3
2
0
2
2
1
0
1
2
2
1
1
1
3
2
0
2
2
1
0
1
0
0
2
0
0
0
4
0
1
2
0
2
0
0
2
0
1
0
0
0
2
3
0
0
4
1
2
1
0
0
1
2
3
0
4
1
0
1
0
3
2
2
1
1
0
0
1
16
1
1
1
1
0
0
1
2
0
4
0
0
2
2
3
0
1
2
0
2
1
1
0
3
0
1
0
1
0
3
2
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
5
0
0
1
0
2
2
0
0
3
4
1
2
3
2
0
0
2
1
0
1
2
2
2
2
1
0
0
4
0
0
1
1
1
1
5
0
0
2
0
4
2
1
2
0
0
2
1
0
3
0
1
0
0
1
1
1
0
2
0
0
0
2
1
2
2
1
1
1
0
1
0
1
0
0
1
1
1
5
5
3
1
2
2
0
1
3
0
2
1
0
2
2
1
1
3
1
1
0
0
0
2
1
2
1
0
1
0
2
3
0
1
0
0
2
0
4
1
0
1
1
1
3
0
1
1
3
0
2
1
1
1
0
0
0
2
0
2
2
3
0
0
1
3
0
0
2
1
2
3
0
1
3
3
0
1
1
2
0
2
1
0
1
0
0
1
1
1
2
1
0
2
1
1
4
1
0
0
0
1
4
1
2
1
1
0
1
1
0
1
0
4
3
2
0
0
0
0
4
1
0
3
0
1
1
2
1
0
2
0
1
1
0
0
3
1
2
2
2
0
1
4
3
0
2
2
2
3
0
3
1
3
1
2
2
2
0
0
3
2
1
2
1
0
1
0
1
0
0
1
1
2
1
3
4
2
3
3
0
3
4
1
1
1
0
4
0
2
4
4
0
2
0
0
0
1
1
0
0
0
0
1
0
3
3
0
0
3
0
1
0
2
0
1
1
2
2
0
1
3
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
2
0
1
1
0
4
1
0
2
1
2
0
2
2
0
0
2
1
0
0
2
2
4
0
0
2
0
1
0
1
0
3
0
4
3
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
2
1
0
2
1
0
3
1
1
1
0
0
3
1
2
0
0
1
2
1
1
1
0
0
0
1
7
0
0
0
3
0
0
0
0
1
2
0
0
4
0
3
4
2
0
2
0
2
0
2
1
1
0
1
1
1
2
0
1
0
0
1
0
0
2
3
2
0
2
0
0
0
0
2
4
2
1
3
1
0
0
4
0
2
3
0
2
0
0
1
0
1
1
0
0
5
2
0
1
2
2
0
0
4
2
0
0
0
4
0
0
0
0
0
2
0
1
4
3
2
0
0
2
0
1
1
1
2
0
1
1
1
0
2
1
0
1
1
2
4
2
2
0
0
0
1
1
3
1
1
2
0
1
2
0
0
3
0
1
1
0
0
0
1
0
0
1
0
2
1
1
0
2
2
1
2
1
1
0
0
0
2
0
3
6
1
0
2
0
0
0
0
0
0
0
29
7
0
4
0
1
4
1
0
4
0
0
1
1
0
2
0
0
2
4
3
4
0
0
2
1
0
2
1
0
0
1
4
1
1
2
0
2
1
1
0
2
0
1
1
1
3
3
0
2
0
1
0
1
0
10
1
2
1
3
3
0
0
3
1
0
1
0
3
0
0
3
2
5
3
0
0
2
0
2
2
2
3
1
0
3
1
2
2
2
5
2
2
4
4
4
4
2
0
1
2
1
2
1
1
0
0
3
2
0
0
2
2
1
0
0
2
1
2
0
2
1
0
1
3
3
2
1
1
0
2
2
0
3
1
3
2
3
3
1
0
0
3
0
0
2
2
2
2
6
2
0
0
3
0
1
2
0
0
2
3
0
3
0
3
3
4
0
3
0
2
2
1
2
1
1
0
0
2
0
3
0
0
0
0
1
1
0
1
1
1
0
3
0
0
1
2
3
0
0
0
0
1
2
3
2
1
3
0
1
0
0
0
2
2
1
18
1
2
0
2
2
1
1
3
2
2
1
0
81
1
2
2
0
0
3
1
1
0
1
0
0
3
1
2
2
0
0
2
0
2
3
2
1
2
0
1
3
3
1
3
1
0
0
1
2
3
1
2
0
1
0
2
1
1
1
3
1
1
0
2
2
0
0
2
2
1
3
6
2
0
1
0
3
0
0
3
1
3
2
3
3
0
2
0
2
0
10
2
0
0
0
1
0
1
0
0
1
0
1
1
2
1
2
1
3
0
1
1
2
1
2
0
0
1
0
2
3
4
3
0
0
4
2
3
0
0
0
5
0
2
1
1
2
4
0
1
0
2
0
2
1
1
1
1
1
2
1
2
4
1
3
3
0
3
0
3
2
2
1
0
1
0
2
1
1
2
3
0
0
2
1
1
2
2
1
0
1
0
0
1
3
4
0
1
0
3
0
1
1
2
0
0
1
0
0
2
1
2
4
0
3
1
3
1
0
0
0
1
1
2
2
0
2
1
1
2
0
1
0
1
0
3
0
2
0
3
4
0
1
0
1
1
0
1
1
3
0
1
1
0
0
0
1
1
0
0
1
2
1
3
0
0
0
2
2
1
2
0
1
1
2
0
1
2
2
3
2
0
0
0
3
0
2
1
0
0
3
0
0
0
3
3
1
0
0
0
1
2
3
1
0
1
1
6
2
1
0
0
2
3
1
0
0
2
0
0
0
7
0
2
0
0
1
3
3
2
0
0
0
0
1
0
0
3
0
0
2
0
1
1
2
1
1
2
0
0
2
2
1
17
3
0
0
1
2
2
0
0
0
1
1
1
1
0
1
2
1
0
1
3
3
0
0
7
2
0
0
1
1
1
2
1
3
2
2
1
1
1
0
2
3
0
0
3
0
1
3
0
0
3
5
0
1
0
2
2
3
0
3
1
2
0
3
3
1
2
0
0
0
1
1
1
3
1
2
0
1
0
2
0
0
0
1
1
0
1
3
1
0
2
1
2
2
1
0
0
3
2
1
1
5
1
2
0
2
0
1
2
0
2
2
2
0
3
4
1
2
0
0
0
2
1
2
0
3
2
4
4
0
0
2
0
3
3
0
1
1
2
1
0
1
0
0
2
2
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
4
0
0
0
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
2
0
2
0
1
2
2
0
1
0
3
0
0
2
1
0
0
0
0
1
1
1
0
2
1
3
4
1
1
5
0
0
0
1
2
1
2
2
4
1
2
1
0
2
2
3
0
0
1
2
0
3
3
0
3
2
4
0
1
2
1
0
1
2
1
2
15
1
1
3
1
0
2
0
0
4
1
1
1
1
1
2
1
0
1
0
1
0
1
3
1
1
0
0
0
1
1
0
1
1
0
1
1
2
0
0
0
0
1
4
0
0
0
1
0
2
1
0
0
5
0
3
0
0
4
2
0
1
2
1
0
2
3
2
1
0
1
1
0
1
1
1
1
2
1
2
1
2
3
0
1
5
3
2
2
1
1
1
3
1
3
0
0
2
0
0
3
1
3
0
0
1
0
2
1
2
1
0
3
2
0
0
1
1
0
2
1
2
3
3
2
3
0
0
1
0
5
1
3
0
3
0
1
2
0
2
6
0
1
0
4
3
0
3
0
4
1
1
0
0
1
3
0
4
2
2
1
1
0
4
1
1
0
0
1
1
4
1
0
1
0
2
0
1
1
1
1
0
1
0
3
1
0
0
2
3
3
0
5
1
2
1
0
3
0
2
1
6
0
2
0
0
0
2
0
0
3
0
1
2
2
1
1
0
2
0
1
2
0
0
0
2
3
1
1
1
3
3
2
1
1
1
1
1
0
0
0
0
1
2
1
2
0
1
1
4
2
3
1
2
0
0
2
3
0
1
2
1
2
1
2
0
5
0
1
0
0
1
1
0
1
1
3
3
2
1
0
1
2
1
1
2
0
3
1
1
1
2
2
3
0
1
0
0
2
0
0
3
1
0
0
2
2
2
1
1
0
2
2
4
0
0
0
0
2
2
1
2
0
1
3
2
0
1
1
3
0
3
1
2
4
2
0
2
0
1
1
0
1
0
0
0
1
3
0
1
2
0
1
1
1
0
3
2
0
1
0
1
1
1
2
0
1
0
3
2
1
0
2
2
5
1
3
2
3
1
0
0
0
3
0
0
0
0
1
1
2
3
1
0
3
0
2
2
3
2
0
1
1
4
1
1
0
0
1
2
2
0
0
1
0
2
0
2
3
1
1
0
1
0
1
1
2
1
2
0
1
0
1
0
2
1
0
5
0
4
1
0
0
2
1
3
4
0
0
2
0
1
0
2
0
0
1
0
0
2
3
1
0
1
1
2
4
2
1
1
0
3
0
2
0
0
0
0
5
4
2
0
0
1
0
1
0
1
0
2
2
3
0
2
3
2
0
0
1
0
1
0
4
3
0
2
3
2
1
0
0
2
1
0
1
0
0
0
1
2
0
1
2
0
2
1
0
1
1
3
1
0
0
1
2
0
1
4
0
1
4
1
2
1
1
6
0
0
0
2
1
2
1
1
2
4
4
0
2
6
2
2
2
2
0
0
2
0
0
0
3
3
1
0
1
1
2
0
1
0
2
1
2
3
0
0
1
0
1
3
0
2
1
1
0
3
0
4
0
2
2
1
2
2
1
0
2
0
2
1
3
1
0
2
0
0
1
0
0
0
2
1
1
4
0
1
0
0
0
0
0
5
1
1
0
0
1
1
0
0
2
6
1
0
1
1
0
0
1
2
1
6
0
3
2
2
2
1
0
0
2
0
0
0
0
0
0
3
2
6
0
2
1
2
1
0
133
0
2
2
1
1
0
2
2
0
0
0
0
2
5
2
2
16
0
1
3
0
0
2
0
3
0
0
2
3
1
0
1
0
0
2
0
2
2
0
0
2
2
1
0
1
0
0
3
0
3
0
2
2
1
1
0
3
1
3
4
3
1
5
0
1
5
1
0
2
2
0
4
2
2
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
0
0
1
0
1
1
3
0
0
0
2
1
2
2
1
0
1
1
3
2
0
4
0
0
3
1
2
0
1
1
0
2
4
2
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
3
1
0
0
0
3
3
1
2
1
0
1
1
1
3
1
0
1
1
1
2
0
0
1
1
2
0
0
3
4
2
1
3
2
2
0
1
3
2
1
0
4
2
0
0
2
0
2
1
0
1
1
0
2
1
0
0
1
0
1
0
0
2
0
1
1
1
0
2
1
0
2
0
4
1
1
0
1
0
2
0
1
1
1
3
1
1
1
1
0
0
1
0
0
0
1
0
2
0
1
0
2
1
1
0
1
1
4
0
1
3
2
0
0
0
1
1
3
4
5
3
4
0
2
4
0
3
2
4
1
0
3
2
1
0
2
3
1
0
0
0
1
1
2
2
0
1
1
0
1
3
3
2
0
0
1
2
1
0
2
0
2
2
0
2
0
3
2
0
1
1
0
1
2
2
0
2
1
0
1
1
2
0
0
4
0
0
2
1
0
0
1
1
0
0
2
0
4
2
0
1
1
0
1
2
4
2
1
3
0
1
2
1
0
1
2
1
2
1
0
2
2
2
1
1
5
3
0
10
2
2
1
2
4
1
0
4
2
2
1
0
2
1
0
1
0
4
0
2
2
0
5
0
2
1
0
1
0
1
1
0
2
0
0
0
3
0
0
1
3
1
1
1
1
0
1
0
2
1
1
1
0
0
0
0
1
1
0
0
0
3
1
0
2
2
0
1
0
0
4
1
5
0
4
2
1
2
1
2
2
1
0
2
1
1
0
2
0
0
1
2
0
0
1
2
0
0
0
1
1
2
1
2
2
0
0
1
2
0
1
0
1
1
0
2
2
9
2
1
2
0
2
0
0
2
1
3
1
0
0
2
1
1
0
1
0
0
2
0
1
0
4
2
4
1
3
0
0
2
1
1
2
2
0
2
0
2
0
0
2
5
3
1
2
1
1
2
1
1
1
3
2
4
3
1
1
3
0
0
0
0
1
0
0
0
0
4
0
1
0
0
1
1
4
2
0
0
3
0
6
0
2
3
2
2
3
0
3
0
0
0
2
0
1
3
1
2
0
0
2
1
1
2
1
1
3
0
0
3
1
0
2
8
2
1
0
0
0
2
2
0
0
1
4
1
0
2
2
1
2
0
1
1
2
2
3
0
1
1
0
0
0
2
0
5
0
2
0
3
1
0
3
1
3
0
4
2
0
1
1
1
0
2
3
2
5
4
0
0
2
4
0
2
1
2
3
0
0
0
1
2
3
1
0
1
4
0
1
3
0
2
0
1
3
0
1
2
0
4
0
0
1
1
2
1
0
3
3
2
1
0
0
1
2
0
2
0
0
0
2
0
0
2
1
0
1
2
1
2
1
1
1
2
1
0
0
0
3
1
0
1
1
0
0
0
3
1
1
0
3
2
1
0
1
0
3
2
0
0
3
0
0
1
1
1
1
1
3
2
0
0
0
2
1
5
0
0
0
1
0
1
4
4
1
2
0
2
0
1
1
0
0
1
3
2
1
0
0
2
0
0
0
0
1
4
1
2
1
2
1
0
2
0
0
0
0
0
0
1
1
1
1
1
1
3
3
1
0
0
1
1
1
0
0
1
3
0
0
3
1
0
1
2
0
0
2
1
1
2
0
0
0
1
3
1
1
0
2
0
0
4
1
0
1
0
1
4
1
0
3
0
2
0
2
2
2
0
0
3
0
1
0
1
0
1
0
2
0
2
0
1
0
2
3
0
1
0
4
0
0
5
1
1
2
1
0
0
0
5
4
1
1
0
3
0
2
0
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
0
2
1
0
2
1
0
0
0
0
2
1
0
2
1
1
0
3
1
3
3
2
0
2
0
1
1
3
1
3
1
1
2
0
1
2
4
0
0
0
2
2
3
3
2
0
1
1
2
1
3
2
1
2
0
0
5
0
2
0
0
0
1
0
1
0
0
1
2
0
0
2
4
1
1
1
0
0
1
2
0
2
0
1
1
0
0
2
0
0
0
1
3
0
0
2
5
0
0
5
0
0
3
3
0
2
0
1
2
1
0
0
2
0
0
3
1
1
0
0
0
1
0
2
1
1
1
0
2
4
2
0
0
1
2
1
3
2
0
2
1
0
1
0
2
1
1
0
0
1
2
1
0
0
2
0
1
2
3
3
1
2
0
2
1
1
2
2
1
0
0
0
0
0
0
1
0
0
0
3
1
0
11
3
1
0
0
2
2
2
0
6
3
2
1
1
2
1
0
0
1
1
1
0
2
2
1
0
1
1
1
2
0
0
3
0
2
1
0
0
1
0
1
2
2
0
0
4
0
1
3
2
1
1
0
0
2
2
3
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
1
3
1
3
0
3
2
2
1
0
0
0
1
3
1
2
0
0
2
1
0
1
0
1
1
0
1
0
2
2
1
0
1
1
3
0
0
1
0
0
1
2
1
0
1
2
1
1
1
0
2
0
0
0
1
0
0
0
0
0
3
3
2
1
0
1
0
0
3
2
1
0
0
3
0
0
1
2
1
1
0
0
2
1
1
1
0
3
2
2
0
0
0
1
3
0
1
1
0
1
1
0
3
1
0
2
0
3
0
3
0
1
6
1
1
1
0
2
3
2
4
1
0
0
0
0
0
3
2
0
3
2
0
0
2
3
1
1
1
2
3
2
0
0
2
0
1
0
1
3
3
1
2
1
3
1
2
0
1
2
0
4
1
0
1
1
1
2
1
0
1
2
0
3
0
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
1
2
0
0
0
0
0
2
0
2
4
1
0
1
0
1
1
1
0
1
1
3
3
2
1
2
4
2
1
0
4
0
1
0
3
1
2
1
2
2
1
0
0
1
3
1
3
0
2
1
0
0
1
0
2
2
1
0
1
3
4
2
1
0
3
0
2
0
1
0
1
0
0
3
1
0
1
1
1
0
2
2
1
4
0
1
3
1
1
1
0
3
17
1
1
2
2
1
2
0
4
2
1
0
0
2
1
1
1
1
3
0
0
2
0
1
1
1
1
0
3
0
1
1
0
1
3
0
2
2
0
2
1
2
2
1
0
0
0
2
1
0
0
1
1
2
4
3
0
1
3
3
1
1
1
3
1
1
0
0
3
2
0
1
0
1
0
1
0
0
0
0
2
0
1
1
0
2
3
0
2
0
3
0
0
1
0
1
1
1
1
0
0
1
4
0
0
0
1
1
2
2
0
3
0
0
0
3
0
2
0
0
2
0
3
1
0
1
2
2
5
0
2
2
0
1
2
2
2
1
2
0
2
1
1
5
0
1
0
2
4
1
0
1
0
0
0
2
2
0
1
0
0
1
3
1
0
0
2
3
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
1
4
1
3
2
3
1
4
1
1
0
0
2
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
3
2
1
0
0
0
1
2
2
5
0
2
0
1
0
0
0
0
1
1
1
2
0
2
0
1
1
2
4
1
0
1
0
2
0
1
1
1
0
0
0
1
1
1
1
0
1
1
4
1
0
3
0
1
1
1
0
4
1
2
1
1
0
0
1
0
1
1
1
1
2
1
0
0
2
0
0
1
2
3
3
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
3
0
0
1
0
2
0
0
2
3
2
5
1
1
0
2
2
3
2
0
0
2
0
1
2
2
0
10
3
6
1
4
1
1
2
1
1
0
0
1
1
1
2
1
2
0
0
1
3
0
0
0
1
0
2
4
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
3
1
2
0
0
0
1
4
2
1
2
1
2
2
2
1
3
1
2
3
4
5
0
1
0
0
0
6
1
3
0
0
0
4
1
4
1
0
0
1
0
1
1
3
1
0
1
2
0
1
1
0
0
1
1
2
1
3
2
6
1
4
0
0
0
3
0
2
1
1
1
0
0
4
3
4
0
2
2
2
0
2
0
2
1
4
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
1
1
0
0
0
0
1
0
3
4
2
1
1
0
0
1
3
2
0
1
2
1
4
2
0
0
1
2
1
2
1
1
1
2
0
2
0
1
1
2
0
1
0
0
0
2
1
0
0
2
1
1
4
0
1
5
1
2
0
2
3
0
0
1
0
2
0
2
2
1
1
1
0
0
0
3
1
1
1
1
2
0
0
3
2
1
1
2
0
1
0
1
0
0
0
1
0
2
0
0
1
2
1
2
0
0
3
3
0
0
2
0
1
0
2
1
3
1
1
1
0
3
2
1
0
2
1
0
2
2
2
0
0
0
2
1
1
3
1
2
0
2
0
1
4
1
0
3
1
0
1
3
1
0
0
1
1
0
3
2
2
1
0
0
0
1
0
1
1
1
1
0
3
1
3
1
1
0
2
2
2
3
4
3
2
3
1
1
1
2
2
0
0
0
0
3
1
0
0
2
1
0
1
0
1
2
0
1
2
0
1
0
1
1
0
0
1
1
2
1
0
0
0
1
1
1
1
11
0
1
1
2
1
0
0
1
1
0
0
1
0
3
2
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
1
3
0
0
3
2
1
0
3
1
2
0
0
1
0
4
0
2
0
2
1
1
2
2
1
0
1
1
0
2
0
2
0
4
3
0
1
4
2
2
1
0
1
0
1
0
2
0
0
2
2
1
2
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
1
1
0
2
0
1
2
1
0
0
1
0
0
1
1
1
1
3
1
0
3
1
1
2
1
1
0
0
1
1
0
2
0
2
2
1
0
0
3
1
3
1
4
0
0
1
0
3
3
1
0
3
0
3
1
4
2
0
1
1
3
1
3
3
0
2
0
3
2
0
1
0
2
2
2
1
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
2
0
0
1
3
0
3
0
1
2
0
1
2
0
2
2
1
2
3
1
1
0
0
2
3
3
2
3
2
1
0
1
0
1
0
1
0
3
3
0
3
0
1
1
0
0
3
2
0
1
1
0
0
1
0
2
1
2
2
1
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
1
0
0
0
4
0
0
0
1
1
3
1
0
0
2
0
1
0
0
0
1
2
0
1
0
7
0
0
0
4
0
1
1
0
1
3
0
4
1
7
1
1
3
3
0
1
0
1
0
2
0
1
0
3
0
3
2
1
2
3
3
1
0
2
1
1
0
0
2
1
2
1
0
2
0
0
1
2
1
0
0
2
0
2
2
2
1
1
1
0
2
1
0
3
0
1
0
2
1
2
0
2
0
2
1
1
1
0
0
2
2
2
0
1
2
3
1
0
1
2
2
0
1
4
2
0
1
0
4
0
0
1
2
0
0
1
1
0
1
0
0
1
0
2
3
0
2
3
0
0
0
2
1
0
0
3
0
1
2
1
2
3
2
0
3
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
5
1
4
0
0
0
1
0
1
1
0
0
0
3
0
0
2
3
0
1
2
0
0
1
1
3
0
1
0
1
1
0
1
2
0
1
1
1
4
0
4
0
3
1
1
2
3
4
0
0
1
0
2
2
4
1
4
3
1
0
2
1
0
3
0
3
1
1
0
2
0
1
1
0
2
0
2
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
2
0
0
1
3
0
0
1
1
1
0
5
0
3
0
1
3
1
0
1
1
0
0
3
0
0
3
0
0
2
0
1
0
2
0
0
0
2
2
1
2
1
0
1
1
3
0
1
0
0
2
1
1
1
5
1
2
4
0
1
35
2
0
0
0
0
2
1
0
2
1
1
1
2
1
2
0
1
0
3
2
0
0
1
1
2
2
0
0
1
2
0
4
0
0
2
0
0
2
1
3
2
2
2
1
0
1
0
3
1
0
0
1
0
1
2
0
3
2
1
0
2
2
0
0
2
0
2
0
3
1
0
0
2
0
0
1
0
3
0
0
0
2
0
2
4
1
5
1
2
4
1
0
1
2
0
0
1
0
0
0
2
2
2
2
4
0
5
4
0
1
0
0
0
0
0
2
3
1
0
0
1
0
1
1
0
1
0
1
0
2
1
1
0
2
2
0
0
2
2
4
4
0
0
2
0
2
1
0
0
12
1
1
1
0
1
0
0
0
1
0
0
0
2
9
2
1
0
0
1
4
0
1
3
0
0
0
2
1
1
0
1
0
2
0
1
2
0
1
1
0
2
1
0
2
0
0
0
2
5
1
0
3
5
1
0
7
2
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
1
1
1
0
1
4
0
2
1
1
0
2
0
1
0
1
0
0
2
0
1
0
0
1
4
1
1
2
0
1
3
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
3
2
3
1
0
1
1
2
0
1
2
0
2
2
0
3
1
2
3
1
1
1
6
0
0
0
3
0
1
0
0
1
0
1
2
0
0
1
1
1
5
0
4
1
0
0
2
1
1
1
2
0
1
2
0
0
0
2
0
1
1
5
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
1
0
1
1
1
1
0
2
0
2
1
0
1
3
0
1
0
1
0
1
1
0
3
0
2
0
0
0
0
2
0
1
0
1
2
3
0
0
2
1
1
1
1
4
2
4
6
0
2
1
1
2
4
0
1
3
1
1
0
1
0
1
1
1
2
0
1
0
0
0
3
2
1
2
1
2
0
1
1
1
1
2
2
2
2
3
2
2
2
2
0
4
2
3
1
1
5
0
1
1
0
0
2
2
0
0
1
0
3
1
2
0
0
1
1
2
0
2
2
0
0
1
1
2
1
1
2
2
2
1
1
1
2
0
0
0
0
0
2
0
0
0
4
1
1
2
1
0
0
3
0
2
1
0
0
1
1
3
3
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
2
1
3
1
3
0
2
3
0
0
0
0
0
3
2
0
0
0
4
1
0
1
0
2
0
0
4
0
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
0
2
2
2
1
2
3
4
1
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
1
0
0
3
3
3
2
0
0
0
2
4
0
0
3
0
3
0
2
0
0
0
2
1
0
0
0
1
1
0
4
2
1
0
0
2
0
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
0
2
0
0
3
0
1
0
0
1
0
3
1
3
1
1
3
2
3
5
0
4
2
0
0
1
2
0
0
3
2
2
0
2
2
3
2
0
1
3
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
0
1
1
0
1
0
1
0
3
1
2
2
3
0
2
1
0
1
2
1
1
2
0
0
2
3
0
3
2
3
1
0
0
0
1
2
1
0
4
1
0
2
3
0
0
1
0
1
0
1
1
0
2
1
1
2
1
2
2
1
2
0
2
1
1
0
2
2
2
0
2
1
2
0
0
0
0
3
2
0
1
0
0
1
0
0
0
3
0
1
1
1
0
2
1
0
0
2
0
0
1
0
0
1
0
2
1
0
2
3
0
0
1
1
2
0
0
2
1
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
2
2
0
1
1
2
2
0
0
2
1
1
1
1
2
0
1
2
0
1
3
3
2
0
0
0
1
0
1
1
2
0
0
6
1
4
0
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
1
2
0
0
1
0
0
0
1
4
0
1
0
0
2
1
1
1
0
0
1
1
3
1
1
1
0
2
4
2
0
3
0
0
0
3
0
1
1
0
1
1
1
2
0
0
3
0
1
2
2
1
2
0
1
2
0
0
0
0
1
4
3
1
1
0
0
0
0
0
1
2
3
3
1
0
0
1
1
1
0
0
3
0
2
0
0
1
1
0
2
3
0
1
1
1
0
0
1
0
0
3
0
1
0
0
0
0
2
1
1
6
0
1
1
1
0
0
0
5
0
1
5
1
0
1
1
0
2
0
0
0
2
0
5
0
1
0
2
0
2
1
3
0
2
3
1
2
0
0
0
2
0
0
2
1
0
3
0
1
1
0
1
1
2
4
2
1
2
0
0
0
3
2
0
1
2
0
0
3
1
2
1
1
1
0
4
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
3
3
2
1
0
0
2
1
0
2
0
3
1
3
0
3
0
2
1
0
2
3
3
0
2
0
0
2
1
2
4
1
0
0
0
0
0
0
0
1
1
1
2
1
0
2
1
0
0
2
0
1
1
1
0
0
5
0
0
3
2
1
3
2
1
1
2
1
2
0
0
1
2
1
0
0
1
2
1
1
4
0
0
0
0
3
0
1
3
1
0
1
3
0
0
1
2
2
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
2
1
3
2
1
0
0
1
0
1
0
5
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
3
2
1
1
0
2
0
1
0
0
5
0
0
2
0
0
1
3
3
0
0
0
0
1
1
0
0
0
1
2
4
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
3
4
0
3
1
1
0
4
1
2
0
1
1
0
0
1
0
0
5
6
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
5
3
1
0
0
0
0
2
2
0
0
0
2
4
2
2
1
0
0
2
3
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
1
3
1
0
1
0
2
1
0
2
4
1
5
2
2
1
0
0
3
0
4
3
2
2
3
2
0
0
0
3
0
1
0
0
0
2
3
1
1
1
3
0
2
0
0
1
0
0
0
0
1
0
3
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
5
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
5
2
3
3
0
0
1
0
4
1
0
3
2
0
2
1
3
0
0
0
5
0
1
1
0
0
2
2
3
1
1
1
0
1
2
0
2
0
4
0
0
1
0
1
1
0
0
1
3
0
0
0
1
1
1
1
0
0
0
4
0
0
0
2
0
0
2
1
0
1
1
1
0
2
1
1
1
0
2
1
0
1
1
3
1
0
2
1
1
3
2
0
4
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
3
0
1
1
2
2
1
2
2
1
1
1
3
2
0
0
0
1
3
2
1
1
1
1
1
0
1
0
1
1
5
0
2
0
1
3
2
3
3
2
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
0
1
3
2
4
0
0
0
0
0
0
1
0
2
0
1
0
3
1
1
1
1
0
1
0
1
0
3
2
0
0
0
1
1
0
0
1
0
0
2
2
3
2
0
1
2
2
1
1
3
0
0
1
1
0
0
2
2
0
1
2
0
1
2
2
0
3
0
1
2
0
1
1
3
3
0
2
0
0
0
2
0
0
2
2
1
4
0
0
2
1
0
2
3
2
2
1
3
1
0
3
2
2
2
0
1
0
1
3
2
2
0
5
1
1
1
0
0
0
1
1
0
1
1
0
2
0
1
3
1
1
1
3
1
4
0
1
0
0
2
2
2
2
2
0
2
2
1
0
1
3
0
2
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
5
0
0
0
0
2
0
0
0
0
0
3
1
0
3
1
0
2
2
1
4
1
3
1
2
1
0
1
0
4
1
1
2
1
0
1
1
1
1
0
2
0
1
0
1
4
1
0
2
2
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
2
2
2
1
4
0
2
2
0
2
3
1
0
1
1
0
1
1
1
1
1
3
0
42
0
0
3
4
0
1
1
0
0
1
0
2
1
1
2
1
1
2
1
1
0
3
1
1
0
0
0
0
0
2
2
1
0
3
0
0
2
2
0
0
0
0
1
0
2
0
0
2
1
3
1
1
2
1
1
1
1
1
6
2
1
3
0
0
2
2
0
1
2
0
0
0
3
1
1
0
1
1
3
1
0
3
1
2
0
0
2
0
0
1
2
2
1
1
1
1
3
1
0
1
1
0
3
2
2
2
0
1
0
1
1
0
3
0
2
0
0
0
2
0
0
0
1
3
1
0
0
1
1
0
1
0
5
0
2
0
1
0
2
0
0
0
3
1
1
0
2
2
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
1
1
2
1
2
0
2
1
1
2
0
0
3
0
1
3
3
3
3
0
2
2
0
0
0
2
0
0
2
0
0
2
1
5
1
1
3
2
0
1
7
4
0
0
0
0
3
0
1
1
2
6
0
1
0
3
1
3
0
2
0
0
2
1
0
0
2
2
0
0
0
2
0
0
3
3
2
0
0
1
0
0
2
0
2
0
2
0
1
5
2
0
0
4
0
0
1
0
1
2
2
0
2
0
1
0
0
3
1
2
2
0
1
3
0
1
3
2
3
2
1
2
1
1
0
1
3
3
0
3
1
0
0
1
3
0
2
0
0
1
1
1
0
1
2
0
1
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
3
1
1
0
0
1
3
2
0
0
5
0
1
1
1
2
1
3
3
3
2
0
1
3
1
0
0
1
0
1
1
0
1
2
3
0
0
0
0
2
1
3
0
0
0
4
1
1
4
2
1
3
1
1
0
0
4
1
1
1
0
3
1
1
0
3
3
1
5
2
1
0
0
1
1
2
1
0
1
1
0
0
1
3
1
0
2
1
2
1
0
0
0
0
1
0
3
3
1
3
1
0
0
1
0
1
2
1
0
0
1
1
0
2
1
4
0
1
1
0
1
1
0
1
0
0
1
0
1
2
2
1
2
0
0
2
1
1
3
0
0
1
2
0
6
2
3
1
2
2
0
2
4
1
4
2
2
4
1
2
2
2
0
0
2
1
0
0
0
1
1
0
2
1
2
0
1
0
1
0
2
2
4
0
0
3
2
2
1
1
4
0
1
1
0
1
1
0
4
0
1
0
2
0
0
2
0
1
2
0
1
1
2
1
1
4
1
0
0
0
1
0
0
1
0
2
0
0
1
0
3
0
1
4
2
0
0
1
2
2
2
0
0
0
1
0
0
0
0
4
3
0
3
2
0
0
1
0
2
2
3
2
2
0
0
1
0
1
0
2
1
2
4
0
2
3
1
2
0
1
0
0
2
1
3
0
2
1
2
1
0
0
0
2
0
10
0
1
0
1
0
1
1
0
0
2
4
0
0
1
4
1
1
1
1
3
2
5
2
0
2
3
4
2
1
0
2
2
2
0
0
2
6
0
0
0
3
1
2
1
1
0
1
2
0
1
0
1
2
0
5
0
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
0
0
2
1
3
3
1
0
1
0
2
1
1
2
1
1
1
1
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
2
1
1
3
0
1
7
0
4
1
1
1
1
0
0
0
0
1
1
2
2
0
3
2
0
0
2
0
0
1
1
4
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
2
0
0
1
1
0
0
2
1
1
0
0
0
1
2
0
0
1
1
2
0
1
2
4
1
1
0
2
1
0
2
4
1
0
1
0
1
3
0
2
1
1
2
1
1
0
2
0
2
3
1
2
0
0
0
0
1
1
3
4
1
3
2
2
2
1
2
1
0
2
2
0
3
2
1
1
1
3
2
1
1
2
2
0
0
0
0
0
1
1
0
1
0
1
3
0
1
0
1
2
2
2
2
1
0
3
2
2
2
2
0
1
4
1
1
1
2
2
1
0
2
0
1
0
1
3
0
1
1
1
0
1
0
5
0
0
0
0
0
0
1
4
3
5
5
0
0
2
1
1
0
1
4
2
0
1
0
3
1
0
2
1
1
0
1
0
1
2
3
1
1
3
1
2
0
2
1
2
1
0
0
0
3
3
0
0
0
1
0
0
1
5
2
1
1
0
0
1
0
0
3
0
1
0
0
0
1
1
1
1
1
2
0
2
2
1
2
0
1
0
2
0
4
0
0
1
0
1
0
2
2
0
1
1
2
1
2
0
0
2
1
2
12
2
0
3
3
0
1
1
2
1
2
0
7
0
0
0
1
1
1
3
0
4
0
2
0
0
1
1
2
0
3
0
0
0
2
0
3
2
1
5
0
2
0
2
3
1
1
3
0
0
1
0
0
0
2
1
1
1
1
2
0
2
0
0
1
1
1
1
2
1
0
0
3
0
0
2
0
1
4
1
1
1
4
1
0
0
0
1
3
0
0
3
0
0
1
1
0
0
2
2
0
2
3
1
4
2
2
2
4
2
1
0
1
3
0
1
4
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
3
0
1
0
3
1
0
1
0
1
0
0
3
0
1
0
2
1
1
1
0
3
0
1
1
1
1
1
1
0
1
0
1
1
2
6
1
1
0
2
3
0
0
0
2
2
2
1
2
1
1
1
5
0
2
3
2
0
1
1
0
2
0
0
1
1
2
0
0
1
2
0
0
1
1
1
2
2
0
0
4
0
1
0
2
0
0
0
0
0
3
0
0
2
1
0
0
1
1
0
2
2
0
3
0
0
1
0
2
0
0
0
0
1
0
0
1
3
5
0
0
0
42
0
3
0
4
0
0
1
2
3
0
2
1
0
0
2
1
2
0
0
1
1
0
0
0
1
6
2
1
1
1
1
1
0
0
0
0
1
1
0
2
1
2
1
1
0
1
0
0
0
1
0
0
1
3
0
2
0
1
1
0
3
1
0
0
0
1
3
0
1
2
0
0
3
0
1
1
0
2
0
1
0
0
0
0
1
4
5
0
2
0
0
1
0
1
0
0
1
0
1
3
0
2
0
2
1
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
3
1
1
5
0
1
0
0
6
0
2
0
0
0
0
1
0
1
1
1
1
0
0
2
2
0
1
0
0
0
2
1
0
4
0
1
2
1
0
1
0
0
1
1
1
2
1
0
0
0
1
1
1
0
1
2
0
3
0
1
2
0
2
0
1
2
4
3
1
1
1
0
2
1
2
1
1
0
3
1
0
2
0
1
2
1
1
0
2
2
1
2
0
1
1
0
2
1
0
1
0
0
1
1
1
2
1
4
0
1
2
0
1
3
3
2
2
3
1
0
0
2
1
3
0
1
1
1
2
2
0
0
2
3
0
0
1
0
1
1
0
1
1
2
2
0
4
1
0
3
0
3
1
0
1
1
2
0
0
2
1
2
0
0
2
0
2
2
4
0
3
1
0
0
3
0
1
0
1
2
1
0
1
0
1
0
1
0
0
0
4
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
3
0
1
1
0
3
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
2
1
1
0
3
1
3
2
1
0
1
0
2
0
0
0
1
1
2
0
1
1
0
2
2
0
3
2
0
2
0
3
1
2
2
3
1
0
0
2
2
1
2
1
2
1
1
1
1
2
2
1
0
0
0
0
0
1
0
2
1
0
1
2
1
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
2
4
1
0
2
3
1
2
3
2
1
0
2
0
1
0
1
1
3
0
2
1
2
3
0
0
2
0
1
0
4
0
1
1
0
0
0
1
5
2
0
0
0
1
1
2
2
1
0
1
1
0
0
3
1
3
1
0
0
0
2
1
1
1
5
2
1
0
1
1
0
0
1
1
0
1
1
0
3
1
1
0
1
3
1
0
1
0
2
0
1
0
5
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
1
0
0
2
1
0
7
3
1
0
0
0
0
4
1
1
1
1
0
0
2
0
3
2
1
3
1
1
0
1
0
1
0
2
1
0
1
2
0
3
0
1
0
0
0
3
0
0
1
3
2
2
0
2
3
1
1
2
3
2
2
1
1
1
1
0
1
1
0
0
0
1
2
0
0
0
2
0
4
1
0
1
3
0
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
1
1
0
0
3
1
0
1
3
3
0
2
0
1
1
0
0
0
0
1
0
1
2
4
0
1
1
0
1
1
1
10
2
0
1
0
0
2
1
0
0
0
1
0
1
1
0
0
1
2
2
1
1
2
1
0
1
0
0
1
3
0
1
3
2
3
1
0
0
1
0
0
1
1
2
2
0
0
2
2
1
3
1
1
1
1
0
1
2
2
0
2
0
2
1
1
0
0
0
0
0
0
1
1
1
1
1
2
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
2
0
0
0
3
2
0
1
0
0
0
2
5
0
2
0
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
1
3
0
1
0
1
2
3
0
0
1
3
3
0
0
0
10
4
1
0
1
2
2
0
2
0
0
0
0
1
0
2
2
0
0
1
1
0
2
0
1
0
1
1
0
1
3
0
2
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
3
1
1
0
2
1
0
1
1
2
0
1
3
0
2
0
0
0
2
4
0
1
2
0
3
2
1
1
3
2
1
2
1
0
0
0
0
0
3
3
1
0
0
0
1
0
0
4
0
2
3
2
3
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
1
2
0
0
2
2
0
0
1
0
2
0
0
1
3
0
1
2
0
1
1
0
0
0
4
1
0
3
1
0
1
2
1
1
1
2
0
1
2
1
0
2
1
0
1
1
0
0
2
2
0
0
4
2
0
1
0
1
3
1
2
0
0
0
1
0
0
1
3
1
0
1
0
0
0
0
5
1
2
2
0
2
0
1
0
0
3
1
0
1
1
3
0
0
1
0
0
1
0
3
1
1
1
3
2
1
0
1
2
0
0
0
1
0
1
1
0
3
2
1
1
1
0
1
2
0
1
0
1
1
0
3
0
0
0
1
3
3
0
0
5
1
0
0
0
1
0
0
1
0
1
2
6
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
5
1
0
4
2
1
0
0
1
3
0
1
2
0
1
0
0
0
0
0
1
1
2
1
0
2
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
2
3
0
1
1
0
1
1
1
2
1
0
2
1
2
2
0
1
1
0
2
1
3
1
2
2
2
0
2
2
2
0
0
3
2
1
3
1
2
1
1
0
0
0
1
1
0
1
1
2
0
0
0
1
3
2
2
1
1
0
1
0
1
0
0
1
1
2
1
1
2
4
0
0
1
2
0
2
1
2
0
3
0
0
2
2
2
0
2
2
2
1
0
3
1
0
3
0
2
2
3
0
1
0
1
0
3
1
0
2
1
0
0
0
1
4
1
2
1
0
3
0
2
1
0
0
0
1
2
1
1
2
1
3
0
0
1
1
1
4
1
0
1
0
1
1
0
1
4
0
3
0
0
1
3
1
0
1
2
1
3
2
0
1
0
1
1
0
2
1
0
3
0
1
1
1
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
4
3
3
0
1
2
0
1
2
0
1
1
0
6
0
1
2
0
1
0
0
0
0
2
3
0
0
2
1
0
1
1
1
1
0
1
0
1
2
1
2
5
0
1
1
0
1
1
0
1
3
1
1
0
2
2
1
2
2
1
2
1
0
0
1
0
2
2
3
1
0
2
0
0
1
1
0
0
0
0
9
0
0
0
1
0
2
1
1
3
0
1
0
1
2
1
2
0
0
2
2
2
0
1
0
1
3
1
2
0
0
1
1
3
2
1
1
3
1
0
2
1
1
0
2
2
0
1
3
1
3
1
0
1
1
0
0
1
0
2
0
0
3
2
2
1
2
2
0
0
0
2
0
1
0
1
1
0
2
1
1
2
0
3
2
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
3
0
0
1
1
13
0
0
0
0
1
1
1
0
3
3
2
1
5
0
5
2
1
0
0
0
0
1
1
2
2
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
2
1
4
2
1
1
2
0
2
2
0
0
3
0
0
1
5
0
2
0
1
0
4
0
4
1
1
0
2
1
6
0
3
3
0
0
2
0
0
1
0
2
2
2
0
2
0
2
2
2
1
2
0
0
2
0
0
0
1
1
0
1
2
1
6
1
0
0
2
2
0
1
0
3
1
0
0
0
0
1
2
1
2
0
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
4
1
2
0
0
2
0
1
1
0
2
1
1
2
0
1
0
6
1
0
5
2
1
1
0
0
0
0
0
1
4
0
1
2
1
2
4
1
0
0
1
0
1
3
0
0
1
0
1
1
0
1
0
0
0
1
0
3
3
0
2
2
5
1
3
0
1
1
1
1
3
0
2
1
1
2
1
0
0
1
1
0
6
0
0
4
1
0
0
3
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
4
0
0
2
1
1
1
2
1
0
0
1
2
0
0
0
0
2
0
0
2
1
1
3
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
0
1
1
2
1
1
1
2
0
0
0
2
2
1
2
1
2
0
2
0
2
1
0
0
2
1
0
0
2
1
3
0
1
0
0
0
0
4
0
0
3
1
0
1
1
2
2
4
2
1
1
0
0
3
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
2
2
3
1
3
0
0
3
0
0
1
0
2
2
1
1
1
3
1
0
2
2
0
4
0
2
2
4
2
0
0
2
2
1
1
0
1
0
0
1
0
2
2
0
0
1
0
2
2
0
1
1
1
0
2
0
0
2
2
1
2
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
2
3
1
0
1
1
5
0
0
0
3
2
0
0
3
0
0
1
1
4
0
2
0
1
0
2
2
2
2
0
3
0
0
2
0
1
2
0
2
0
0
0
2
2
0
0
3
1
0
0
0
4
0
0
1
2
0
2
2
0
0
0
0
1
1
4
2
0
1
1
2
0
0
2
6
0
1
0
1
0
3
1
3
0
2
1
0
3
1
0
1
1
1
0
2
2
1
2
2
1
0
1
3
0
2
2
0
1
0
2
1
1
0
1
0
2
1
0
0
1
2
3
0
1
0
2
1
0
2
2
1
5
1
2
0
3
2
2
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
2
1
0
1
1
2
2
1
2
0
0
0
1
5
3
0
0
1
1
0
0
2
1
1
3
0
1
2
3
2
0
2
1
1
0
0
1
1
2
2
0
0
3
0
0
1
2
0
0
1
2
0
4
2
1
0
1
1
2
0
0
2
0
0
1
1
0
1
1
3
2
2
0
2
2
3
3
0
2
2
0
0
2
0
2
2
1
1
2
0
2
0
4
0
1
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
3
1
0
0
3
0
1
0
0
1
0
0
2
0
0
2
0
0
2
4
3
1
0
2
0
1
1
2
0
1
1
3
3
0
0
0
1
1
3
2
0
0
2
0
2
0
0
0
4
3
2
0
0
1
1
2
1
0
1
4
0
1
1
0
0
1
0
2
2
0
0
1
0
1
3
2
1
0
0
2
1
0
1
4
2
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
4
1
2
0
0
0
0
1
0
1
1
1
1
0
1
3
2
3
1
0
1
1
0
0
0
2
1
2
2
2
3
0
3
1
0
0
2
0
1
3
0
4
0
0
0
1
0
0
58
2
1
2
0
1
3
0
0
0
0
3
0
1
0
0
0
1
0
1
3
1
2
0
1
0
2
0
1
1
1
1
0
1
0
0
3
0
0
1
1
1
2
3
2
1
0
7
1
0
1
3
0
0
1
0
1
1
0
1
0
0
1
2
1
3
0
0
2
0
0
0
0
1
1
0
1
0
1
4
1
2
0
0
1
0
0
3
0
1
2
0
2
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
0
3
1
19
2
0
1
1
0
1
1
0
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
5
0
0
2
0
1
0
1
0
1
1
0
2
0
1
0
2
2
0
2
0
2
2
2
1
1
5
0
1
0
5
0
1
5
2
0
1
1
0
0
0
0
1
1
0
0
3
0
2
1
1
0
0
2
0
0
2
3
1
1
2
0
1
0
1
1
1
3
1
1
1
0
0
3
2
1
1
0
0
2
1
0
1
0
3
4
2
2
0
2
3
1
2
0
2
0
2
1
0
1
1
6
3
2
0
2
1
3
1
0
0
0
0
0
0
0
1
0
1
2
1
1
4
1
0
1
1
0
1
2
1
2
1
2
1
0
1
2
1
1
0
1
2
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
2
2
3
1
1
0
1
0
1
0
0
1
2
2
0
0
1
1
2
2
1
1
0
3
1
0
1
0
1
0
1
0
2
3
1
3
0
0
0
0
0
1
2
2
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
0
2
0
3
0
2
1
0
1
2
0
2
0
2
0
0
2
1
1
0
1
1
1
2
3
0
2
0
0
1
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
1
1
0
1
3
2
3
2
0
2
1
0
1
1
2
1
0
0
0
1
1
0
2
0
1
0
2
4
0
1
0
0
1
1
1
2
0
1
1
0
1
2
1
3
0
0
0
1
1
1
0
0
0
2
0
2
0
2
1
1
0
2
0
0
0
3
1
3
1
0
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
2
1
0
0
1
3
0
3
1
1
0
0
4
1
1
2
0
0
1
0
1
0
0
1
1
3
1
1
1
0
2
1
1
0
1
0
2
0
1
2
1
1
2
1
0
2
0
1
0
0
0
0
2
0
1
0
3
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
1
0
3
0
0
1
0
2
1
2
2
0
0
2
0
1
0
3
1
1
0
0
0
1
0
1
2
1
1
2
1
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
2
2
2
2
0
0
1
1
0
1
0
1
1
2
2
0
0
2
0
0
2
1
2
1
0
0
0
1
0
2
0
3
2
2
1
2
3
1
1
0
0
2
1
0
1
5
3
0
1
0
0
2
2
4
0
2
1
0
0
0
2
0
1
18
2
1
0
2
2
2
1
3
2
2
0
0
1
1
1
3
1
2
0
0
2
1
0
2
5
1
0
2
0
1
1
1
0
0
3
2
2
2
0
3
0
2
1
0
1
1
1
0
4
1
0
1
0
1
2
4
0
0
2
2
1
0
1
1
1
0
0
1
0
1
2
0
1
0
1
0
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
2
3
2
1
1
0
1
2
0
0
1
1
1
1
3
1
1
0
2
1
1
1
0
2
3
0
2
0
0
0
1
1
2
0
1
0
3
4
2
0
0
0
0
1
1
2
4
1
2
2
0
0
2
0
1
2
3
0
0
1
2
0
2
0
1
0
2
0
2
2
1
2
0
1
1
2
2
1
1
0
1
4
1
13
0
0
3
0
1
1
1
1
0
2
0
3
0
3
0
0
2
1
1
2
1
2
2
0
0
0
1
1
1
0
0
2
0
0
3
1
3
0
0
0
1
0
0
2
4
0
0
1
3
0
0
2
0
2
1
3
0
1
0
0
2
0
2
2
2
0
1
3
2
0
0
1
0
0
2
2
1
3
0
0
0
0
1
0
1
11
1
1
4
0
0
0
2
0
1
4
0
1
0
0
4
0
0
0
1
3
0
1
0
4
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
2
1
0
4
4
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
2
3
3
0
2
1
2
0
0
0
2
1
0
1
0
1
1
0
1
1
2
0
0
1
2
0
2
0
1
1
0
1
2
2
0
0
2
0
0
2
2
1
3
0
0
2
2
0
1
1
3
1
2
1
3
1
0
3
1
1
3
0
2
0
0
3
1
0
1
1
4
0
0
0
1
1
3
2
2
1
2
1
2
1
0
0
2
1
0
1
0
2
1
5
2
1
0
1
0
2
1
0
1
0
1
2
0
3
3
0
2
0
2
1
1
0
0
0
1
2
1
0
2
0
0
2
0
0
1
1
0
1
0
1
1
2
0
1
1
1
0
0
2
0
0
1
2
0
1
0
4
1
2
1
0
2
1
2
1
1
1
1
3
3
0
0
3
0
0
0
0
2
1
2
4
1
0
1
0
1
1
0
1
0
1
0
3
1
0
0
3
0
1
1
4
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
4
0
0
1
1
0
0
4
1
0
1
2
1
0
0
1
0
1
0
3
2
1
0
0
3
2
0
0
1
2
0
4
0
2
1
3
0
0
0
2
2
0
0
0
0
1
3
2
1
2
0
0
4
1
0
1
1
2
1
2
0
0
3
0
0
2
0
0
3
3
3
0
1
0
0
1
1
0
0
1
1
0
3
0
1
0
0
0
1
0
0
3
1
0
2
1
0
0
2
0
0
1
0
1
3
0
2
4
2
1
0
22
0
1
2
1
1
4
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
2
1
0
2
0
0
1
2
1
0
0
1
3
0
0
2
1
1
1
0
0
0
0
0
1
2
1
1
2
1
1
0
0
0
1
2
2
0
0
0
1
1
2
2
1
1
0
2
2
3
0
0
1
0
1
0
0
1
2
0
1
2
0
1
2
0
1
0
2
1
0
0
0
2
2
2
0
3
2
1
1
2
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
1
0
0
2
0
2
0
1
1
0
2
0
0
2
2
2
4
4
3
1
1
2
0
0
2
1
0
0
0
3
1
1
0
1
1
1
0
1
3
1
0
1
0
1
1
4
1
2
1
0
1
1
1
3
0
0
0
0
0
2
1
1
0
1
1
2
0
2
0
0
2
1
2
0
0
0
1
1
0
1
3
0
0
2
1
1
1
0
0
0
0
1
1
0
1
3
1
4
0
1
1
1
1
1
3
1
3
2
0
0
0
0
2
0
1
0
3
3
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
1
1
1
4
1
4
0
1
0
1
3
0
0
1
1
0
1
0
0
0
1
2
0
0
1
4
1
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
4
1
0
1
0
1
0
1
1
3
1
2
0
0
2
3
0
1
3
1
5
0
1
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
0
2
3
0
0
3
0
2
0
0
0
0
0
2
3
0
0
1
2
0
2
1
0
2
1
2
3
2
1
0
2
0
1
1
1
1
1
3
1
0
0
0
1
3
0
1
0
0
1
0
1
1
1
1
0
2
0
1
0
0
2
2
4
0
0
2
3
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
4
2
2
1
1
0
0
3
4
2
0
0
3
0
3
0
0
0
0
0
0
0
1
2
1
0
2
1
1
1
0
1
0
1
2
0
0
4
1
1
2
0
3
0
2
0
0
0
3
0
1
1
4
3
0
4
0
2
0
1
1
4
0
0
1
3
0
0
2
0
2
1
2
1
2
0
0
0
0
1
0
2
1
0
3
0
0
0
3
2
0
1
1
0
1
1
0
1
2
3
0
0
0
0
2
3
1
1
0
0
0
0
1
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
2
1
2
1
4
1
0
1
0
0
0
0
1
6
1
1
0
0
1
1
2
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
1
5
2
1
2
1
1
3
0
1
0
1
2
1
0
0
2
1
1
0
0
0
1
0
2
0
1
0
3
2
1
0
3
2
0
3
0
0
2
0
2
1
1
1
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
2
1
0
3
0
0
1
3
0
0
0
1
0
1
0
0
0
1
0
1
2
2
3
0
0
1
1
0
0
0
4
0
2
2
2
0
0
1
1
0
1
0
2
1
0
3
5
1
0
1
0
3
2
0
1
0
1
0
2
0
0
0
1
0
2
1
1
1
0
1
1
1
0
0
4
2
1
0
1
1
1
0
1
2
2
2
0
2
2
1
2
0
3
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
2
1
2
0
0
3
1
0
1
0
0
2
1
0
1
3
2
2
0
1
1
0
1
1
0
1
0
0
1
0
2
1
0
2
4
0
0
3
0
1
0
0
1
3
1
1
1
2
1
0
0
2
0
3
0
3
0
1
0
2
0
1
1
0
0
2
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
3
3
1
3
2
1
1
0
1
0
0
3
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
2
1
1
1
1
0
3
1
2
1
1
1
3
1
2
1
0
0
0
0
2
0
1
0
1
2
2
0
3
2
2
1
1
0
1
0
3
0
0
0
0
2
0
1
3
0
2
0
2
0
0
0
1
0
0
2
1
10
0
2
0
1
0
0
1
1
2
3
1
0
0
0
0
1
3
1
1
1
2
0
2
0
2
1
0
2
1
0
1
0
0
3
1
0
1
1
0
0
1
1
2
1
1
4
0
0
0
0
1
2
1
0
3
1
2
0
1
0
3
1
3
0
1
1
0
1
3
0
3
1
1
0
0
1
2
0
2
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
2
0
1
0
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
3
0
0
3
1
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
1
3
1
1
1
0
1
2
0
1
0
0
1
1
1
2
3
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
2
4
1
1
0
1
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
1
2
0
1
1
0
2
0
1
0
0
0
1
4
0
0
0
0
2
0
1
4
1
0
0
1
4
0
2
0
2
0
2
0
1
0
0
0
0
0
2
3
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
0
0
1
1
0
1
2
1
0
1
0
2
0
1
2
0
0
0
1
1
2
1
1
3
0
1
0
0
0
1
1
0
2
1
2
0
1
1
0
0
2
0
4
1
0
6
0
2
1
0
1
0
0
0
0
3
1
1
0
2
3
0
0
2
2
0
2
1
1
2
0
1
0
0
0
1
5
0
1
0
1
0
2
1
1
1
0
0
1
1
0
2
0
0
0
0
2
1
1
2
1
2
1
2
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
1
4
0
2
2
2
0
1
1
2
0
1
3
1
3
0
2
1
0
0
2
1
0
0
0
2
0
0
2
1
2
1
0
0
1
2
0
0
0
2
2
1
1
1
0
2
0
0
0
1
3
1
3
0
1
0
2
0
1
0
0
1
0
0
2
1
1
0
1
2
1
0
1
3
4
0
1
3
0
0
0
1
1
2
1
0
1
1
3
1
1
2
1
0
1
0
0
0
0
3
2
1
1
0
1
4
0
4
1
0
2
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
3
1
0
1
1
1
0
1
3
2
0
0
2
1
1
1
0
0
1
1
0
1
3
0
0
1
4
4
1
4
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
7
2
1
2
0
3
0
2
0
3
2
1
0
1
3
2
1
1
0
3
0
3
1
0
1
1
1
1
3
1
2
2
2
0
1
2
0
0
1
2
2
1
2
1
0
1
2
3
1
1
1
0
0
0
1
0
3
4
0
1
1
0
3
1
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
3
0
1
0
0
3
0
1
1
0
2
0
2
1
2
4
2
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
2
0
1
0
0
0
1
0
1
0
1
3
1
1
0
1
1
2
0
0
3
2
1
3
1
3
1
0
2
0
0
0
0
2
0
0
2
0
5
0
0
0
0
1
2
2
0
1
0
0
2
1
0
0
1
0
0
0
0
6
0
1
1
3
1
1
3
1
1
0
2
2
1
0
0
2
0
0
1
2
1
0
1
0
0
2
2
1
0
2
0
0
1
1
2
1
0
1
3
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
2
2
1
1
0
3
2
0
2
0
2
0
1
2
1
3
0
1
0
1
0
2
1
2
0
1
0
0
0
2
1
1
1
1
0
0
0
0
3
0
1
0
0
3
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
1
2
1
2
1
0
2
2
0
0
0
0
0
1
1
1
1
2
0
0
2
0
2
0
0
0
0
1
2
1
0
1
2
0
0
2
0
4
1
0
0
1
3
1
2
0
0
0
0
1
3
1
1
0
1
1
3
2
1
1
0
1
1
1
1
1
0
2
0
2
0
0
0
2
0
0
0
1
2
1
0
0
2
1
0
1
2
1
1
0
0
2
0
0
1
0
5
0
0
0
2
2
3
0
1
2
2
0
2
0
1
1
0
0
0
2
0
1
2
3
1
2
1
0
1
3
2
3
2
4
1
1
1
2
1
2
0
1
0
1
1
0
2
0
1
0
2
1
2
1
1
0
2
2
0
0
0
1
0
0
2
0
2
1
0
0
3
2
0
0
1
0
0
0
0
1
3
1
0
0
1
0
2
2
0
3
0
0
0
0
0
3
0
1
3
1
0
0
3
1
0
1
1
0
0
2
1
0
1
0
2
1
0
1
1
0
1
1
3
0
2
3
0
0
3
0
1
1
0
0
3
2
0
0
0
0
0
0
1
1
5
0
0
1
3
0
2
2
0
1
1
1
0
2
3
1
1
2
1
3
0
1
0
2
5
1
0
3
2
1
2
0
2
3
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
1
0
1
1
0
0
3
2
0
0
5
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
1
4
0
0
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
0
2
0
0
1
3
0
2
3
1
0
0
2
1
0
1
1
0
1
4
0
0
1
2
1
0
1
2
1
1
0
0
0
0
1
0
2
2
1
2
1
2
2
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
4
0
0
1
2
1
3
2
0
0
1
0
0
2
1
0
1
0
2
1
0
1
2
0
1
1
0
2
0
0
2
1
2
0
4
1
0
4
0
0
1
0
0
4
2
1
0
2
0
0
1
0
0
2
2
1
1
0
0
3
0
2
2
0
2
0
3
0
0
0
3
0
0
1
1
0
1
1
0
0
2
2
5
1
1
1
2
0
3
0
2
4
0
0
1
1
0
2
0
0
1
1
0
1
3
1
2
0
1
0
0
0
2
1
0
0
0
1
0
5
2
1
0
1
2
0
1
0
0
0
1
1
2
0
0
0
1
0
3
2
2
0
0
0
0
1
3
0
2
0
0
1
0
0
1
0
4
2
0
0
0
0
3
3
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
3
1
1
1
1
0
0
1
0
0
1
2
0
1
3
3
3
3
1
1
1
0
1
69
2
1
1
0
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
3
0
0
2
0
0
1
1
2
1
2
1
1
0
1
2
0
3
0
0
5
0
0
1
0
0
0
0
2
0
3
1
1
2
1
0
0
2
2
1
2
0
1
3
0
1
1
0
1
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
2
1
0
2
1
1
0
2
1
2
2
0
0
2
0
0
1
1
0
2
0
4
1
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
1
1
0
0
2
1
1
3
2
0
0
0
0
3
0
0
1
1
1
0
2
1
0
1
2
0
0
0
1
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
4
1
2
2
2
0
0
0
0
1
1
0
0
2
0
0
0
2
5
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
3
0
2
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
2
2
1
1
0
2
3
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
3
1
0
1
4
2
0
0
1
0
2
0
0
2
2
0
1
1
0
1
2
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
1
1
2
3
2
0
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
2
2
0
0
1
1
0
1
2
1
1
1
1
1
5
2
1
0
2
0
0
1
0
4
3
2
4
2
0
0
2
0
0
1
1
1
2
0
14
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
4
0
2
0
1
1
2
0
1
3
0
1
0
5
1
1
1
1
2
0
0
0
0
2
1
1
3
0
0
1
3
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
3
0
2
2
1
2
0
2
0
0
1
0
1
0
1
1
0
0
3
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
1
3
0
2
4
2
2
1
0
0
2
3
1
2
2
0
0
1
0
0
1
1
0
0
0
4
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
2
5
1
0
0
1
0
0
2
1
4
0
0
0
1
0
1
0
0
1
1
0
2
2
0
4
3
0
3
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
1
2
0
0
1
1
0
1
1
1
0
2
1
0
1
1
3
1
1
0
1
2
0
1
1
3
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
3
0
1
1
1
2
0
2
0
2
0
1
0
0
1
1
0
0
2
0
1
1
3
2
0
1
0
0
3
0
1
0
1
0
1
1
0
1
3
0
4
1
0
2
1
1
2
0
0
1
0
2
0
1
4
2
2
1
0
1
2
0
2
1
3
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
4
0
1
0
1
0
2
3
1
2
3
2
2
0
0
1
1
0
3
2
0
3
1
0
0
0
2
1
3
2
0
1
3
0
0
1
8
2
3
0
1
1
1
2
1
0
0
1
2
2
3
0
0
0
0
4
0
2
0
1
1
1
2
0
1
4
1
1
2
0
2
0
0
0
0
0
0
1
5
0
1
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
2
1
1
2
0
2
3
2
1
1
3
1
3
2
0
1
1
0
1
3
0
1
0
0
1
2
0
1
1
1
3
1
0
2
0
1
0
3
1
0
2
0
3
2
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
3
0
1
1
1
0
1
0
0
0
0
0
1
3
1
0
2
0
2
1
2
0
1
1
0
1
0
2
0
0
0
2
1
2
2
0
0
0
2
1
0
0
1
2
2
0
0
0
0
3
0
0
1
1
4
1
1
1
0
1
0
0
0
4
4
1
3
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
3
4
0
0
2
0
0
0
1
1
1
1
0
3
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
1
1
0
2
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
1
1
2
3
0
0
3
3
0
0
2
1
1
2
0
4
1
1
0
0
0
0
0
2
2
0
1
0
0
1
1
4
0
2
1
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
58
0
0
1
0
0
0
0
0
3
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
2
2
0
4
0
1
0
1
0
1
1
0
0
0
2
1
0
1
1
1
0
1
75
0
0
0
1
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
3
0
1
2
2
3
1
0
1
1
0
1
0
0
1
3
1
2
1
0
0
3
0
2
3
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
4
0
0
0
3
0
0
0
1
0
0
0
2
3
3
3
1
1
0
2
0
2
1
0
0
0
2
0
1
3
0
1
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
1
3
2
0
1
0
1
3
1
3
2
1
0
0
2
1
0
2
3
1
0
10
0
1
2
0
1
1
0
0
1
1
1
0
0
0
1
2
1
1
2
0
0
3
1
0
1
1
2
2
2
0
0
1
2
2
1
0
0
0
4
0
0
1
0
1
1
2
0
3
0
0
0
2
0
1
0
0
0
2
0
0
1
3
3
5
0
0
2
0
4
1
2
0
0
0
2
0
1
1
0
2
3
2
1
0
1
0
0
2
1
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
7
0
1
4
1
0
1
1
2
0
1
0
1
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
3
1
4
0
0
1
0
0
0
0
2
0
0
5
2
1
0
1
2
1
0
1
1
1
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
4
0
0
1
0
2
2
1
3
0
1
0
0
0
0
1
0
3
0
1
0
2
0
1
1
0
1
1
2
3
0
1
0
0
0
2
0
2
1
1
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
1
5
1
1
0
1
1
0
1
0
0
0
0
3
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
3
0
1
2
1
1
2
0
0
3
0
2
4
1
0
1
0
0
3
5
0
0
1
1
2
2
1
0
0
1
0
0
0
2
1
0
0
0
2
2
3
1
0
0
1
1
0
0
0
0
0
0
0
2
1
3
1
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
1
1
2
0
1
2
2
3
0
2
2
1
2
1
0
2
2
0
0
0
2
3
0
0
0
0
1
2
1
0
0
2
1
1
0
0
1
2
2
0
2
1
4
2
0
0
0
1
1
0
3
0
2
2
4
1
0
1
3
0
1
1
0
0
3
5
1
3
1
2
1
1
1
0
2
2
1
0
1
0
0
1
2
1
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
0
0
1
0
0
1
13
2
1
0
0
1
1
1
1
2
0
2
2
3
1
1
1
1
3
0
0
2
2
0
1
0
3
0
1
3
2
2
1
1
0
0
0
3
0
3
1
1
1
0
1
0
0
0
1
0
1
1
3
1
1
1
1
3
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
2
0
1
1
1
3
1
0
0
0
3
1
1
1
0
0
1
3
2
0
1
0
0
0
2
1
0
1
1
0
0
4
7
1
2
0
4
0
0
3
3
1
0
1
0
2
4
1
2
0
0
2
0
1
0
0
3
1
2
0
1
0
1
0
1
0
2
0
0
5
1
0
2
2
1
1
0
1
0
0
1
1
0
0
0
1
3
0
6
1
1
2
1
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
1
0
87
0
0
0
0
0
0
1
1
1
0
0
2
2
3
2
1
0
0
0
2
3
0
0
1
2
0
2
0
0
1
1
2
0
0
3
3
2
2
0
0
4
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
0
2
1
2
0
0
0
1
0
0
1
0
0
0
1
3
1
2
0
2
1
0
1
0
3
0
1
2
0
1
1
1
2
0
1
0
0
3
2
4
1
2
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
1
1
0
2
0
0
15
1
1
2
2
0
0
1
2
0
0
1
1
1
0
2
4
3
3
0
1
2
0
2
0
1
1
1
0
2
1
0
3
1
0
2
0
1
2
0
0
2
6
1
9
1
1
2
0
2
0
1
0
4
1
0
2
0
1
2
0
0
0
0
4
3
0
2
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
1
1
5
1
1
1
0
0
1
0
2
1
0
2
2
4
1
1
0
0
1
0
0
0
1
0
0
1
2
2
1
0
2
0
3
3
1
0
1
1
3
1
0
3
1
1
1
0
1
0
2
0
1
3
1
4
2
3
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
3
1
0
0
1
1
0
0
0
1
0
4
2
2
0
2
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
14
0
0
1
0
0
0
0
2
0
1
0
3
2
0
0
1
1
0
2
0
1
2
0
2
5
4
1
3
1
1
1
2
0
0
0
0
1
1
1
0
0
0
2
1
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
1
6
2
0
2
1
0
4
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
2
2
1
2
0
1
1
4
2
2
1
1
1
0
0
1
1
2
0
2
0
0
0
4
1
1
1
2
1
0
0
4
1
1
0
1
1
1
0
0
0
0
0
4
1
1
0
4
1
1
1
2
2
1
1
1
1
2
0
1
0
0
1
1
1
2
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
3
1
2
0
0
3
1
0
0
1
0
1
1
1
7
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
1
2
1
1
0
1
1
3
1
3
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
2
3
3
0
1
0
0
2
2
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
1
1
0
1
0
1
0
1
0
2
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
3
1
1
0
2
3
0
1
0
1
2
1
3
3
2
1
0
1
0
2
0
0
0
0
0
6
1
1
2
0
2
0
0
1
2
0
1
2
0
1
0
2
2
1
0
1
1
2
1
0
1
1
0
1
1
1
0
2
1
0
1
0
0
5
200
0
2
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
2
1
0
4
1
0
0
2
0
0
3
0
2
1
1
0
0
2
1
1
0
0
1
1
2
0
1
0
0
1
1
3
0
0
1
0
1
1
2
0
0
0
1
1
0
1
3
0
1
0
4
1
1
1
0
2
2
1
0
1
1
0
2
0
1
0
0
0
0
2
1
1
2
0
1
2
0
1
1
0
0
0
0
0
0
1
1
0
3
2
0
2
0
1
2
2
1
0
0
1
0
0
0
1
2
3
1
2
0
0
0
0
0
0
0
1
0
0
1
11
3
0
1
3
2
1
3
1
1
0
0
2
2
1
0
0
0
0
2
1
0
1
2
1
3
0
1
3
1
0
0
3
1
1
0
2
0
1
1
1
3
0
1
3
1
0
2
0
4
0
0
1
2
1
0
1
4
0
2
0
0
2
3
1
1
0
1
1
1
1
4
0
5
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
3
0
0
1
1
3
1
0
1
0
0
0
1
2
0
2
0
0
0
0
5
5
0
1
0
1
0
0
2
2
1
0
0
0
1
0
0
4
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
2
0
1
0
1
0
0
1
1
0
1
1
2
2
1
0
1
0
1
0
0
0
0
1
1
3
0
0
1
3
2
0
0
1
0
0
3
0
0
2
1
1
2
0
0
0
1
0
0
2
2
1
0
1
2
0
0
1
1
0
4
1
1
1
0
1
1
0
0
3
2
0
1
1
1
1
1
4
0
1
0
0
0
0
0
0
268
0
1
1
3
0
0
2
0
1
0
0
2
0
0
0
2
0
3
0
2
0
2
0
2
1
4
0
0
2
0
0
0
0
0
2
2
3
1
2
1
1
1
2
0
0
1
0
1
4
1
1
1
5
0
0
1
1
1
3
1
1
2
0
2
0
3
0
3
0
2
1
4
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
3
6
1
3
0
0
2
0
2
2
1
0
4
0
2
0
0
1
0
1
1
1
0
1
0
1
0
3
2
2
1
1
1
0
0
2
1
1
1
2
0
1
0
0
2
0
3
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
1
1
1
0
0
2
1
1
1
0
0
2
4
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
2
0
5
3
1
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
3
2
0
0
2
0
0
0
0
1
1
4
0
1
1
1
0
0
1
5
1
1
2
1
0
2
1
0
0
1
2
3
0
1
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
3
0
1
0
0
1
0
1
0
2
1
0
4
1
0
1
0
3
0
1
2
0
3
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
4
0
1
0
0
0
1
2
1
0
0
0
3
1
1
1
3
0
1
1
0
0
1
2
2
2
0
1
2
0
0
1
1
0
2
3
3
0
0
0
1
0
0
1
2
1
1
3
1
3
3
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
1
3
0
0
1
1
1
1
1
1
2
0
1
0
0
0
2
1
1
0
2
0
0
2
2
2
2
2
0
3
0
1
2
0
0
1
2
0
2
3
1
4
1
0
1
0
1
2
2
2
2
1
0
0
1
0
1
2
0
0
0
2
2
1
1
1
0
0
2
0
0
2
1
0
3
1
0
0
2
0
0
2
0
2
0
2
3
2
1
0
0
1
0
2
1
0
1
2
0
0
0
0
2
1
0
1
1
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
1
1
1
0
1
0
0
0
0
0
1
4
0
0
0
1
0
2
1
4
2
0
1
0
1
1
0
0
0
0
2
1
0
0
3
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
3
0
2
0
0
2
1
2
1
1
0
0
2
0
3
1
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
1
0
1
0
0
0
2
4
0
1
5
0
5
3
0
1
2
0
1
1
2
4
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
2
0
0
2
1
0
1
2
1
1
3
0
0
3
2
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
6
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
4
1
2
1
0
1
0
0
1
0
0
1
1
1
1
2
0
0
0
0
2
0
1
1
2
3
1
1
0
3
0
1
2
0
0
0
0
0
2
1
1
0
2
1
1
1
0
0
1
3
0
3
0
1
1
0
4
0
0
0
1
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
1
0
3
0
1
1
1
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
3
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
3
1
1
0
1
2
0
0
1
2
0
2
1
1
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
4
1
0
2
0
1
2
2
0
1
2
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
3
3
0
0
2
3
3
1
0
2
2
0
1
1
2
1
1
1
0
0
3
0
1
2
1
3
0
0
1
0
0
2
1
0
0
2
0
3
1
2
2
1
1
0
0
1
0
1
0
0
4
0
1
0
1
1
0
2
1
2
0
1
1
1
0
0
0
3
3
1
3
0
1
1
0
1
2
0
1
2
3
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
1
1
2
1
0
2
1
1
6
1
0
3
2
0
1
2
0
1
4
0
0
0
0
1
1
3
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
2
0
0
1
0
3
1
0
0
0
2
1
0
0
1
0
0
0
3
0
1
1
0
1
0
0
3
1
2
1
1
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
12
3
0
0
0
1
1
0
1
0
1
0
0
2
2
1
1
1
0
0
1
2
0
2
0
0
1
0
1
1
1
1
2
0
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
5
0
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
1
1
1
0
3
0
0
1
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
5
0
1
0
1
2
0
0
2
0
1
0
0
1
1
3
0
3
2
0
0
2
1
0
0
1
2
1
9
1
0
0
0
1
1
3
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
3
3
2
1
3
0
1
0
2
0
1
0
3
2
0
1
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
0
5
0
2
0
0
1
1
0
1
2
0
2
3
1
0
6
1
0
1
1
1
1
0
4
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
4
3
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
3
0
2
0
1
1
0
4
4
0
0
3
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
0
1
1
1
1
3
1
0
0
0
2
1
0
6
1
3
2
1
2
0
1
2
1
0
22
1
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
3
1
2
2
0
3
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
0
3
1
1
0
0
0
0
2
0
2
0
1
0
4
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
1
2
1
1
2
1
2
3
2
0
2
1
0
0
1
0
2
0
1
2
0
0
1
2
1
0
1
0
1
1
0
0
0
0
1
2
0
1
4
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
2
2
1
1
2
4
0
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
1
0
1
2
0
0
1
1
1
0
1
0
0
2
0
1
0
2
1
0
1
0
2
0
0
2
2
0
1
4
0
2
3
0
1
0
1
0
0
0
0
0
3
0
3
0
1
0
1
2
4
1
1
1
0
1
0
2
0
2
1
0
0
2
2
0
1
2
0
1
0
0
1
1
0
2
1
1
0
0
1
1
2
2
3
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
0
1
2
0
0
0
1
1
0
3
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
3
0
2
0
2
0
1
3
3
0
2
0
0
0
0
0
16
2
1
0
1
1
1
0
0
2
0
3
2
0
1
1
0
0
2
3
3
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
2
4
2
2
0
0
1
0
9
1
1
0
0
1
0
0
3
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
3
2
2
0
0
0
1
0
0
6
0
0
0
0
0
1
0
2
0
0
0
3
1
1
2
1
1
2
2
1
1
2
0
1
0
0
2
1
2
4
1
1
1
1
0
0
0
2
1
1
0
3
0
0
1
5
2
1
0
0
2
0
1
1
2
5
0
2
1
1
1
0
0
0
1
3
0
0
1
0
1
0
1
0
0
2
1
2
4
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
17
1
1
0
0
1
0
2
1
3
1
2
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
2
1
0
2
2
0
4
0
1
0
1
1
0
0
1
3
0
0
1
0
2
0
1
2
0
2
0
2
4
1
0
1
2
0
0
1
0
0
9
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
5
0
0
0
2
3
2
3
0
51
2
1
2
2
0
1
0
2
1
2
3
0
0
1
3
1
2
2
0
0
0
0
0
2
1
1
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
5
0
5
1
2
0
1
1
0
0
0
0
1
0
0
1
2
1
1
2
0
0
1
1
1
3
0
0
2
1
2
2
0
1
1
0
1
2
1
2
0
2
2
2
2
0
1
2
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
2
7
2
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
3
3
1
0
2
1
0
3
1
1
1
0
1
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
1
0
2
1
3
0
0
0
0
0
2
1
1
0
1
5
0
0
1
0
3
2
0
1
0
0
2
0
0
1
4
1
0
2
0
3
0
1
0
1
0
0
2
0
0
0
1
0
2
3
1
4
0
2
0
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
5
0
0
0
1
1
3
0
0
1
1
2
2
0
1
4
0
1
0
1
1
0
3
0
0
0
0
1
2
0
0
0
2
1
2
0
2
1
1
0
2
0
3
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
3
1
1
2
1
2
2
0
3
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
4
0
0
0
2
1
1
1
3
0
1
0
1
3
0
0
0
1
0
3
0
1
2
1
1
1
1
1
0
0
1
1
2
1
0
2
0
1
1
1
1
1
0
3
2
0
0
3
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
5
1
0
1
0
0
0
0
1
0
0
0
3
1
2
1
0
0
0
5
1
0
4
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
3
1
1
2
0
0
0
0
4
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
2
1
1
2
1
1
3
0
1
0
1
0
1
0
1
1
0
0
1
2
0
2
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
2
1
2
1
1
2
0
3
0
2
1
0
0
1
1
1
1
0
0
4
0
2
1
0
0
0
2
0
0
4
2
0
0
1
0
0
0
0
1
1
1
0
1
1
3
0
1
0
0
0
2
1
2
0
2
0
3
0
0
2
2
0
0
2
0
0
1
0
1
2
0
0
2
2
4
0
1
1
0
2
2
2
3
0
2
1
1
1
2
0
1
1
1
3
1
3
0
1
1
0
2
0
2
0
1
0
1
0
0
1
3
1
0
2
1
1
1
0
1
0
2
1
1
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
2
1
1
2
0
0
1
4
1
0
0
1
3
1
2
0
1
0
0
1
3
0
2
0
1
2
1
0
3
2
0
3
0
4
0
1
0
1
0
1
2
2
0
1
0
0
3
0
2
0
0
2
1
0
1
0
1
2
1
0
2
2
1
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
0
4
1
0
0
1
0
0
0
0
2
2
1
0
4
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
2
0
1
1
1
0
1
0
1
0
3
1
1
16
0
0
0
0
1
2
0
3
0
0
0
1
0
4
0
1
0
0
0
1
0
3
3
0
1
1
0
3
1
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
2
1
1
2
0
0
0
0
1
0
0
2
1
1
1
0
0
2
1
0
1
1
1
0
4
1
0
4
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
3
2
0
0
1
1
0
1
0
0
0
3
1
1
1
1
0
2
0
0
0
3
2
1
1
0
0
1
2
2
1
0
0
0
0
0
1
1
2
1
1
1
1
1
0
2
1
2
0
0
1
1
1
0
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
1
2
1
3
1
0
1
0
0
1
1
0
0
1
0
0
2
0
0
2
5
1
1
4
1
0
0
1
1
1
0
1
0
1
0
3
1
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
8
0
2
1
0
0
1
0
0
0
3
0
1
0
0
1
0
4
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
2
0
2
2
0
3
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
1
2
1
0
0
1
1
2
1
1
2
0
0
0
0
0
1
2
1
2
1
0
2
4
1
0
2
0
1
0
0
1
1
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
0
0
0
4
0
1
2
0
0
4
1
1
1
0
1
2
1
3
2
0
1
2
0
0
2
2
0
0
0
0
1
0
5
4
3
0
1
1
1
0
3
1
0
3
1
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
1
0
2
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
2
3
0
1
2
0
0
1
1
0
2
1
1
0
0
0
4
0
1
0
0
0
0
1
2
3
0
1
2
1
1
3
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
3
1
0
1
0
1
1
0
0
2
2
0
3
0
1
0
2
0
11
0
0
3
1
0
0
2
1
1
1
0
1
0
0
3
0
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
3
3
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
3
2
0
5
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
1
1
1
4
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
1
1
1
1
0
2
2
1
1
2
0
1
0
1
1
0
1
0
1
3
2
2
0
0
0
4
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
2
1
0
5
1
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
1
3
1
2
4
1
2
2
0
0
0
0
0
1
1
3
0
1
1
0
3
0
0
0
2
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
1
1
0
1
0
0
2
1
7
0
2
0
3
0
1
1
1
0
0
1
1
0
0
2
0
0
0
3
2
1
0
1
2
3
0
2
1
1
1
0
0
3
1
0
1
1
0
0
0
1
0
1
1
0
0
0
7
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
2
1
0
1
0
3
0
0
0
0
5
0
0
1
1
1
1
0
1
1
4
2
1
0
1
0
0
2
1
1
1
2
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
1
1
1
2
1
2
3
0
0
10
0
0
1
0
0
0
2
0
0
2
1
1
1
0
4
1
0
0
1
1
2
1
1
0
1
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
0
2
3
0
1
1
4
2
1
1
2
0
0
2
0
0
0
0
2
1
2
0
1
0
1
1
1
0
0
1
1
1
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
3
0
0
1
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
4
1
1
1
2
1
2
1
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
0
5
2
0
1
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
1
2
0
4
0
1
1
4
6
2
1
1
0
2
1
1
1
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
3
1
1
0
1
1
1
1
0
0
1
0
0
2
0
2
0
0
1
1
0
4
0
0
0
1
0
0
1
0
0
2
1
0
0
0
3
0
5
2
0
0
1
1
1
1
0
0
3
2
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
2
2
1
3
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
4
0
0
1
3
0
0
3
1
0
0
2
1
1
2
0
0
2
1
0
2
1
3
0
4
1
1
1
0
1
0
6
0
2
0
0
0
1
0
2
2
0
2
0
3
0
0
0
0
1
0
3
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
3
3
1
2
0
1
2
1
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
1
1
0
2
0
0
1
0
0
2
1
2
0
4
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
2
0
3
0
2
6
0
0
1
1
0
0
2
1
1
0
1
0
0
1
11
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
2
0
2
1
0
6
0
3
1
2
3
2
1
1
0
4
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
4
2
0
2
1
1
0
1
0
2
0
0
2
0
0
3
0
0
0
1
3
0
0
0
2
1
1
1
0
4
1
0
1
2
0
1
0
0
2
0
2
1
0
2
2
0
0
0
1
3
0
0
1
1
1
2
0
0
0
1
3
2
0
1
0
1
1
1
2
0
0
1
1
3
1
2
21
1
0
2
2
0
0
2
0
0
1
0
1
0
0
0
1
4
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
3
1
3
0
0
0
3
1
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
3
6
0
4
1
0
1
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
2
1
0
1
2
1
0
1
1
0
1
1
0
0
1
2
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
2
0
1
1
3
0
4
0
0
0
1
0
2
0
2
1
1
1
1
0
1
1
3
1
4
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
1
1
3
0
3
1
0
0
0
0
0
2
4
1
2
0
0
0
0
2
1
0
1
1
3
2
1
3
1
0
0
1
1
2
1
0
2
1
1
0
3
1
1
0
0
1
0
0
1
1
0
1
2
0
1
1
2
0
1
1
0
0
2
0
0
2
2
0
7
1
0
0
1
0
0
1
0
0
1
1
1
4
1
0
0
1
0
1
3
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
1
0
2
1
1
1
0
4
1
0
2
3
3
2
0
1
1
1
0
2
0
2
0
1
3
0
2
1
0
0
1
0
0
2
1
3
0
0
1
0
1
0
2
2
2
0
1
1
4
1
0
1
1
0
1
4
0
2
0
3
1
1
0
2
2
0
1
1
1
0
0
0
2
0
0
1
1
0
2
2
1
0
1
2
1
1
3
1
0
1
0
0
0
0
0
2
2
2
0
0
1
2
0
1
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
3
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
4
1
2
0
0
0
0
0
2
2
0
6
1
1
1
0
0
3
1
1
0
0
1
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
2
2
0
0
0
1
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
11
0
2
1
1
0
3
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
3
0
0
2
2
0
1
1
0
2
0
1
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
1
2
0
0
2
1
2
0
1
2
1
2
0
0
10
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
4
2
0
2
0
1
1
1
1
1
0
1
0
0
2
1
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
3
0
1
1
1
1
1
1
3
1
0
1
1
0
1
4
0
1
1
1
0
0
3
0
17
1
0
1
0
0
3
1
2
1
1
0
0
0
0
0
1
0
1
1
2
1
2
0
2
1
0
3
1
0
0
3
1
0
0
0
0
1
5
3
0
0
1
2
0
1
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
2
1
2
1
2
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
0
1
0
1
2
4
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
0
1
0
0
2
0
0
2
2
0
1
2
1
1
0
2
0
1
0
0
0
0
0
1
1
2
2
0
0
0
3
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
0
4
1
0
0
0
0
1
2
1
1
2
0
3
1
0
1
0
1
2
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
1
0
0
1
1
0
2
1
0
0
6
0
0
3
0
3
1
2
0
0
0
2
0
0
2
0
0
0
1
0
3
1
2
1
0
0
0
1
0
0
1
2
0
2
0
1
4
0
0
2
3
0
0
1
0
0
1
1
0
1
0
1
1
3
1
1
0
0
0
0
2
1
0
0
0
3
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
0
1
2
1
0
2
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
3
0
1
0
1
0
0
1
3
3
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
2
0
0
1
1
4
1
0
1
0
2
0
2
0
4
0
2
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
3
0
1
0
0
1
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
3
1
0
2
2
4
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
3
0
0
1
0
2
0
2
1
4
18
2
0
6
0
1
0
0
0
0
1
1
0
3
0
3
1
1
1
2
2
0
0
0
1
1
0
1
2
0
1
6
0
3
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
2
0
1
0
1
0
1
1
1
1
0
1
2
0
1
1
1
2
4
0
0
0
1
0
0
1
2
0
1
1
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
2
0
6
1
0
0
2
3
0
2
1
0
2
1
7
1
2
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
3
1
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
5
0
0
3
0
1
1
0
0
0
1
0
1
0
1
0
2
1
0
3
0
1
1
1
1
2
1
1
0
0
0
0
2
3
1
0
0
3
1
0
0
2
0
0
0
1
0
1
0
2
0
3
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
3
1
1
0
2
1
1
1
0
1
0
1
0
1
0
1
1
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
4
0
0
0
0
2
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
3
3
3
0
0
2
0
2
2
1
1
1
1
9
3
1
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
1
5
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
1
2
0
1
1
1
0
1
0
1
2
2
0
1
2
1
0
0
0
1
0
3
1
0
0
2
0
1
1
0
1
0
0
1
0
3
1
1
1
1
0
0
0
1
0
0
3
1
1
0
1
0
2
2
1
3
1
1
0
1
0
2
0
2
1
1
0
0
0
0
2
0
2
1
0
3
0
1
2
3
1
0
1
1
0
0
1
1
4
0
2
2
0
0
2
1
0
0
0
0
1
1
2
0
1
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
1
2
1
0
1
3
0
2
1
1
1
2
0
0
1
2
0
0
0
2
1
3
2
0
0
0
0
0
2
1
1
3
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
3
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
3
1
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
3
1
5
0
1
1
0
1
0
3
1
0
4
1
0
0
0
2
0
1
1
0
2
1
0
2
2
0
0
0
1
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
3
2
3
3
2
0
0
0
1
2
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
5
1
0
0
0
2
0
2
1
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
2
9
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
3
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
4
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
3
0
1
0
0
1
3
3
0
2
1
0
0
0
2
1
0
0
0
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
2
2
0
2
1
0
1
1
0
1
32
0
5
1
0
0
1
0
4
1
0
1
1
0
4
1
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
2
0
1
0
2
0
0
0
1
1
1
0
0
1
0
3
0
1
0
2
3
1
0
1
2
1
1
0
1
0
2
0
0
1
1
0
0
2
1
7
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
2
0
1
2
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
3
1
0
0
0
0
1
0
1
2
0
0
0
1
3
2
1
3
2
2
2
2
2
3
0
1
5
2
1
1
0
1
2
1
3
0
2
0
0
0
1
1
3
1
0
0
1
4
0
0
0
1
0
0
2
1
1
0
0
0
2
2
0
0
1
2
0
0
1
2
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
3
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
1
1
0
1
0
2
0
3
1
0
0
2
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
0
3
1
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
3
0
0
0
0
1
3
1
0
0
0
0
3
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
3
0
1
0
1
0
0
1
1
2
2
17
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
1
1
1
1
4
0
3
1
0
0
0
0
1
0
1
0
0
4
0
0
0
0
1
3
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
4
1
0
0
1
0
0
1
1
0
1
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
3
0
0
2
7
3
1
2
1
2
1
5
1
0
1
1
1
3
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
2
1
0
4
1
1
2
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
0
2
0
1
0
3
13
1
1
0
6
0
1
2
0
1
0
1
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
3
1
0
2
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
2
0
12
0
4
6
2
2
1
1
2
0
0
0
1
1
0
0
1
1
5
2
0
0
1
0
2
1
0
3
0
3
2
0
2
0
1
0
1
0
0
1
1
2
2
2
0
1
0
0
1
1
0
0
0
2
1
1
2
0
1
0
1
0
1
2
0
1
3
0
1
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
3
0
1
1
0
1
1
1
1
1
0
0
4
1
1
0
3
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
0
2
0
1
1
2
1
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
1
5
3
0
2
2
0
2
0
1
1
2
2
0
1
0
1
1
0
2
0
6
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
3
2
0
1
1
2
1
0
0
3
1
2
2
1
1
0
0
1
0
1
2
1
0
1
1
0
3
2
0
2
0
1
0
1
3
1
2
3
2
0
5
1
0
1
2
1
0
2
1
0
1
1
2
2
0
3
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
4
0
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
1
1
1
1
1
1
3
1
1
0
2
0
0
1
0
0
0
1
0
3
0
1
2
0
1
0
0
1
0
0
1
1
1
1
0
3
0
0
2
0
0
2
0
1
3
1
2
0
0
0
0
1
0
2
0
1
1
1
3
9
128
0
0
0
2
1
1
2
2
2
0
3
0
1
1
1
1
1
1
2
0
0
0
2
10
0
1
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
1
4
3
2
0
1
2
1
1
1
0
1
0
0
1
3
0
0
0
2
0
0
0
1
3
0
1
1
6
6
1
0
3
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
3
3
0
1
0
1
1
1
0
0
1
0
1
2
0
1
0
3
0
0
0
0
0
3
1
0
1
24
0
0
1
1
2
1
4
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
2
0
1
1
0
0
0
19
1
2
2
5
0
1
1
0
1
0
1
1
2
2
0
0
1
1
2
1
0
0
0
1
2
0
1
2
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
2
5
0
1
0
0
1
1
1
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
2
2
0
4
0
0
0
2
1
0
2
1
1
2
1
2
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
3
3
0
2
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
2
2
0
3
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
1
0
1
1
3
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
4
0
2
1
5
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
4
1
0
1
0
0
2
0
0
3
1
0
2
0
0
2
0
1
0
0
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
1
1
3
0
0
2
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
1
2
0
1
1
1
2
1
0
0
6
2
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
2
1
0
2
1
1
0
2
0
0
2
0
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
2
3
0
7
0
0
1
0
2
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
2
4
0
1
0
0
0
1
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
1
1
2
1
1
0
1
0
0
0
0
1
0
2
0
1
2
0
3
1
0
0
0
1
0
1
1
0
1
3
0
3
2
1
0
0
1
0
1
1
1
0
2
2
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
9
0
0
0
0
1
2
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
2
3
3
3
1
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
6
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
5
0
1
3
0
0
0
0
2
1
0
1
1
0
0
0
2
1
1
2
2
5
1
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
25
0
0
1
0
0
19
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
31
0
0
5
1
1
3
1
2
0
0
4
0
1
0
1
2
1
2
0
1
1
2
1
0
0
0
2
0
0
1
0
1
3
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
3
3
1
0
0
0
1
2
1
1
3
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
3
0
0
0
1
2
3
1
1
1
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
10
1
0
0
0
0
0
1
2
1
0
0
2
4
0
0
0
1
0
0
0
0
2
2
1
2
0
1
0
1
1
0
0
0
2
1
3
0
0
0
2
0
2
1
0
2
0
1
0
0
2
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
2
1
0
3
1
0
1
2
0
3
0
1
1
0
0
1
0
1
0
0
1
1
2
1
2
2
2
1
1
0
0
1
2
0
1
1
2
2
0
0
2
3
1
0
1
1
0
1
0
0
0
1
1
0
0
0
5
0
1
1
0
1
0
0
2
1
1
3
0
0
1
0
3
2
2
0
1
1
0
0
4
0
0
0
1
1
2
1
0
2
0
0
1
0
2
0
1
1
3
1
0
1
1
2
0
0
0
3
0
0
0
1
0
0
1
4
1
0
1
1
1
0
0
0
0
0
0
3
0
1
1
0
1
1
0
1
1
0
1
0
1
1
2
0
1
2
1
1
1
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
4
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
3
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
2
1
1
1
1
3
1
2
1
0
0
0
0
0
0
0
0
1
3
0
0
5
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
1
1
1
0
0
0
0
2
2
0
0
1
2
2
2
0
0
0
2
1
0
1
2
1
0
0
1
0
0
2
4
1
2
0
0
9
0
1
0
0
1
3
1
0
0
0
0
1
1
0
1
0
2
0
1
1
0
1
1
0
3
0
2
1
1
3
1
1
1
2
0
0
0
1
0
1
0
0
1
1
4
1
0
0
1
1
0
1
1
2
0
2
1
0
0
0
3
2
2
4
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
0
2
1
2
1
2
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
1
0
0
3
2
0
1
0
0
4
1
0
0
1
4
0
0
0
1
1
0
1
1
0
1
1
2
2
1
0
0
1
1
2
0
0
2
2
1
1
1
1
0
0
0
3
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
0
1
1
4
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
3
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
3
1
1
0
1
1
1
0
2
0
0
1
1
0
2
1
2
0
4
1
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
3
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
5
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
1
4
1
0
1
0
0
4
3
0
1
1
3
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
3
0
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
4
0
1
1
0
0
0
1
2
1
0
0
1
0
0
1
8
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
2
3
0
1
0
4
0
0
0
1
1
1
0
1
0
1
1
0
0
3
1
0
1
0
1
0
0
0
1
2
0
2
0
2
0
0
0
2
1
0
0
1
2
2
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
1
4
1
2
0
0
0
1
3
2
0
0
0
1
0
5
0
0
1
2
1
1
1
1
1
1
0
0
0
0
2
1
2
1
0
0
0
1
5
0
0
0
1
0
0
0
2
1
1
0
1
2
1
3
0
0
0
5
0
0
1
1
2
0
3
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
1
2
41
0
1
0
0
0
0
2
0
1
2
0
1
1
0
1
1
1
2
2
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
1
4
1
0
0
1
1
0
2
1
0
0
2
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
6
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
3
0
1
2
2
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
1
2
0
1
3
1
1
0
0
1
1
0
3
0
3
0
0
0
1
0
1
0
0
0
1
1
2
1
0
1
0
1
0
0
1
0
1
3
4
2
0
1
1
1
0
0
0
0
1
3
7
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
2
1
0
1
3
0
2
0
2
1
2
1
1
0
2
0
2
2
0
0
0
2
0
0
0
1
0
8
1
1
1
1
1
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
3
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
3
0
1
2
0
0
0
3
0
0
2
0
1
1
0
3
0
1
2
0
1
0
1
2
0
1
2
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
4
1
0
1
0
0
1
0
2
0
1
5
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
0
0
0
4
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
3
1
1
0
2
0
2
1
2
0
0
0
2
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
3
4
3
1
1
2
1
1
0
1
0
2
0
1
1
0
0
4
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
5
2
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
1
3
0
0
0
0
1
0
0
0
4
3
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
2
1
9
2
1
0
1
0
2
2
0
1
0
1
1
0
0
0
0
3
3
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
3
0
2
0
0
1
1
8
1
0
0
0
1
0
3
0
0
3
0
0
1
0
0
0
0
1
2
3
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
2
3
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
3
2
1
1
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
3
1
0
0
0
1
1
1
0
1
1
5
0
1
0
3
2
2
2
0
0
3
0
0
1
1
4
0
1
2
1
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
1
1
1
1
0
1
0
1
1
1
3
5
0
2
1
0
3
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
3
1
1
0
0
1
2
0
3
2
0
23
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
3
0
0
1
0
125
1
0
4
2
1
0
2
1
1
0
2
0
4
0
1
0
0
1
0
4
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
3
0
0
1
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
1
2
1
0
1
1
2
0
0
1
0
0
0
1
0
1
2
0
1
2
1
0
0
0
0
2
0
3
0
2
0
1
1
1
3
1
1
0
0
2
1
0
2
0
1
0
0
0
1
1
0
2
2
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
2
3
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
9
0
0
1
8
3
1
3
0
0
1
0
0
0
1
0
0
0
0
1
1
4
0
1
1
3
1
0
2
1
0
3
1
0
1
1
1
2
0
0
2
0
0
3
1
1
0
0
0
2
1
1
0
0
1
1
2
0
4
0
1
2
2
1
0
1
1
2
1
0
4
1
1
0
1
0
2
0
1
1
1
0
2
2
0
1
2
0
2
62
0
0
0
1
0
1
0
0
2
1
0
2
2
2
0
2
2
1
0
0
1
4
0
1
0
2
1
0
0
2
1
1
1
1
0
3
0
0
3
0
0
0
15
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
1
0
1
0
13
1
1
1
0
0
2
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
79
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
1
2
1
0
0
1
1
1
1
0
0
1
0
3
2
0
2
0
0
0
0
0
4
2
0
15
0
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
1
0
3
2
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
1
0
2
2
0
3
0
0
0
0
0
0
1
3
2
1
0
1
1
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
1
1
2
0
4
0
1
1
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
7
3
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
1
3
2
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
3
4
0
0
0
0
4
1
0
1
8
3
0
1
3
1
0
10
1
0
0
0
1
2
0
2
3
0
0
0
0
0
2
3
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
3
0
2
1
0
0
1
1
0
0
0
2
4
2
1
1
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
3
0
0
0
1
1
0
1
0
0
1
0
1
0
3
1
1
1
1
2
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
2
0
3
2
0
0
0
2
1
0
0
3
1
0
0
0
2
0
0
0
2
2
0
1
2
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
2
0
1
2
2
2
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
2
1
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
1
0
1
1
1
0
5
1
2
3
0
1
3
0
0
0
0
0
1
2
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
3
2
1
1
1
1
1
1
0
1
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
5
0
0
1
2
0
1
1
2
0
3
1
3
0
2
1
0
1
0
0
0
1
2
0
0
1
1
3
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
3
1
4
0
2
1
0
0
2
0
0
0
1
1
0
0
4
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
12
1
0
0
4
0
2
0
0
1
1
0
1
2
0
0
1
10
1
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
4
0
2
1
0
2
2
0
1
0
1
0
0
3
0
1
1
1
1
2
1
1
2
0
0
0
0
3
1
1
1
0
0
1
1
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
4
2
2
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
27
0
0
3
1
1
3
1
0
0
1
0
1
0
2
0
1
1
0
1
0
1
0
4
2
0
1
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
1
2
1
0
0
0
0
0
190
0
1
0
1
0
1
3
1
1
0
1
2
2
0
1
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
3
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
3
4
1
2
0
1
0
4
1
1
7
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
4
0
1
2
6
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
6
3
1
0
1
1
0
1
2
0
81
3
1
0
1
0
5
2
0
0
6
0
1
0
0
0
1
0
1
2
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
3
0
1
1
5
1
0
0
2
0
1
0
2
2
0
2
2
2
0
0
0
3
1
3
0
1
1
0
2
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
7
1
3
0
2
1
1
0
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
4
0
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
4
0
1
1
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
9
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
1
1
2
0
0
1
3
0
0
0
0
1
1
0
1
1
0
1
3
1
0
0
0
2
1
0
1
0
0
1
2
2
2
0
1
0
4
3
1
1
0
0
1
0
0
0
1
0
0
0
0
5
0
0
1
0
1
2
2
0
2
1
2
3
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
1
0
0
1
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
3
0
2
1
1
2
1
0
1
0
0
0
2
2
0
2
0
2
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
1
1
2
1
0
4
1
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
2
0
3
2
0
0
0
1
0
0
2
0
5
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
0
0
2
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
1
4
0
1
4
1
0
0
1
3
2
0
1
5
0
3
3
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
4
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
2
1
2
1
1
1
2
0
1
0
1
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
19
2
3
0
0
0
0
0
3
1
1
0
2
0
0
2
0
0
0
0
3
1
0
0
4
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
3
0
1
0
10
2
0
0
1
3
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
4
0
0
1
0
1
2
2
2
0
1
0
2
1
1
0
2
1
2
2
0
1
0
0
0
1
0
0
1
1
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
2
0
0
0
1
0
1
1
0
1
0
1
1
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
1
0
0
0
1
2
0
1
1
3
3
0
0
0
2
0
0
0
0
0
0
1
2
3
1
0
0
0
1
0
1
0
1
1
0
0
0
0
9
0
2
1
1
1
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
2
1
1
0
1
3
4
0
1
1
0
1
0
0
3
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
5
3
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
37
1
1
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
2
0
1
1
2
0
1
2
0
0
1
1
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
1
3
0
0
0
2
0
1
2
0
1
1
1
1
0
0
0
2
2
1
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
4
0
1
0
0
0
1
1
0
3
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
1
1
1
0
0
10
0
0
2
0
1
0
2
1
2
0
3
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
3
0
1
1
0
1
1
1
0
3
0
1
0
1
0
2
0
2
0
2
1
2
0
0
1
0
1
1
2
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
1
2
1
0
3
2
0
0
1
0
0
1
1
0
1
1
0
1
4
6
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
3
0
1
1
1
1
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
75
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
4
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
3
0
0
0
2
1
1
1
0
4
0
0
0
2
0
0
1
1
0
0
1
0
1
2
1
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
2
1
2
0
0
0
0
2
2
0
0
0
0
2
2
2
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
2
1
0
0
1
0
1
0
1
3
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
4
1
0
1
2
0
0
0
0
1
0
1
0
1
0
1
2
1
0
2
1
2
0
1
1
1
0
1
0
3
0
1
0
1
3
1
0
1
0
0
1
0
2
2
0
0
2
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
0
4
5
0
1
0
0
1
2
0
1
3
1
0
1
1
1
1
0
0
1
0
3
1
5
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
2
1
1
0
0
2
0
2
2
2
1
0
0
2
0
1
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
1
0
1
2
0
2
1
0
0
1
3
0
1
0
2
0
0
1
1
0
0
3
2
0
0
0
2
0
2
3
0
0
2
0
0
1
0
2
1
1
1
1
2
1
0
0
3
1
0
0
0
0
3
1
1
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
1
1
2
0
6
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
17
0
0
0
0
2
1
0
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
3
0
1
1
1
0
1
0
3
1
1
38
1
0
0
0
0
0
0
1
4
0
2
1
3
3
0
0
3
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
3
3
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
2
1
0
3
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
1
1
0
2
1
58
0
1
0
1
0
0
5
1
0
0
1
1
3
0
1
0
0
0
1
1
1
1
0
1
3
2
2
0
1
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
8
3
1
2
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
1
0
1
0
0
0
1
0
0
5
0
1
2
0
2
0
1
2
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
3
1
0
3
0
1
3
1
0
1
0
0
0
0
1
1
1
0
4
1
0
2
1
1
7
2
0
2
4
1
3
0
3
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
0
1
1
2
0
2
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
4
0
0
3
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
1
2
2
1
2
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
3
3
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
2
2
0
1
1
4
0
1
0
1
0
0
3
0
0
0
0
0
1
1
5
0
0
2
2
2
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
1
0
1
1
0
0
1
2
1
0
0
0
2
3
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
4
0
0
1
3
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
3
1
0
0
1
1
1
0
2
0
0
1
0
1
0
0
1
1
5
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
4
2
2
0
1
1
1
1
1
0
1
1
0
1
2
0
1
2
0
0
1
1
0
0
0
2
0
3
3
0
0
1
0
0
3
0
0
0
4
1
1
0
6
0
1
0
7
0
1
0
0
0
0
1
1
1
4
0
5
0
1
5
3
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
1
0
3
1
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
4
1
1
1
0
0
0
1
0
0
1
0
0
2
0
1
1
1
0
3
0
1
0
3
0
2
0
1
1
3
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
3
2
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
1
3
4
1
0
1
2
1
0
0
1
1
0
0
2
1
0
1
1
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
1
4
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
2
0
1
1
1
0
3
0
0
1
1
0
0
0
0
0
0
1
7
1
0
0
1
1
2
1
1
0
3
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
2
0
4
0
1
1
3
1
0
0
1
2
0
2
1
1
1
1
2
0
0
1
1
1
0
0
3
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
3
1
2
1
2
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
4
1
3
1
2
0
0
0
2
0
1
1
1
0
2
0
0
0
1
3
0
1
0
0
1
0
0
2
1
1
1
1
0
0
1
0
1
2
1
0
0
0
0
0
3
0
1
0
1
0
0
4
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
1
0
2
2
0
1
2
0
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
5
0
0
0
1
1
0
2
5
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
3
1
0
0
1
0
3
1
2
1
0
2
0
0
1
0
1
0
2
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
7
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
3
0
1
0
3
1
0
0
1
2
0
0
0
3
0
2
2
0
1
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
2
4
0
0
0
0
0
2
0
1
1
1
3
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
5
0
0
1
1
0
1
0
0
1
0
1
3
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
5
0
0
0
0
3
0
2
0
1
7
1
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
3
5
2
1
1
0
0
2
0
0
2
0
3
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
1
2
3
1
0
0
0
0
1
0
1
1
2
0
5
0
0
0
0
0
0
3
0
0
1
1
1
3
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
1
2
0
1
0
5
0
2
1
1
0
0
2
0
3
2
1
2
1
0
2
0
1
0
0
1
0
2
3
0
1
0
1
1
0
0
0
3
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
2
1
0
0
1
0
2
0
2
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
1
1
0
7
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
10
0
0
1
0
1
1
0
0
0
2
0
3
0
0
0
0
1
1
1
3
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
2
1
0
1
0
0
2
0
1
0
0
3
0
1
0
1
2
0
2
1
2
1
0
2
0
0
0
1
0
1
0
4
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
3
0
1
0
0
0
3
1
2
1
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
2
10
2
2
0
0
0
1
0
2
0
0
2
0
1
0
0
2
1
0
0
1
1
3
2
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
4
1
1
0
1
0
1
0
0
0
4
4
0
0
1
1
0
2
1
2
0
0
0
0
1
3
1
2
0
2
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
3
0
1
2
0
4
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
4
1
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
4
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
2
2
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
4
0
0
1
0
1
0
1
1
0
0
4
1
1
1
1
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
1
2
2
0
0
1
0
1
1
0
0
4
3
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
1
3
1
0
0
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
3
1
0
0
1
1
1
3
0
0
1
0
0
0
0
1
0
0
2
4
0
3
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
4
0
8
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
4
5
4
0
1
1
0
0
1
1
0
1
0
1
2
1
1
2
0
0
1
0
1
0
1
1
1
0
1
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
2
0
0
0
1
3
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
1
0
1
2
0
7
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
2
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
4
0
0
3
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
12
1
1
0
1
0
0
6
4
1
2
0
1
1
1
1
0
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
3
1
0
1
1
1
3
1
0
2
0
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
2
0
0
1
1
0
0
1
1
1
0
0
0
4
8
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
3
1
0
0
1
1
2
0
1
0
0
1
0
0
1
3
1
1
0
0
1
0
0
0
1
1
5
2
1
1
1
0
3
1
0
0
0
1
0
1
0
2
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
2
2
1
1
0
2
2
0
3
0
0
0
0
0
3
1
0
0
3
1
1
2
1
0
4
0
1
2
2
0
1
0
2
0
2
1
1
0
0
3
3
1
0
2
0
1
1
0
1
0
1
2
1
0
2
0
0
1
1
0
0
0
0
6
2
1
0
0
0
1
1
1
1
2
1
0
0
2
1
2
1
1
0
0
0
0
3
0
0
1
0
2
1
4
1
1
0
0
1
1
0
2
0
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
4
0
1
2
0
2
0
1
1
3
0
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
4
0
0
1
0
1
0
2
1
0
4
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
3
1
0
1
0
2
2
0
1
1
1
0
0
0
1
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
1
1
1
0
4
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
1
2
0
0
0
1
0
1
1
0
1
0
3
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
4
0
0
3
0
2
0
3
0
0
0
0
0
1
0
0
2
3
2
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
6
0
0
0
0
1
0
1
2
1
0
4
0
0
2
0
0
0
2
1
0
0
0
1
0
2
1
1
1
0
0
1
0
2
1
3
0
1
2
2
0
0
1
0
1
1
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
1
0
1
1
1
3
0
2
0
3
3
0
1
1
3
2
1
0
0
1
0
1
1
2
3
1
0
0
2
2
3
0
1
1
0
1
0
1
0
2
0
0
1
4
1
1
1
1
3
1
0
0
1
1
1
0
1
1
0
0
0
2
0
1
1
1
4
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
3
2
1
2
1
0
0
0
0
1
0
3
0
1
0
1
0
2
0
0
3
1
3
0
1
1
0
1
3
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
4
0
1
2
0
0
2
0
0
1
0
1
0
0
1
2
3
0
1
2
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
2
2
2
1
1
1
1
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
5
3
1
2
0
0
0
2
0
1
2
1
1
4
0
1
0
5
0
2
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
4
1
0
1
0
1
0
2
2
0
1
1
0
0
0
0
1
0
3
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
14
0
2
2
0
0
0
1
0
1
0
31
1
1
0
0
0
0
4
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
3
0
2
1
0
0
1
2
1
0
1
0
1
1
0
1
2
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
1
0
1
3
0
0
1
0
2
0
0
1
0
4
0
0
0
2
1
1
1
2
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
7
0
2
0
0
0
1
1
1
1
1
1
1
0
0
0
2
1
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
3
1
2
1
0
1
0
1
1
2
0
0
1
2
0
0
3
1
0
0
0
0
1
0
0
2
0
0
2
4
1
1
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
3
0
1
5
0
1
0
0
0
0
1
0
1
1
2
2
1
0
2
0
4
0
1
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
15
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
1
1
0
4
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
2
0
1
0
0
1
1
0
1
0
2
0
1
0
0
1
2
1
2
1
0
1
2
0
2
2
4
0
1
0
0
2
0
0
0
3
1
0
2
1
0
1
1
0
2
1
3
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
1
1
0
1
1
1
1
2
0
0
0
2
0
1
0
0
0
2
1
1
1
0
1
2
3
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
2
4
1
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
1
2
1
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
3
0
0
2
0
1
1
0
2
0
2
1
0
3
1
0
1
0
0
1
0
0
0
0
0
3
1
0
3
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
4
1
0
0
1
1
0
2
3
2
1
0
0
2
0
3
1
1
1
2
0
2
0
2
0
0
0
3
0
0
1
2
1
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
3
1
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
1
3
1
0
0
1
0
0
1
2
0
1
1
1
0
1
1
1
1
0
3
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
2
3
1
1
0
1
0
0
0
0
1
1
0
0
0
1
4
0
0
0
0
0
3
1
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
3
1
1
1
0
0
1
0
0
1
0
1
3
4
1
0
1
0
2
1
1
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
2
0
1
2
1
1
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
4
0
0
1
1
0
0
0
0
1
0
0
0
4
1
0
0
0
1
1
0
0
0
0
1
1
0
1
3
0
1
2
5
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
3
0
1
0
0
0
1
0
0
4
0
2
3
0
1
0
0
0
3
1
1
0
0
0
1
0
0
2
2
1
0
1
0
1
1
1
0
0
2
2
3
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
1
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
1
2
3
1
0
0
0
4
0
0
2
0
1
0
2
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
3
1
1
1
0
0
0
0
1
1
0
1
1
1
0
3
0
1
0
0
0
0
0
2
1
1
1
0
1
0
4
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
3
0
1
0
0
1
0
0
1
3
0
0
0
2
0
0
1
2
0
1
0
2
2
1
1
1
2
0
1
0
0
1
0
1
1
1
4
1
1
5
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
3
1
1
1
0
1
0
1
2
3
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
1
1
0
1
1
4
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
4
0
0
1
1
3
1
1
0
1
1
1
0
0
2
0
1
4
1
1
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
6
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
2
0
2
0
1
1
0
1
0
0
1
0
0
2
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
1
0
2
0
1
3
0
0
0
0
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
2
3
0
2
0
0
2
3
1
2
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
7
0
1
1
0
1
0
2
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
1
3
1
1
0
0
1
2
2
0
2
0
4
1
0
0
0
0
0
1
0
0
1
2
0
1
0
4108
0
0
1
6
0
1
0
0
0
12
1
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
3
0
0
7
0
4
0
5
0
1
0
0
3
2
1
0
1
0
2
0
0
4
0
10
0
8
2
3
1
0
1
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
8
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
6
0
0
2
0
1
2
0
1
3
0
0
2
1
0
1
2
0
3
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
5
1
0
3
0
1
0
4
1
0
6
0
1
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
9
0
0
0
0
2
0
2
4
0
5
0
0
0
0
0
1
6
0
0
1
3
1
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
1
1
0
0
4
7
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
1
0
0
0
15
2
0
1
0
0
0
0
1
0
0
0
0
0
7
0
6
0
2
2
1
0
0
0
2
0
3
0
0
1
1
1
1
7
5
4
1
6
1
0
0
1
0
0
3
0
2
0
3
1
0
7
1
0
2
2
0
0
0
3
0
0
0
1
0
1
5
0
1
0
1
1
1
0
0
0
1
0
1
0
2
0
2
0
0
3
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
1
2
0
0
0
0
0
2
1
0
0
4
0
1
0
0
0
4
1
0
0
0
0
0
2
0
0
5
1
0
1
1
0
4
0
3
0
1
0
1
0
0
1
3
0
0
0
0
0
0
4
0
2
0
0
0
4
1
1
1
6
1
1
2
0
0
2
0
0
1
0
8
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
1
0
4
2
2
1
0
3
1
2
0
0
0
0
0
1
1
1
0
0
0
1
3
3
1
2
0
1
2
1
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
2
0
4
0
0
0
0
3
3
0
3
0
1
0
1
3
2
0
0
1
0
0
1
0
0
0
2
0
0
3
1
1
0
0
2
1
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
1
12
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
6
1
1
0
1
0
1
0
1
0
1
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
4
0
0
0
1
1
1
1
2
0
0
5
0
0
1
0
0
0
13
1
2
0
2
1
0
1
1
3
0
1
0
0
0
1
0
0
6
1
0
2
0
1
4
0
0
0
1
0
0
0
2
1
2
1
0
2
1
1
1
2
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
2
2
1
4
5
1
1
0
0
0
0
2
0
1
0
0
1
0
0
3
0
1
2
0
0
0
1
3
0
0
1
0
0
0
1
4
0
4
1
0
0
1
0
3
0
1
0
1
1
1
0
0
2
1
1
0
1
0
4
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
5
1
2
0
1
0
2
1
1
1
2
1
8
1
0
1
0
0
0
3
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
5
2
1
2
25
2
0
0
0
1
2
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
2
1
0
5
1
0
5
1
0
1
1
0
1
1
0
0
1
6
9583
14
1
0
1
0
1
8
0
1
2
0
2
4
0
0
1
0
0
3
1
6
8
0
0
7
0
1
0
0
0
1
1
0
0
11
9
0
3
0
0
1
0
2
5
1
0
0
1
0
0
6
1
1
5
0
0
7
0
1
7
6
0
7
0
1
0
2
0
1
1
2
1
10
0
0
1
6
6
0
0
0
0
4
1
0
1
1
6
5
1
0
0
8
0
0
1
0
0
0
9
4
0
2
0
0
0
1
0
1
1
5
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
4
0
0
0
1
1
0
1
2
7
1
0
1
1
4
1
5
8
0
0
7
3
1
1
2
5
2
1
6
1
0
7
0
10
0
0
0
0
4
0
4
0
2
0
1
3
11
3
1
10
1
0
0
4
0
1
4
5
0
6
3
1
0
6
1
0
0
0
0
1
0
9
0
0
0
0
0
0
0
5
3
0
1
2
0
0
2
0
2
1
1
0
1
4
0
2
2
3
0
0
1
4
0
1
0
0
1
3
0
0
0
0
0
0
4
0
0
0
1
2
1
1
5
0
1
0
3
1
10
0
2
0
6
1
0
0
0
3
1
0
1
0
0
6
0
1
0
0
0
0
0
0
0
9
0
3
1
0
0
0
0
0
0
1
0
0
5
1
1
0
0
7
0
6
0
3
2
7
0
2
2
1
1
0
1
1
0
0
1
1
1
1
8
0
0
2
8
1
0
0
5
0
0
0
0
1
0
0
0
0
3
9
0
1
3
2
0
7
1
0
0
0
1
5
0
0
1
5
1
0
5
0
0
1
4
1
1
0
1
0
1
5
0
0
0
2
0
0
0
1
3
1
0
0
1
0
0
0
1
5
0
4
0
6
2
0
0
7
2
1
7
1
6
0
2
4
0
2
0
0
0
1
0
1
0
1
0
0
6
0
5
1
5
2
1
7
0
0
0
2
0
4
0
2
0
0
1
6
1
3
1
5
1
3
0
1
4
1
0
0
0
0
1
2
8
2
0
1
4
5
0
5
0
0
7
0
0
0
7
2
0
3
0
0
3
0
1
2
0
1
0
4
0
0
0
1
1
0
1
0
3
0
0
0
0
3
0
1
0
4
0
1
1
0
0
0
0
1
5
2
0
0
2
0
0
0
3
7
0
2
0
1
1
0
0
0
0
0
1
0
1
1
3
0
1
4
0
2
0
0
0
3
0
1
1
0
0
3
0
6
0
0
0
8
0
7
0
1
2
2
1
2
0
1
2
1
4
0
0
0
3
0
0
1
1
4
0
0
7
3
2
0
1
0
0
0
11
0
5
0
0
0
2
2
0
6
0
0
0
1
4
2
0
0
1
1
3
0
7
2
0
2
4
6
0
0
1
0
0
3
1
2
0
0
0
7
1
5
1
1
0
1
4
3
0
0
3
0
0
2
1
7
7
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
3
2
0
4
2
1
2
0
1
3
1
0
0
1
5
1
0
2
0
0
0
0
0
5
0
1
2
0
2
1
0
1
0
1
4
0
0
1
0
0
0
1
0
2
5
3
0
3
2
4
2
8
0
9
2
8
1
0
2
8
0
0
2
1
0
0
0
2
3
0
0
5
0
0
0
0
0
0
0
0
1
1
1
1
5
2
3
1
0
4
1
0
4
0
0
0
2
0
1
5
1
1
0
2
1
2
0
0
2
4
0
0
3
0
0
1
0
7
1
3
0
1
0
4
4
0
0
5
3
1
1
0
0
2
1
0
0
6
1
0
0
0
0
0
0
2
0
4
9
6
1
0
10
6
0
6
4
1
2
4
1
3
2
6
1
1
1
5
2
0
2
0
0
0
1
0
5
0
4
0
0
4
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
3
6
0
8
0
1
0
1
4
1
1
5
3
0
1
0
1
0
1
0
2
1
2
1
0
1
1
5
4
0
1
2
0
9
0
6
1
4
1
2
6
5
1
0
0
1
0
3
1
1
2
2
0
1
2
0
0
6
0
1
1
0
0
1
1
1
2
5
0
3
2
0
3
2
0
1
0
3
1
1
1
0
2
1
0
6
3
0
1
0
1
3
5
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
5
4
1
0
1
2
0
0
2
1
0
0
2
0
1
1
7
1
8
0
2
1
2
2
0
2
0
0
5
0
0
0
1
1
2
0
0
3
2
0
1
0
0
1
0
0
0
1
1
4
0
0
3
1
0
8
0
3
3
1
0
2
0
0
2
0
0
5
0
5
1
0
1
0
1
1
0
3
0
7
0
7
0
3
1
2
0
0
3
4
0
3
4
1
2
3
0
0
0
2
0
0
0
2
1
0
1
1
4
3
0
0
0
4
2
0
0
2
2
4
2
2
3
1
3
2
2
0
0
1
0
5
1
3
0
0
1
0
2
1
0
10
0
1
0
0
0
0
0
3
1
0
0
0
0
1
6
1
0
2
1
0
0
1
1
0
1
0
0
1
0
0
1
1
3
7
0
3
0
1
2
0
4
9
0
1
4
0
0
1
1
0
0
3
0
1
0
0
2
0
5
0
1
0
2
0
2
0
1
1
0
1
0
0
0
3
1
0
3
0
1
1
1
0
2
0
1
0
1
0
3
5
2
0
1
0
0
1
2
2
0
6
1
0
2
0
1
2
4
0
2
0
1
1
1
0
1
0
0
4
1
0
3
4
1
3
0
0
3
5
0
0
1
3
4
0
0
2
0
0
6
3
1
1
0
0
0
0
0
1
2
1
0
2
0
1
0
1
1
0
0
0
3
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
3
4
1
0
1
0
0
4
1
3
3
4
1
0
0
0
0
0
2
0
4
2
4
0
0
1
0
3
0
0
2
2
1
0
0
4
0
0
2
0
3
0
0
2
1
2
0
0
5
3
2
0
1
1
0
0
1
0
8
2
2
2
0
2
1
0
0
1
1
0
1
0
0
1
2
1
0
0
0
3
2
0
1
2
0
0
0
0
0
0
5
0
0
0
0
1
2
17
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
1
0
1
4
0
0
1
0
0
8
2
0
3
0
0
1
0
0
1
0
1
5
7
0
0
0
1
1
0
1
0
0
1
0
1
1
5
1
2
1
0
1
4
0
3
1
0
1
6
3
1
1
0
0
0
0
0
6
0
2
0
0
0
0
0
0
5
0
1
0
2
1
1
0
0
0
6
2
2
0
0
0
0
2
1
2
0
0
3
0
0
3
0
5
0
1
5
0
0
0
0
4
1
6
0
0
0
0
1
1
2
1
0
0
1
1
1
1
0
2
1
4
1
1
1
0
1
4
0
1
0
0
1
1
2
2
0
0
155
1
1
0
4
2
3
0
7
3
3
2
0
2
1
1
0
2
11
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
5
4
0
2
0
1
0
1
1
3
0
0
1
0
0
0
1
0
0
0
5
0
0
0
4
5
0
4
2
1
0
5
5
0
1
0
1
1
1
2
3
1
4
1
2
1
0
18
1
0
1
0
0
1
5
0
0
0
2
5
6
0
1
1
6
0
2
5
0
0
0
0
0
3
3
1
0
3
1
1
5
2
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
4
0
0
0
2
3
0
1
1
1
0
0
0
0
0
1
5
3
0
2
0
2
0
0
1
3
2
1
0
0
4
1
6
1
0
0
5
0
0
0
5
3
0
1
1
0
0
0
0
2
0
0
0
4
1
0
0
1
7
4
5
0
6
0
0
1
2
1
0
0
0
1
3
0
0
3
0
0
0
1
2
4
5
0
1
0
4
0
0
4
1
4
1
0
1
2
1
0
4
1
1
0
2
2
3
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
7
0
5
5
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
1
0
0
2
3
0
1
0
1
2
1
1
1
1
2
0
0
0
0
6
0
0
0
7
1
0
0
4
0
1
7
0
1
0
1
1
0
0
1
0
0
0
0
1
4
0
1
1
3
0
0
0
0
2
2
0
0
0
1
1
1
3
0
0
2
0
3
3
7
3
3
0
1
0
0
2
0
0
0
2
1
0
0
1
2
4
0
1
1
0
3
1
0
0
0
3
1
2
1
0
2
0
0
6
1
1
4
1
2
2
0
0
0
2
0
0
2
0
0
0
6
1
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
2
2
1
0
0
0
1
0
3
0
2
2
7
4
0
2
1
4
2
0
6
0
2
0
1
0
0
0
0
1
3
2
1
9
2
0
1
0
1
0
4
1
1
4
1
4
1
1
1
0
0
1
2
3
0
0
1
1
1
0
0
3
1
4
0
1
0
0
0
0
2
1
1
0
1
1
2
0
1
0
1
1
1
1
0
0
0
0
0
1
0
7
1
1
1
0
1
0
1
0
2
4
0
0
2
1
1
1
0
2
0
5
0
3
0
3
0
4
2
0
1
4
0
0
1
0
0
0
1
0
1
0
1
1
2
0
5
1
1
0
0
3
0
7
1
2
0
3
9
4
0
3
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
2
0
0
0
3
0
1
0
5
2
1
4
1
0
1
2
5
0
2
1
1
1
3
0
1
0
3
0
0
3
1
1
1
0
1
1
3
3
0
0
1
0
2
2
112
0
0
2
0
2
1
0
0
1
1
0
0
0
6
1
1
0
1
4
0
0
0
0
0
0
0
7
2
1
1
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
6
0
2
0
2
2
1
4
4
2
0
1
0
3
1
0
1
0
4
0
0
1
0
2
0
1
1
4
1
0
0
0
2
2
0
1
0
1
1
3
0
0
0
1
0
0
0
2
1
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
5
0
1
1
1
1
2
0
0
2
0
4
1
2
0
0
2
0
0
0
0
1
0
1
0
2
0
1
3
2
0
0
0
0
0
2
1
1
0
5
0
0
0
0
0
4
2
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
1
1
2
1
0
2
0
4
1
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
5
2
0
0
1
1
4
0
0
0
1
0
3
0
1
0
1
3
1
3
1
0
0
0
0
1
1
1
0
2
1
1
0
2
0
1
3
0
3
2
1
1
3
0
2
2
0
0
2
3
0
0
4
0
0
0
0
1
0
1
0
1
3
0
2
1
0
1
1
5
0
0
1
1
3
6
0
5
2
3
0
1
0
2
1
5
0
0
1
0
0
1
0
0
0
4
3
0
0
3
2
0
0
5
0
1
0
0
5
0
1
0
2
1
4
0
2
0
1
1
0
0
2
2
4
0
6
0
0
4
0
1
3
2
1
1
0
0
0
0
0
0
3
1
3
4
0
0
1
2
0
0
0
0
1
0
2
2
1
2
0
0
0
0
5
0
0
1
0
0
2
0
0
0
1
4
0
0
0
0
5
1
0
2
0
1
0
0
4
4
0
2
0
1
0
10
1
0
1
0
0
2
0
1
1
2
0
1
1
2
1
2
1
0
0
1
4
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
4
57
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
3
1
4
1
0
0
2
5
1
0
0
5
0
2
2
1
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
3
5
2
0
1
0
1
1
0
1
0
2
1
4
2
4
2
0
2
2
1
0
0
3
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
1
0
0
1
0
1
2
1
2
0
1
0
1
3
0
3
0
1
1
1
0
2
1
4
3
1
2
1
0
0
1
5
0
0
0
0
0
1
1
3
1
2
0
5
2
2
1
1
0
2
1
0
0
3
1
1
3
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
3
0
0
1
1
5
1
2
8
3
0
0
3
1
1
0
1
0
1
0
2
0
1
2
1
0
2
0
0
0
3
0
0
1
3
1
1
0
0
0
1
1
2
2
0
3
2
2
4
2
1
0
2
0
0
7
0
0
2
2
0
0
3
0
1
0
2
0
0
4
0
0
0
1
1
4
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
2
2
0
4
0
2
0
3
2
0
1
0
0
1
3
0
0
0
0
0
7
0
1
0
0
0
4
0
0
3
1
0
1
0
2
0
0
0
0
1
0
2
4
0
0
0
3
0
0
5
0
0
0
0
0
2
4
2
3
2
0
2
1
1
0
2
1
3
1
5
0
2
1
0
1
0
3
0
0
1
0
0
0
0
0
2
1
5
1
2
0
4
3
0
0
0
1
0
0
0
0
4
1
1
5
3
13
0
0
1
0
3
1
1
1
0
0
1
2
2
1
3
1
0
6
0
0
1
6
1
0
2
2
2
1
1
3
0
2
1
1
1
0
0
2
0
4
0
5
1
3
0
1
3
1
0
1
2
4
0
0
2
0
1
4
0
2
1
0
0
0
0
2
2
0
1
0
2
2
0
0
1
1
0
0
0
0
3
3
0
0
5
2
1
8
5
1
0
0
0
0
2
3
0
1
0
1
3
1
0
0
2
0
0
0
1
3
1
2
0
3
1
3
3
0
1
0
6
1
0
0
1
2
0
0
2
2
0
0
6
0
0
0
0
1
1
1
2
0
0
0
1
2
0
1
0
0
1
3
0
1
3
0
0
0
0
0
0
0
0
1
3
0
1
0
3
2
0
1
0
3
2
2
1
0
1
2
1
1
3
0
0
1
1
1
0
1
2
0
2
4
0
0
0
0
1
2
2
2
0
8
1
1
0
3
1
1
0
1
0
0
2
0
0
0
1
0
2
0
1
1
2
2
3
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
4
3
0
0
0
1
4
1
4
2
0
0
0
1
2
1
0
0
1
0
2
0
5
0
0
2
1
1
0
1
2
1
0
0
0
0
1
1
2
0
2
2
3
4
1
1
1
9
4
0
1
0
1
0
0
1
0
3
3
1
2
0
1
0
1
0
1
0
1
0
1
1
3
2
2
2
2
3
0
0
0
1
5
0
0
0
0
0
0
5
0
2
3
3
3
3
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
0
3
2
3
0
0
0
8
1
5
1
0
4
0
1
0
0
1
0
0
0
1
2
2
1
0
1
16
2
0
1
5
0
0
1
5
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
1
1
3
0
1
5
4
0
2
0
2
1
0
0
1
0
1
2
1
0
0
2
4
1
2
1
1
0
1
0
1
0
1
0
1
0
4
0
0
0
1
3
0
4
3
0
0
6
3
2
0
2
0
0
0
0
1
0
1
3
0
0
0
2
1
0
1
0
0
0
1
4
0
2
0
0
1
0
1
1
2
1
0
2
0
0
1
0
2
0
1
1
2
1
2
0
0
2
1
0
0
6
5
0
0
0
1
0
0
0
0
2
1
0
0
1
3
1
0
0
0
0
1
1
0
0
5
0
0
0
2
0
0
0
1
7
0
6
3
0
0
2
0
0
1
0
0
7
1
1
0
0
0
1
0
0
0
1
0
6
0
3
6
0
0
0
1
0
1
0
1
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
6
1
5
4
0
3
0
4
1
0
0
1
1
0
6
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
3
0
0
0
4
2
1
0
2
3
1
0
0
4
2
0
2
1
1
1
0
1
3
2
0
0
0
1
2
0
0
1
0
3
0
6
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
3
1
5
0
0
7
0
0
0
0
3
0
2
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
5
0
2
2
1
1
2
1
6
1
2
0
2
1
2
2
0
0
0
1
0
0
1
1
1
0
1
0
5
0
0
0
2
1
1
1
0
2
1
2
2
0
3
6
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
4
4
0
2
1
0
0
0
3
0
0
2
0
2
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
6
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
4
0
1
4
4
0
0
0
3
0
2
0
0
6
0
1
4
0
0
1
0
0
2
1
2
2
1
1
1
0
1
7
0
1
5
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
3
2
3
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
3
4
0
0
1
4
0
1
0
0
5
0
1
2
3
1
0
4
2
3
1
0
0
0
2
0
0
3
1
6
0
0
0
2
2
2
0
1
0
0
0
1
6
1
4
0
0
0
0
1
0
2
4
1
1
0
2
0
0
1
4
2
0
0
2
0
3
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
6
0
4
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
4
1
0
1
1
1
0
0
1
3
3
1
0
0
0
1
1
0
0
1
2
0
0
1
3
0
1
1
7
3
0
1
2
4
1
0
0
0
0
3
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
1
1
2
3
1
1
2
4
2
0
0
2
2
1
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
3
12
0
0
0
1
0
0
1
2
0
1
0
1
1
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
1
0
3
1
0
2
0
2
0
0
1
0
2
1
1
2
0
2
3
0
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
0
2
3
1
2
0
3
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
3
3
0
0
3
0
0
3
0
0
0
0
1
0
4
0
6
0
1
0
2
0
0
1
0
0
3
0
1
0
0
1
0
0
4
8
1
0
0
0
0
1
6
0
1
3
0
0
1
0
3
3
0
1
1
0
3
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
3
4
3
0
0
0
0
0
2
1
1
0
0
0
1
1
4
0
322
0
2
1
0
0
0
5
5
2
0
1
0
0
0
0
3
0
0
0
2
0
1
1
0
1
0
1
1
0
0
1
1
0
1
2
1
1
0
2
0
1
0
0
0
4
1
0
0
3
0
0
2
3
5
3
2
0
7
0
4
4
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
3
1
0
0
0
5
3
4
0
6
0
0
2
4
0
0
1
1
0
6
5
0
1
1
0
0
3
3
1
0
4
1
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
2
2
1
1
0
0
2
0
1
0
0
1
0
4
0
3
0
1
1
0
1
3
3
1
0
0
0
4
0
1
2
0
7
2
3
1
1
0
0
1
0
0
1
0
1
3
0
0
0
1
1
2
4
0
0
0
1
0
0
2
0
0
0
5
0
6
1
0
0
1
1
2
1
0
0
0
1
7
0
2
0
0
0
1
0
1
1
0
0
0
10
0
2
1
1
0
3
1
0
0
2
1
0
0
3
0
2
1
0
0
2
2
1
0
1
1
1
2
4
1
0
0
0
0
0
1
1
0
0
6
2
0
0
1
0
3
2
0
0
1
0
2
0
0
2
0
0
1
0
2
2
1
1
0
1
0
0
4
2
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
1
1
1
1
0
1
0
0
0
3
0
0
0
0
1
1
3
2
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
3
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
4
0
0
0
0
1
3
4
1
1
1
1
0
1
0
0
1
4
2
3
2
1
2
4
0
1
0
4
0
2
0
2
0
1
0
6
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
3
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
0
1
1
2
0
1
0
0
1
5
0
3
5
2
0
4
2
1
0
2
1
0
2
1
1
1
1
0
2
0
1
0
6
1
3
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
4
3
2
0
1
3
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
1
2
1
0
0
0
1
0
1
4
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
7
0
1
1
0
0
0
0
2
3
1
1
0
0
0
1
0
1
1
0
0
3
1
0
0
0
0
7
0
0
0
0
1
1
0
2
2
0
1
2
1
2
1
0
0
2
1
0
1
0
0
0
3
1
0
0
5
1
0
3
2
1
0
0
4
2
0
1
1
0
0
2
5
1
1
0
0
0
0
1
2
0
1
0
1
2
1
6
0
0
4
0
0
4
1
0
0
1
0
1
1
3
0
4
0
2
0
0
3
0
0
0
0
1
0
1
3
1
0
5
3
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
3
1
7
0
2
2
0
0
0
0
0
2
0
1
0
5
0
0
2
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
3
0
1
6
0
1
0
1
0
0
0
0
0
1
0
0
1
3
0
3
2
0
0
0
1
1
2
2
1
0
2
3
0
2
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
2
0
5
0
0
2
1
0
2
0
0
0
1
0
3
6
0
2
0
1
0
2
1
0
0
2
4
0
1
2
2
0
1
2
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
7
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
3
0
0
1
1
0
0
3
1
0
1
2
0
4
2
0
0
1
1
0
2
0
1
1
0
0
4
6
0
1
0
1
0
4
0
1
0
5
1
2
5
1
1
1
2
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
110
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
6
0
0
0
0
0
1
2
2
8
0
1
0
2
0
0
8
1
2
1
1
2
0
0
1
0
0
1
3
0
2
6
1
0
0
0
1
4
1
0
2
3
4
1
0
0
0
1
3
0
1
1
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
1
1
0
7
2
0
0
0
1
1
0
2
1
2
0
0
0
4
5
1
0
0
0
0
2
0
1
0
1
1
0
2
4
7
0
0
6
1
0
1
4
1
2
1
1
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
4
1
1
8
0
1
2
2
1
0
1
0
0
0
0
0
2
2
0
2
0
1
1
0
1
3
1
0
2
1
1
0
0
0
1
0
2
0
0
0
2
0
10
1
1
6
0
0
2
0
0
2
0
1
0
1
1
1
0
4
0
0
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
2
4
0
1
0
0
4
1
0
2
5
4
2
2
0
1
1
0
2
0
0
0
10
0
0
0
0
0
0
0
7
0
2
0
1
1
0
1
2
2
0
0
1
3
0
15
4
0
1
0
0
1
1
1
4
1
3
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
0
1
1
0
1
0
1
0
0
3
2
0
0
1
2
1
2
2
0
0
3
0
0
1
9
1
1
0
1
3
0
4
0
0
0
0
0
0
0
5
1
1
0
3
1
0
1
0
1
0
0
0
0
1
0
0
2
0
6
1
1
1
0
0
0
0
1
0
0
1
3
1
2
0
0
0
5
0
1
2
0
0
5
0
0
1
1
2
0
2
0
1
2
0
1
0
1
2
0
2
0
0
3
2
0
0
2
2
3
1
0
4
0
1
0
0
0
1
1
1
0
0
1
3
0
0
1
0
0
1
4
0
1
0
2
0
0
0
0
3
3
5
1
0
2
0
0
0
0
3
0
1
1
0
0
5
0
1
0
1
0
0
4
1
0
3
1
0
0
5
0
0
1
1
1
0
1
0
0
0
1
4
0
1
4
1
1
3
1
1
4
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
3
0
0
2
0
4
0
0
0
0
2
2
0
1
3
0
0
5
0
1
1
3
1
17
0
0
2
1
3
0
0
2
1
1
0
5
1
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
1
0
0
3
0
0
2
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
6
0
0
0
2
1
1
0
4
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
1
0
4
0
3
0
4
1
0
1
2
0
3
0
2
0
0
0
0
0
1
1
3
1
6
0
0
3
0
2
0
1
0
2
1
0
0
0
0
5
3
2
0
1
1
1
0
1
3
1
1
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
2
3
1
0
2
0
0
1
2
0
0
1
3
0
3
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
3
0
0
2
0
0
0
1
0
0
1
0
0
3
0
2
1
0
1
0
0
6
1
3
0
0
8
5
1
0
2
1
0
0
0
1
1
1
2
1
0
0
3
0
2
0
3
1
0
0
0
0
0
0
2
1
0
1
2
1
0
4
0
1
0
1
0
2
0
1
0
1
0
0
3
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
4
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
6
2
0
2
2
1
0
1
0
3
4
1
0
4
0
0
0
0
2
0
6
1
0
1
0
0
1
0
1
0
1
0
0
2
2
4
0
4
0
1
0
2
1
0
1
1
0
2
0
3
1
4
1
2
0
0
1
2
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
6
2
0
0
0
0
0
0
4
2
0
1
0
1
0
1
1
0
1
1
2
1
0
0
0
1
4
1
0
0
0
0
1
4
0
0
3
1
0
2
7
0
4
3
0
2
2
0
0
0
0
0
0
0
0
0
1
5
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
3
0
1
1
0
0
1
1
1
0
0
2
2
0
0
2
0
1
2
0
3
0
0
1
0
0
2
0
3
1
1
0
1
1
0
2
0
1
0
1
3
0
0
1
0
1
0
0
3
0
4
2
0
1
0
0
0
3
0
1
1
4
2
0
0
0
0
0
0
2
0
0
3
0
3
0
2
1
0
0
1
1
1
1
2
1
2
2
1
1
0
1
0
0
1
1
3
2
1
0
4
0
1
1
2
1
1
3
0
2
0
2
0
0
0
2
1
0
0
0
0
5
2
0
0
1
0
1
2
0
2
2
1
1
0
0
1
0
0
0
3
2
0
0
1
2
1
1
3
0
0
0
0
0
0
0
2
3
0
1
1
2
0
2
0
1
2
1
4
1
2
2
0
1
0
0
0
1
1
0
1
4
1
0
0
0
1
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
2
6
1
2
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
4
1
2
4
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
2
4
1
3
2
0
1
2
0
0
1
1
1
0
0
4
0
1
1
1
0
0
1
0
0
0
1
0
1
2
1
2
0
1
0
2
0
0
1
1
0
0
0
0
4
0
1
1
1
0
0
7
2
0
6
0
1
5
0
0
0
1
3
2
0
3
2
1
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
1
0
1
1
1
0
0
1
2
0
0
8
1
1
3
0
0
0
0
0
0
1
4
0
1
0
6
1
0
0
2
2
4
3
1
0
0
0
0
0
0
1
2
0
3
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
3
0
0
3
3
1
0
0
2
0
2
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
5
2
1
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
3
1
0
1
0
1
4
1
0
2
0
2
0
2
1
0
1
0
5
0
1
1
0
3
0
3
0
0
0
2
1
0
0
0
2
0
0
0
8
1
2
0
0
0
0
2
0
0
0
0
6
1
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
1
0
3
1
0
3
0
5
4
1
0
0
2
2
0
0
0
1
0
2
0
0
1
5
0
0
44
38
2
0
1
0
0
1
0
5
0
1
0
2
0
0
7
0
0
0
0
1
0
1
0
1
1
3
0
0
0
2
0
2
0
2
0
1
1
1
4
4
1
0
0
1
1
0
0
0
6
1
0
0
0
1
1
9
2
2
1
1
0
1
0
0
0
0
5
0
0
0
4
0
0
2
2
1
0
1
1
1
4
3
6
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
3
0
0
1
1
4
1
0
1
1
2
0
2
2
0
2
2
0
2
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
4
1
3
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
4
1
6
0
1
0
4
0
0
3
0
3
1
1
4
0
3
0
0
4
0
0
2
0
0
1
0
3
1
1
4
2
1
1
2
1
0
1
1
2
0
3
1
5
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
3
0
1
1
0
0
1
1
2
2
1
0
5
3
0
4
3
0
0
0
1
1
2
1
1
1
0
1
1
0
0
6
1
0
0
0
0
0
2
2
1
0
2
2
2
0
1
2
0
1
6
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
2
1
1
0
1
2
1
1
1
2
0
4
4
1
0
0
0
1
1
1
0
0
0
3
1
0
1
1
0
1
4
0
0
0
0
1
0
0
0
1
1
0
0
1
3
0
5
0
3
1
0
2
0
1
1
0
0
0
7
0
0
0
1
0
0
5
2
2
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
3
3
2
3
3
0
0
0
0
2
1
0
3
2
0
0
0
1
0
0
0
1
0
0
3
0
2
1
1
0
0
4
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
4
3
0
2
2
1
3
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
4
1
2
2
0
0
1
2
3
1
0
0
1
1
1
0
2
1
0
0
1
2
1
0
1
0
0
4
4
0
1
1
1
0
1
2
0
0
1
0
0
0
2
1
5
1
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
2
0
3
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
1
5
0
1
1
0
0
2
3
0
0
0
2
0
1
1
0
0
0
3
2
0
0
1
0
2
0
1
0
0
0
5
0
2
1
3
4
0
0
0
2
1
0
0
1
1
2
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
1
1
2
0
1
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
2
2
1
0
3
2
1
0
0
0
2
2
1
0
0
4
0
4
0
2
0
3
1
0
0
0
0
1
2
1
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
3
0
1
0
1
0
3
1
0
1
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
1
0
4
1
1
1
0
2
0
0
0
4
0
0
2
0
5
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
2
1
1
0
1
0
5
0
4
1
0
1
1
0
0
0
0
1
2
0
1
0
3
1
0
0
1
1
2
0
0
0
0
3
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
3
0
1
0
2
3
0
0
0
1
0
0
1
0
1
2
3
2
3
0
1
0
1
0
3
38
1
5
1
3
1
0
1
0
12
1
0
0
3
0
0
3
1
1
2
0
0
2
3
1
0
0
2
0
0
2
2
0
1
2
1
1
1
0
0
0
2
0
0
1
0
2
0
2
7
0
0
0
0
2
0
3
1
1
1
0
1
0
1
1
0
1
0
5
0
0
0
0
0
2
0
1
0
0
0
1
5
0
0
1
0
0
0
0
3
0
3
0
0
1
0
0
2
0
0
0
0
1
2
0
2
2
1
0
1
0
3
2
2
0
0
0
1
2
0
1
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
4
2
4
0
1
1
0
1
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
4
4
0
0
2
1
0
2
1
0
0
4
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
1
0
5
1
2
3
0
0
3
1
1
0
1
0
0
2
1
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
3
0
0
0
1
0
0
1
1
1
0
2
2
1
0
0
2
1
3
0
0
1
2
0
0
0
1
0
1
0
1
2
1
2
0
3
0
0
1
1
1
0
2
1
0
0
2
3
2
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
7
0
0
1
2
2
0
2
1
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
1
2
0
2
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
3
2
1
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
5
1
0
0
2
1
0
5
1
0
0
0
0
3
3
0
0
0
0
2
4
1
0
0
0
5
0
0
0
1
4
0
2
0
0
0
0
2
0
0
0
2
0
1
1
1
1
1
1
1
0
0
1
5
2
0
2
0
0
3
3
0
3
0
0
1
2
2
2
1
3
3
0
0
2
1
1
0
0
0
0
0
0
3
1
1
0
7
1
0
4
0
2
0
0
0
1
2
1
14
4
0
1
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
2
1
1
2
1
0
0
1
1
3
1
0
0
0
0
0
0
6
0
0
0
5
0
0
0
1
1
1
1
1
2
0
0
1
2
4
1
0
1
0
1
1
1
0
2
2
0
0
1
5
1
1
1
0
5
1
1
2
0
0
0
2
0
1
2
1
1
0
0
0
1
2
3
0
1
0
2
0
0
1
1
1
0
2
0
0
3
0
1
0
0
0
3
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
2
13
1
4
1
0
0
1
0
0
3
0
0
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
1
2
1
0
1
1
2
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
5
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
2
1
1
4
1
0
0
0
4
0
2
0
1
0
1
3
0
0
1
4
0
0
1
0
1
0
15
0
1
4
0
0
1
0
2
1
2
0
1
0
0
3
3
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
3
2
1
2
2
1
2
0
1
1
1
2
1
3
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
1
3
1
3
3
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
3
0
1
2
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
22
0
3
0
0
2
1
2
0
2
0
0
2
0
0
1
1
1
1
1
3
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
1
0
2
4
0
0
1
3
0
1
1
0
1
0
0
0
6
0
0
2
0
3
1
3
4
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
5
0
3
1
5
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
2
3
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
4
1
1
0
2
3
2
2
1
1
0
0
0
0
1
1
2
1
2
0
0
1
0
0
0
1
1
3
3
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
5
0
0
0
1
0
0
0
0
1
0
4
0
1
2
0
2
1
0
1
1
0
0
0
1
0
6
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
2
2
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
5
0
0
1
1
0
0
4
0
4
0
0
0
0
0
1
1
2
2
1
0
1
0
2
0
0
0
2
1
3
1
2
1
0
1
2
2
2
2
2
1
0
1
0
2
1
1
1
0
4
0
7
1
0
0
0
3
0
0
1
5
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
3
0
0
0
0
0
0
1
3
1
0
1
0
2
0
6
2
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
4
1
3
2
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
1
0
1
0
2
3
1
0
0
1
3
1
0
0
0
0
0
3
0
1
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
1
3
1
0
0
1
0
1
1
1
1
0
0
0
0
2
1
2
5
1
0
0
0
3
0
0
0
0
2
3
1
1
1
0
2
0
1
1
0
5
1
1
0
1
0
2
1
0
0
1
0
1
3
0
0
0
0
1
0
2
4
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
1
0
1
1
4
0
1
1
1
1
0
1
3
0
0
1
0
0
0
0
1
0
0
5
0
0
0
2
0
0
1
1
2
1
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
2
2
1
4
0
0
1
2
1
0
0
0
0
3
1
0
1
2
2
0
0
0
0
2
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
5
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
2
0
1
1
2
0
1
0
3
1
0
1
0
0
1
5
0
1
0
2
1
2
0
0
1
3
0
2
0
11
0
1
0
0
0
7
6
1
0
0
0
1
0
1
0
1
1
4
3
0
0
1
2
1
2
5
1
0
0
0
0
0
0
0
0
0
2
3
4
0
2
2
1
1
2
0
0
1
1
1
0
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
1
0
1
4
0
0
0
0
0
0
0
1
4
0
0
1
3
1
1
2
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
2
0
2
4
0
4
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
1
0
0
1
2
1
0
1
2
0
2
1
0
1
2
0
8
0
2
0
2
5
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
3
0
4
0
1
1
0
0
4
2
0
0
1
2
3
1
0
0
0
5
4
0
2
3
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
3
1
1
26
1
1
1
1
1
0
0
0
1
0
2
1
5
2
3
1
0
1
0
1
1
1
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
3
1
4
0
0
0
0
0
1
2
2
1
4
0
3
0
3
0
2
0
0
2
0
0
3
1
0
0
3
9
0
0
1
0
0
0
0
0
0
0
0
0
1
0
17
1
0
1
1
1
0
1
2
0
0
0
1
1
1
3
0
0
0
1
0
0
1
2
1
2
1
0
2
1
0
0
2
1
3
0
0
0
1
0
0
3
0
2
3
1
0
0
3
0
1
1
2
0
5
3
0
6
1
1
1
44
1
0
0
1
1
1
0
3
0
0
1
3
0
1
1
0
0
1
0
0
1
5
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
3
0
1
0
5
1
0
1
3
1
1
0
1
0
0
0
2
1
0
5
2
2
0
3
2
0
0
0
1
1
0
0
0
0
3
1
0
0
1
1
0
0
1
2
2
0
2
2
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
3
3
0
0
2
1
0
1
2
2
2
0
2
1
0
1
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
3
3
1
1
0
4
0
1
3
3
0
2
0
4
0
0
1
0
0
2
2
4
2
0
2
0
1
0
1
0
1
0
5
0
3
0
1
1
3
1
0
3
1
3
0
0
1
3
2
0
0
3
1
1
0
0
2
1
0
1
1
5
1
4
2
0
0
2
3
2
0
0
1
4
2
1
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
2
1
1
0
1
2
0
0
2
2
0
3
1
0
0
1
0
1
0
3
1
1
5
0
2
0
1
2
0
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
1
0
3
0
0
2
0
1
0
2
0
2
1
0
4
0
0
1
0
2
1
1
2
4
0
0
6
0
1
0
0
2
2
0
1
1
1
0
1
0
0
7
1
3
1
3
3
1
0
2
1
5
2
0
4
1
0
2
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
1
0
0
3
1
0
3
0
3
0
2
0
0
0
2
3
2
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
1
0
3
1
0
0
0
1
1
1
0
0
5
3
3
1
1
5
1
1
1
1
2
1
0
0
1
0
1
0
0
0
1
2
3
0
0
2
0
3
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
3
0
4
0
0
5
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
3
5
4
0
0
2
0
3
3
9
1
1
0
0
2
0
2
0
2
0
0
0
0
2
5
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
4
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
5
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
153
0
3
0
0
0
4
1
1
2
0
2
0
1
1
0
0
3
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
1
0
2
2
1
5
0
0
1
6
0
0
0
1
3
5
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
5
1
0
4
0
0
0
0
0
3
0
0
0
3
2
0
0
0
2
1
3
0
5
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
3
1
1
2
0
0
0
0
2
1
1
2
2
0
0
1
3
2
0
1
1
0
0
1
0
1
0
0
4
1
2
0
0
60
0
2
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
1
0
4
1
1
0
0
0
2
0
1
0
0
0
0
3
0
1
0
3
5
1
1
0
3
0
3
0
0
0
0
0
1
1
2
1
0
4
2
0
0
0
2
0
1
1
0
0
0
0
0
3
1
1
4
0
1
5
3
0
0
0
1
0
0
0
0
0
1
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
5
1
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
3
2
4
0
4
0
3
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
5
2
0
0
0
2
1
1
0
1
2
0
0
1
4
0
0
1
0
2
1
1
0
1
0
3
0
0
1
2
2
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
2
3
2
0
1
0
0
0
2
0
0
3
0
0
1
1
0
2
4
2
2
0
0
1
0
1
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
3
0
0
3
1
3
0
0
0
1
0
0
0
2
1
1
1
2
1
0
0
3
0
1
14
1
2
0
0
3
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
2
3
0
0
0
0
1
0
0
2
1
0
3
1
0
0
0
1
1
3
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
1
1
0
0
6
1
1
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
2
0
0
1
0
0
3
4
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
1
2
1
4
1
0
0
0
3
2
0
0
1
1
0
0
1
4
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
4
0
0
0
3
0
1
1
1
0
2
2
3
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
1
0
3
0
0
2
1
2
1
2
3
4
3
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
1
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
4
3
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
5
0
3
1
0
1
0
2
0
1
0
0
0
1
1
2
0
2
0
0
1
2
1
1
1
3
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
4
1
0
0
0
1
1
2
0
0
0
1
0
2
1
0
1
1
2
3
0
0
0
0
1
2
1
2
1
0
1
1
1
1
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
1
0
3
2
0
2
0
0
0
1
0
2
2
0
0
1
1
1
1
2
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
3
0
0
0
0
4
2
1
1
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
3
1
1
0
0
0
1
0
0
0
0
0
8
1
2
3
1
2
0
1
1
0
3
0
0
0
0
1
0
0
3
0
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
3
0
2
1
0
1
2
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
3
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
2
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
2
1
0
3
1
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
4
3
2
0
0
0
1
1
0
2
0
1
1
4
1
0
0
1
1
0
1
5
0
1
3
0
0
0
6
2
0
1
0
2
2
0
1
0
0
1
3
0
1
1
1
2
1
0
1
1
0
1
0
2
0
0
3
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
1
1
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
4
0
1
0
0
0
4
1
1
0
0
2
0
2
0
1
2
4
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
1
1
1
2
2
0
0
1
1
2
1
1
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
3
1
1
0
0
2
0
1
0
1
58
0
3
0
1
0
0
2
1
2
3
3
0
0
0
0
0
2
0
7
0
0
2
0
0
0
0
0
2
0
0
1
4
0
0
2
1
1
0
1
0
1
0
2
3
2
1
0
0
3
3
0
1
0
0
0
1
1
1
3
0
0
0
0
1
2
0
1
0
0
2
0
4
0
4
0
1
0
1
0
1
0
0
1
1
0
3
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
1
2
0
0
1
1
1
0
3
0
0
1
1
0
1
3
0
6
1
3
0
0
0
0
3
0
2
2
0
1
0
3
1
1
1
0
0
0
0
0
1
7
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
1
1
0
2
2
1
1
2
2
1
0
0
1
4
0
0
0
0
2
4
0
0
0
2
0
3
0
2
0
0
0
0
0
1
1
1
3
0
2
0
0
1
1
0
1
0
0
1
1
9
1
1
0
6
2
0
0
0
1
12
0
6
0
0
3
0
0
0
2
0
0
0
0
0
4
1
0
0
0
1
7
4
0
1
1
3
2
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
1
0
0
2
1
0
3
0
1
0
1
0
0
1
24
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
2
856
0
1
1
1
1
0
0
0
0
3
2
4
2
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
3
0
0
1
0
0
3
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
3
1
0
3
2
0
0
0
0
0
0
1
2
1
10
0
1
1
2
4
1
0
3
0
3
0
0
0
0
1
3
0
9
3
7
0
1
2
0
1
0
1
5
4
0
2
2
0
0
0
0
0
0
0
3
1
1
0
1
1
0
1
0
0
0
1
8
1
0
0
1
1
2
1
3
1
1
0
3
1
1
0
13
0
0
0
0
0
3
1
0
4
1
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
7
1
4
0
1
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
5
1
0
0
1
0
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
1
0
0
3
2
2
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
1
0
0
1
1
2
0
3
1
2
0
0
1
0
0
1
1
1
0
0
0
1
2
3
0
0
1
1
0
0
1
3
2
2
1
0
2
0
1
2
2
2
1
1
0
5
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
3
0
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
4
1
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
1
0
1
0
7
2
0
0
0
4
2
2
0
0
0
0
0
0
1
0
4
1
1
0
2
2
1
1
1
0
0
0
0
1
4
0
1
0
0
1
3
0
2
2
1
0
0
0
1
1
2
0
4
2
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
2
1
4
2
1
0
0
2
0
2
4
0
0
3
0
2
2
1
4
0
1
0
0
2
1
0
2
1
0
4
0
0
1
0
0
2
1
2
4
0
1
1
0
4
4
0
0
1
0
3
1
0
2
1
0
2
1
2
0
1
0
1
1
0
1
4
1
0
0
1
0
1
1
1
0
2
0
3
0
2
4
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
4
5
1
2
1
0
0
3
2
0
0
0
6
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
2
0
0
1
0
3
0
4
0
0
2
0
1
0
2
0
0
1
2
0
1
1
1
0
0
1
0
1
2
2
2
5
0
0
0
0
5
0
0
0
0
2
5
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
3
0
2
1
5
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
3
0
1
0
4
1
1
1
2
0
2
1
2
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
4
3
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
0
4
2
0
2
0
4
0
0
0
0
0
1
5
0
1
0
1
1
6
0
3
0
2
0
0
4
0
2
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
0
1
0
3
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
0
3
1
0
1
2
0
0
6
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
2
0
1
0
1
0
4
5
0
1
0
2
0
0
0
1
2
5
0
0
0
1
2
1
0
5
1
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
4
0
0
0
2
1
1
0
0
0
1
0
0
1
2
4
2
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
17
0
3
1
0
2
1
0
1
3
0
2
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
1
2
0
1
0
3
1
0
1
2
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
12
1
1
0
0
0
0
4
0
1
1
1
0
0
1
2
0
0
1
0
1
0
0
1
0
3
2
1
1
4
0
0
0
0
0
0
5
1
0
1
0
1
0
1
0
4
0
6
0
3
1
1
0
1
0
0
1
1
2
0
0
3
0
0
0
1
0
0
1
1
0
0
2
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
12
0
3
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
3
1
2
2
11
2
0
0
3
1
0
1
5
1
0
1
1
0
1
1
0
0
0
2
0
1
5
0
0
1
0
1
0
0
0
0
0
1
0
3
0
2
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
2
2
1
0
0
3
1
3
0
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
1
0
1
2
0
1
0
0
0
14
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
4
0
0
0
0
1
1
1
0
1
0
3
2
2
0
3
0
1
0
0
1
0
2
0
3
0
1
0
1
0
2
0
3
2
0
2
2
3
0
0
1
0
1
0
0
3
1
0
3
3
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
5
0
0
1
0
1
0
4
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
4
1
0
1
0
1
3
0
0
0
0
1
1
0
1
0
1
1
0
2
0
3
0
3
2
0
0
1
1
2
1
0
0
0
1
5
0
0
0
0
1
1
2
0
1
0
1
1
0
3
0
0
0
1
1
0
1
0
2
0
3
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
1
0
0
1
1
0
2
1
1
2
1
2
0
5
0
0
1
2
0
1
0
1
0
2
0
0
1
0
3
0
0
0
2
0
3
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
3
1
0
1
1
1
2
0
0
2
2
0
2
0
3
0
2
0
6
0
1
2
1
0
2
0
1
1
4
2
1
0
1
3
0
0
0
2
1
0
2
2
2
1
0
1
0
1
0
0
11
0
0
2
3
0
0
1
0
0
0
0
2
0
3
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
2
0
2
1
0
2
2
2
1
3
12
1
0
0
2
2
1
5
0
0
0
0
0
0
0
3
0
1
1
0
1
0
2
0
0
1
0
1
1
1
1
0
2
1
3
1
0
1
0
0
2
0
0
0
3
0
1
1
0
0
1
1
1
5
1
0
0
0
1
1
2
1
0
0
3
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
11
2
1
1
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
6
0
1
2
0
1
1
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
1
5
0
0
1
3
1
0
0
1
0
0
2
0
0
1
2
5
0
0
0
0
0
3
0
2
0
0
6
1
2
0
1
0
0
0
1
2
2
1
0
0
2
2
1
0
3
0
0
0
2
0
0
5
0
1
0
1
0
0
1
1
3
1
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
2
1
0
2
0
0
6
0
3
0
1
3
0
0
1
0
2
0
0
0
1
3
0
0
0
0
4
0
0
0
0
1
6
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
3
1
4
0
1
0
1
0
0
0
2
2
4
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
5
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
1
2
0
0
3
1
1
4
0
0
0
0
0
0
0
0
1
4
2
1
0
1
1
0
1
2
0
0
4
0
0
3
0
0
0
2
1
0
1
0
5
0
1
2
0
2
2
3
0
1
0
1
0
0
2
0
2
0
1
1
0
2
6
0
0
2
3
0
1
1
3
1
2
1
0
0
0
0
2
1
0
4
1
0
0
0
3
0
0
1
1
1
3
1
1
2
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
2
0
0
4
0
3
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
1
0
2
1
4
2
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
0
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
1
2
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
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
4
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
3
7
2
0
1
1
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
2
0
5
0
0
0
0
2
1
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
4
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
1
1
0
0
1
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
3
5
0
0
0
2
2
0
0
0
2
0
1
1
1
2
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
5
1
0
3
0
1
1
0
1
0
0
1
0
0
0
3
0
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
2
1
3
2
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
5
1
1
3
2
3
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
3
2
1
2
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
3
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
1
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
2
1
4
0
1
0
4
3
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
1
1
1
0
1
0
0
3
5
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
1
3
3
1
4
4
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
1
5
1
2
0
0
3
0
0
1
1
1
0
0
0
2
0
5
0
1
2
0
1
2
1
0
0
0
2
0
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
3
1
0
2
2
1
0
0
2
0
2
1
0
0
1
0
3
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
1
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
1
0
1
3
0
1
2
4
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
4
2
0
0
1
0
0
1
0
3
0
1
3
0
0
3
1
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
4
0
0
2
0
1
2
0
3
1
1
3
0
0
0
0
2
2
2
1
1
1
0
1
0
0
0
0
2
0
1
1
0
3
2
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
1
1
1
1
0
2
1
1
0
2
5
1
0
1
0
0
0
0
1
3
3
1
0
0
0
2
3
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
4
0
1
2
0
1
0
0
0
0
1
0
0
0
4
1
1
0
0
1
1
0
0
0
0
0
0
0
0
3
3
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
2
2
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
1
2
0
1
1
4
1
0
1
2
0
0
2
0
0
1
0
0
0
3
0
1
1
0
3
1
1
0
0
1
1
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
3
2
1
5
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
1
3
2
1
4
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
3
5
1
0
0
1
2
0
1
0
2
3
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
4
1
3
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
3
2
0
0
0
0
2
1
0
0
1
0
1
3
0
0
2
1
0
1
3
0
0
2
1
0
1
0
3
0
1
0
0
0
0
1
1
2
1
1
1
6
1
1
1
3
3
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
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
0
0
0
1
0
1
1
0
1
0
0
0
5
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
3
0
0
0
1
0
2
1
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
0
3
1
0
0
0
0
1
3
0
1
1
0
1
1
2
0
0
1
1
1
0
0
0
2
0
4
0
0
0
1
4
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
2
3
0
0
0
1
2
1
1
1
1
0
3
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
2
0
1
0
1
1
0
1
0
1
0
2
0
0
2
5
3
0
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
2
0
3
0
0
0
0
2
1
1
0
1
2
0
2
1
2
2
1
0
0
0
0
2
4
0
1
2
1
1
1
1
2
3
0
0
1
0
2
3
0
1
1
0
0
4
0
1
0
0
0
1
0
0
0
1
0
6
2
2
0
4
2
2
0
3
1
0
1
3
0
1
0
0
0
2
0
0
0
2
0
5
2
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
5
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
1
0
5
1
1
1
0
0
8
2
0
1
1
6
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
1
2
1
0
0
0
3
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
4
1
0
2
0
1
0
1
0
1
0
3
0
0
1
0
0
1
0
1
2
0
2
1
1
0
0
0
1
1
0
5
0
1
0
2
1
2
0
2
0
1
0
0
1
1
1
0
3
1
1
1
2
0
0
0
4
1
2
1
2
0
5
0
0
0
0
0
0
0
1
0
0
3
1
2
1
1
0
0
2
0
0
3
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
2
0
0
104
0
1
0
9
0
1
13
2
0
1
2
0
0
0
0
0
0
0
0
2
1
1
6
2
2
0
1
0
0
1
2
1
0
0
0
0
4
3
0
0
1
2
0
0
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
1
3
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
7
1
0
0
0
0
2
0
0
0
2
1
5
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
2
2
1
0
0
0
3
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
0
2
0
0
0
1
4
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
2
3
1
1
0
2
0
1
0
0
2
4
0
0
0
4
0
1
0
0
1
0
0
1
4
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
2
3
0
0
1
1
3
4
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
1
2
0
1
0
1
2
1
1
2
1
0
0
1
0
1
3
2
0
1
0
0
0
0
0
3
1
8
0
0
2
0
0
0
0
1
0
0
7
0
0
4
0
50
1
1
1
0
2
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
3
0
0
1
1
2
0
0
5
1
0
0
0
0
5
2
0
3
0
0
1
1
0
0
33
1
2
0
0
0
1
2
2
1
1
0
0
0
1
3
1
2
0
0
1
0
1
1
1
3
1
3
1
0
1
3
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
3
0
0
0
3
2
0
1
1
1
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
3
0
4
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
1
0
1
0
1
0
1
0
2
2
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
3
0
2
2
1
1
0
2
1
1
1
0
1
2
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
1
1
2
0
0
1
0
0
2
0
0
3
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
1
1
3
1
4
1
1
2
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
5
0
0
2
0
1
2
3
3
2
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
39
0
1
0
0
0
4
0
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
3
3
1
1
1
0
1
1
0
3
0
0
4
0
0
0
1
1
0
0
2
2
0
2
0
1
0
1
1
0
2
1
2
3
0
0
1
0
1
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
8
0
0
1
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
4
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
6
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
5
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
1
1
0
1
2
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
2
0
0
1
1
1
0
1
0
1
0
0
2
2
0
0
2
3
0
0
0
0
1
1
0
3
1
0
2
1
2
1
0
4
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
4
0
2
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
4
4
3
1
2
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
2
1
0
0
2
2
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
2
2
0
0
3
0
0
4
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
3
2
3
1
1
0
0
0
1
1
0
0
2
0
0
2
2
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
1
3
0
3
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
3
3
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
2
2
1
0
0
1
2
0
1
0
1
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
4
2
0
1
2
1
1
0
2
3
0
1
2
1
0
0
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
2
0
2
5
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
4
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
1
3
0
3
1
1
1
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
2
0
1
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
2
1
0
1
2
0
0
0
1
1
3
1
0
3
0
0
0
2
1
38
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
1
2
3
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
4
0
1
0
12
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
3
0
0
0
3
1
0
0
0
1
1
1
0
1
1
0
0
3
0
1
2
0
0
0
0
3
0
1
1
1
0
0
0
0
5
1
0
2
1
1
2
1
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
4
0
0
1
1
0
2
0
0
0
0
4
1
0
4
0
0
0
0
0
0
3
1
0
3
0
2
2
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
2
2
1
0
0
1
0
0
0
7
0
2
0
0
1
2
0
0
0
0
2
0
1
1
1
4
0
0
0
0
3
0
0
3
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
2
1
1
0
5
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
181
2
5
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
4
1
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
1
1
4
0
2
8
1
0
0
2
0
1
0
1
1
1
0
0
2
2
0
2
1
0
34
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
1
1
0
1
0
4
0
2
2
1
0
1
1
0
0
0
1
0
0
4
0
4
0
0
0
2
0
3
0
1
1
0
0
2
2
2
0
2
0
0
0
4
0
1
0
1
1
0
0
1
10
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
1
0
2
0
0
0
2
1
2
1
1
1
1
1
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
2
1
4
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
3
1
1
1
0
1
0
0
0
2
4
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
3
0
0
0
1
1
0
0
1
1
3
1
1
0
0
2
1
2
0
1
1
0
0
0
6
1
0
1
1
2
1
0
2
0
0
0
4
2
72
0
0
37
0
1
0
1
0
2
0
0
5
0
0
0
3
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
38
0
3
0
1
2
1
0
0
0
1
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
4
1
279
1
1
0
2
0
0
0
0
0
0
1
1
1
0
3
1
1
0
2
0
1
1
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
3
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
1
1
0
0
1
0
1
4
2
1
1
0
1
0
0
1
3
1
0
3
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
30
2
0
1
0
0
0
0
0
3
0
1
0
0
0
2
4
1
0
3
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
30
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
4
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
1
1
3
0
1
1
2
0
0
0
6
0
2
1
0
0
0
0
1
1
0
3
20
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
1
0
2
1
1
3
1
0
0
3
0
1
2
0
0
1
0
1
2
1
0
0
0
0
2
0
3
0
3
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
3
8
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
1
3
1
1
0
1
1
0
1
0
0
1
0
4
1
2
0
0
0
4
0
0
1
0
1
0
0
5
1
0
0
0
0
0
5
0
0
0
0
1
0
3
0
0
0
1
4
0
4
0
0
0
0
1
0
1
1
1
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
3
1
0
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
0
0
1
0
1
1
0
2
0
3
2
1
1
0
0
1
1
0
1
1
0
0
0
1
1
2
0
0
2
0
1
0
2
2
0
2
4
0
1
0
0
3
0
1
2
0
0
1
1
1
0
1
0
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
1
1
1
1
0
2
0
0
0
4
0
0
1
1
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
1
3
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
1
0
5
0
1
0
3
0
1
1
0
2
0
0
0
1
3
1
1
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
2
9
1
1
5
0
1
3
1
0
1
0
0
0
7
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
3
1
0
1
0
0
0
3
1
0
0
1
0
1
0
0
0
1
0
1
3
0
5
0
1
0
0
1
0
0
2
4
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
2
3
0
0
1
0
1
1
0
2
2
0
2
0
0
1
0
3
1
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
4
1
0
0
0
3
0
2
0
0
3
0
1
0
1
3
0
0
0
2
3
1
3
1
0
1
0
0
4
0
0
0
2
1
1
0
0
2
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
2
0
0
4
4
1
3
0
1
0
0
3
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
3
5
1
0
1
0
1
3
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
0
1
0
1
0
1
0
2
4
4
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
3
0
1
3
1
0
1
0
3
4
2
1
1
0
0
0
5
0
1
3
0
2
1
1
2
0
1
3
0
0
0
1
0
0
0
0
3
1
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
1
3
0
0
1
2
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
4
2
0
5
2
0
1
1
0
0
0
1
0
1
0
0
2
3
3
0
0
1
1
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
7
3
3
1
0
1
0
0
0
0
3
0
1
1
0
0
0
2
0
1
1
1
1
0
1
0
1
0
1
1
2
1
2
1
0
0
3
0
0
0
2
1
0
1
4
3
1
0
0
0
0
0
1
0
0
3
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
2
1
4
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
1
1
0
1
2
2
0
2
0
0
0
4
1
0
0
0
0
0
0
3
0
0
3
0
0
0
2
1
0
0
1
0
4
3
2
1
0
0
0
0
0
20
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
1
1
0
0
2
0
0
0
0
1
2
2
1
2
0
1
1
0
0
0
1
2
2
1
0
0
2
5
0
1
1
0
1
0
4
0
0
0
0
0
0
2
1
3
2
2
0
1
0
1
1
2
0
1
2
0
0
1
0
0
1
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
1
2
0
0
1
2
1
0
0
1
0
1
0
1
0
2
2
2
1
1
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
1
2
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
2
0
3
1
2
3
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
1
2
1
1
0
0
2
0
2
0
1
1
2
1
0
0
0
3
0
0
0
3
0
0
1
0
0
0
2
4
2
1
1
0
0
0
1
2
0
0
0
0
4
2
0
3
0
0
0
1
0
0
1
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
1
0
1
0
1
1
40
0
1
0
3
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
0
1
2
0
1
0
4
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
1
0
1
2
1
1
2
1
4
0
0
1
2
2
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
272
2
0
0
2
0
0
1
0
0
2
1
2
0
0
1
4
0
1
0
0
0
0
0
0
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
0
1
4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
0
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
2
0
0
2
3
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
5
0
0
1
2
1
0
0
7
1
1
1
0
1
0
1
0
2
0
0
0
0
3
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
1
1
0
2
1
0
4
0
1
1
0
0
1
3
0
2
0
1
0
2
2
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
4
0
3
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
3
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
2
2
3
0
3
0
0
1
1
1
0
0
3
3
0
0
0
0
0
1
3
0
1
0
0
1
2
3
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
3
4
1
1
1
0
1
4
2
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
5
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
3
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
3
4
0
0
0
1
0
2
3
1
1
1
0
0
1
1
0
0
1
2
5
0
0
0
0
0
0
0
3
1
1
2
0
1
0
1
0
0
2
2
0
0
1
3
3
0
1
1
0
0
1
1
1
1
1
2
3
0
0
0
7
2
1
4
1
2
1
0
1
1
0
1
0
0
0
0
1
3
0
1
1
2
0
0
2
0
1
4
0
1
1
0
2
0
1
0
0
1
0
0
3
1
0
0
0
0
3
0
0
1
1
1
0
4
1
4
0
1
1
7
1
0
0
2
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
6
0
1
0
1
0
2
1
1
1
1
0
2
1
2
0
0
0
6
2
1
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
3
3
0
0
3
2
0
6
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
5
1
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
2
5
1
0
2
1
0
1
2
0
1
0
1
0
0
0
0
1
0
27
1
0
0
0
0
1
2
2
0
0
0
0
0
2
3
1
2
3
2
0
1
0
0
0
3
1
0
1
1
3
1
1
3
2
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
21
0
0
0
1
2
0
0
6
2
1
0
0
0
0
4
0
1
1
3
3
0
1
1
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
1
0
0
9
2
1
0
0
0
1
0
0
0
0
0
1
3
1
3
1
0
2
0
1
1
1
0
3
1
0
4
3
0
1
1
0
1
0
1
0
2
0
1
1
0
0
3
0
0
3
0
0
0
0
2
1
1
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
0
3
2
1
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
4
0
1
0
0
1
3
1
0
0
0
1
0
0
1
0
0
0
0
2
0
4
1
3
0
0
0
0
0
0
2
3
1
2
1
0
2
0
0
1
1
0
1
2
2
1
0
2
0
1
0
1
0
2
0
1
0
0
250
1
0
0
0
0
0
3
0
0
0
0
0
2
0
3
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
0
1
0
0
0
0
4
3
0
0
0
2
0
1
0
2
0
1
0
1
1
1
2
5
0
1
1
0
0
1
1
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
3
1
1
0
0
2
1
0
5
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
5
0
1
0
0
4
1
1
1
0
0
0
2
1
0
0
1
0
2
0
2
6
4
1
1
0
1
0
0
5
0
0
1
2
1
1
1
2
2
1
0
0
1
0
3
0
1
1
0
1
1
1
0
0
3
0
0
1
1
0
0
0
3
0
0
1
0
0
3
0
1
0
0
1
3
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
4
1
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
2
0
1
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
31
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
5
0
1
2
0
2
0
0
3
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
1
1
3
0
0
0
9
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
4
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
3
0
0
5
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
4
1
0
0
0
0
0
0
0
3
0
0
1
0
3
0
1
6
0
1
1
3
0
1
1
1
0
0
21
0
1
1
1
1
0
0
0
1
3
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
4
0
1
21
1
0
0
0
1
1
1
0
2
0
2
0
0
2
4
1
1
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
5
2
3
1
0
0
0
0
0
0
5
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
1
6
0
2
0
1
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
4
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
3
1
1
1
4
1
0
3
3
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
2
0
0
1
1
2
3
0
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
2
0
0
1
3
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
4
0
0
1
5
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
1
1
0
0
3
0
0
1
0
2
0
2
1
0
0
1
1
0
0
1
0
1
0
0
2
2
1
2
0
0
0
1
0
0
0
1
0
1
1
4
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
4
2
0
0
0
2
1
0
0
1
1
2
0
2
0
1
1
0
2
2
1
0
0
1
1
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
1
5
0
1
0
0
0
0
3
0
0
1
6
0
0
0
1
0
0
0
0
1
2
0
2
0
1
33
1
0
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
5
2
0
1
1
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
1
0
3
0
1
1
1
2
1
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
3
0
0
0
1
2
0
0
2
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
2
1
0
4
1
0
0
0
0
0
0
1
0
5
1
2
0
1
0
0
2
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
18
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
1
2
0
3
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
9
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
1
4
2
0
4
1
0
0
1
3
0
0
0
1
1
4
3
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
4
0
1
2
0
3
0
0
0
1
3
0
1
2
0
0
1
0
0
2
0
1
1
1
2
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
4
0
1
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
1
1
2
3
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
1
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
3
0
0
1
3
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
1
0
2
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
8
0
0
0
1
0
0
1
2
1
0
0
1
2
2
1
0
0
1
1
0
1
2
1
2
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
5
1
2
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
3
0
2
0
1
0
0
5
14
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
6
2
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
1
1
0
2
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
3
0
0
0
0
0
6
0
1
0
1
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
1
1
0
2
1
0
0
1
3
0
0
0
0
2
1
3
1
1
0
0
0
4
3
1
0
0
4
0
0
0
0
1
0
1
1
1
1
0
0
3
0
0
2
2
0
1
0
0
0
0
1
0
0
1
3
0
1
0
1
2
1
0
1
0
3
0
1
3
0
0
1
0
0
1
0
0
1
1
1
0
1
0
2
2
0
0
0
0
1
2
1
1
3
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
3
0
0
2
1
0
0
0
1
0
2
2
0
4
0
1
0
0
1
0
0
0
1
2
1
0
1
2
0
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
3
3
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
7
2
0
1
0
1
0
2
0
2
0
2
0
2
0
0
1
1
2
0
1
4
0
2
1
2
1
0
3
2
1
2
1
0
1
0
0
0
0
1
3
4
0
1
1
0
1
0
0
0
2
0
1
0
3
0
1
0
1
0
0
0
0
0
0
1
4
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
7
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
1
0
3
2
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
4
1
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
4
0
0
0
0
3
3
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
3
0
0
2
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
13
1
0
0
0
3
0
0
3
0
0
4
0
0
2
2
3
0
2
2
0
3
0
0
1
0
1
5
1
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
4
1
1
1
0
3
0
0
1
1
0
1
0
0
0
1
2
3
1
0
2
1
0
2
1
0
35
1
3
0
4
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
0
1
5
0
1
0
3
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
4
1
0
4
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
4
1
0
0
0
10
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
1
1
0
0
2
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
3
0
3
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
4
4
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
121
0
0
1
0
0
0
5
3
0
2
0
0
0
1
1
0
0
1
0
2
3
0
0
0
5
2
3
2
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
1
5
0
2
1
0
0
1
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
36
1
1
7
2
0
0
1
0
3
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
4
0
0
1
0
0
1
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
3
1
0
0
0
1
1
2
0
1
0
1
0
2
0
3
2
0
1
0
3
1
0
0
0
1
2
2
0
0
3
2
1
2
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
0
0
2
0
3
1
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
3
5
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
70
0
0
0
0
0
0
3
1
0
2
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
1
2
0
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
2
1
1
2
1
0
0
5
0
2
0
0
2
1
0
0
0
5
4
1
1
0
1
0
0
0
1
7
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
0
0
0
41
0
2
0
1
0
0
2
1
1
1
0
1
0
0
1
0
1
2
1
2
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
3
0
0
0
0
0
3
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
4
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
1
1
3
2
3
3
1
0
2
0
0
1
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
1
1
2
1
3
2
2
1
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
1
0
4
0
0
1
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
0
0
0
1
2
0
1
1
1
0
1
1
0
0
2
4
2
1
0
0
0
0
1
2
0
1
1
1
2
1
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
1
0
0
3
0
1
3
0
0
4
2
1
0
1
1
0
0
2
1
1
0
6
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
3
0
1
0
0
1
4
16
0
0
1
0
1
0
3
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
1
0
1
2
2
0
3
0
0
1
2
0
1
0
0
6
3
0
2
0
0
1
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
13
0
0
1
1
1
1
2
0
2
1
3
1
2
0
1
2
2
0
0
0
1
2
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
5
0
1
1
0
2
1
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
0
0
0
4
0
0
0
2
1
3
0
2
1
1
1
0
0
0
1
1
1
0
0
3
1
0
1
1
0
0
0
3
1
0
1
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
1
4
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
3
0
1
1
0
0
0
1
1
1
2
1
1
0
0
0
2
0
0
0
2
0
2
1
3
0
0
0
0
0
1
1
0
0
0
0
41
2
1
0
1
0
2
0
1
2
1
3
1
1
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
4
0
1
3
0
0
1
0
0
0
0
0
0
1
2
7
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
2
0
2
1
2
1
2
0
0
1
0
1
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
11
2
0
1
3
0
1
0
0
0
0
0
2
0
0
0
1
6
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
5
1
1
0
2
3
0
1
1
0
0
2
2
2
2
0
0
0
1
0
0
0
1
2
2
1
2
0
1
0
3
2
3
0
0
0
0
1
0
1
0
2
1
0
3
0
3
2
0
0
0
2
0
2
0
0
1
0
0
3
1
3
0
2
1
0
0
0
3
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
5
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
2
0
3
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
1
1
0
1
0
1
0
2
2
1
0
1
1
1
0
1
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
2
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
3
2
0
0
2
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
3
0
1
3
0
0
0
0
0
0
1
1
0
5
2
3
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
1
1
3
0
1
2
0
0
0
1
1
0
1
3
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
6
1
2
0
1
0
0
1
0
1
2
2
0
0
2
0
0
1
2
3
0
0
2
3
0
0
3
1
1
1
0
0
3
1
0
0
4
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
1
2
0
3
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
2
0
1
0
5
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
1
1
1
0
0
1
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
7
2
0
3
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
3
2
0
0
0
0
3
0
1
1
4
2
0
2
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
1
0
0
1
0
1
2
0
0
0
0
1
2
1
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
2
1
0
1
0
1
1
1
0
0
0
0
3
0
1
3
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
3
2
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
4
0
1
0
1
5
1
0
0
0
2
1
0
0
3
0
0
3
0
2
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
0
1
1
1
0
0
0
1
3
0
0
1
1
0
4
0
1
0
0
1
0
1
1
6
0
0
1
2
0
0
1
2
0
0
1
0
3
0
0
0
1
0
3
0
4
3
0
0
3
0
2
0
0
0
0
0
1
0
5
2
0
0
1
1
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
5
0
0
0
0
2
1
3
2
0
0
1
1
0
2
0
0
1
3
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
0
2
0
1
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
2
1
1
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
2
0
0
2
2
1
1
1
0
3
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
2
2
1
0
1
1
2
0
3
0
0
10
0
3
0
1
0
2
1
1
0
1
0
0
1
1
0
0
0
4
0
3
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
2
0
2
3
0
1
0
1
1
2
0
0
0
1
0
4
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
1
0
2
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
7
1
0
1
5
1
0
0
4
1
0
2
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
3
2
0
3
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
2
2
0
4
0
0
2
0
0
0
2
1
0
1
1
0
0
2
1
0
2
0
0
1
0
2
0
3
0
0
4
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
3
3
0
0
2
0
1
1
0
1
1
0
1
0
1
0
3
0
1
0
1
0
2
0
0
1
2
2
1
3
1
0
0
3
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
3
1
0
1
0
3
0
0
1
0
0
0
1
1
0
0
2
2
1
4
2
7
2
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
1
2
2
0
2
1
0
1
0
1
1
1
1
0
0
0
2
0
4
1
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
1
1
1
0
3
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
1
0
0
2
1
1
0
1
1
0
0
2
0
0
9
3
2
0
0
2
0
0
0
2
6
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
1
9
0
2
0
1
0
1
0
0
0
1
3
1
1
3
0
3
0
1
1
0
0
1
1
0
0
1
1
1
3
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
2
2
0
1
2
0
1
2
0
1
1
5
0
1
1
0
0
2
1
0
0
0
2
1
0
1
1
2
1
0
1
0
0
0
1
1
1
1
4
0
0
0
0
0
3
1
0
1
3
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
3
0
1
1
3
0
0
1
0
4
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
3
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
1
0
1
0
0
5
5
1
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
3
5
1
0
0
0
0
0
0
5
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
3
1
1
2
2
0
1
0
0
1
0
0
0
2
0
0
0
4
0
1
1
0
0
0
1
1
2
0
3
0
0
1
1
4
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
3
0
1
1
1
0
5
0
0
1
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
2
3
4
3
0
2
1
0
1
2
0
6
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
1
2
0
1
0
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
1
2
0
1
0
0
2
0
1
1
0
0
0
1
2
0
1
2
0
0
1
0
7
0
0
1
3
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
0
3
0
2
1
1
0
0
0
0
1
0
0
3
0
0
3
1
0
0
1
0
0
0
1
0
3
3
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
1
6
0
1
0
0
2
1
1
0
0
3
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
2
1
0
0
0
3
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
3
8
0
1
0
3
0
0
1
13
0
0
2
1
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
77
1
4
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
2
1
0
3
0
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
5
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
4
0
3
4
0
1
3
1
1
1
1
0
4
0
0
0
0
0
4
0
1
0
1
0
1
1
0
1
1
2
0
1
0
0
0
6
0
0
1
0
0
1
0
1
0
3
182
0
1
0
2
1
0
0
0
0
0
1
0
1
2
1
1
0
2
1
3
0
0
1
0
0
0
1
2
0
0
0
2
1
2
1
0
0
9
0
2
1
0
2
1
0
0
1
0
2
0
2
2
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
4
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
1
2
0
1
0
0
0
3
0
0
1
4
0
2
0
0
2
0
5
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
3
1
1
0
1
1
1
5
1
0
6
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
4
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1970
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
0
2
0
1
2
3
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
7
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
1
0
0
3
0
0
1
0
2
15
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
2
1
1
0
3
0
1
0
1
1
1
0
0
0
0
1
1
1
2
0
1
0
1
0
4
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
1
0
1
2
3
0
1
0
8
1
0
0
0
1
3
0
0
1
2
0
2
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
5
1
6
0
6
0
5
0
1
0
2
0
3
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
1
0
0
0
0
1
1
1
1
0
0
2
0
0
7
0
3
2
1
0
1
0
1
7
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
5
0
8
0
1
1
0
0
0
0
0
2
0
3
0
0
0
3
0
0
1
0
0
1
5
0
0
3
0
2
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
3
0
0
1
0
0
0
0
3
8
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
1
1
0
4
0
0
0
1
0
0
1
0
0
1
10
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
2
0
0
0
5
0
0
3
0
0
1
3
1
1
0
0
0
2
0
0
0
0
2
0
2
5
3
1
3
0
3
4
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
3
1
164
1
0
0
0
0
1
2
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
0
1
0
0
2
0
1
1
0
0
0
4
0
0
0
0
1
1
0
4
2
1
0
1
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
1
3
1
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
2
1
0
0
3
0
0
0
1
0
0
0
13
0
1
0
0
0
0
3
1
0
0
1
0
12
2
0
2
0
0
1
1
2
2
3
0
0
2
0
1
1
1
6
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
3
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
2
1
0
0
0
42
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
7
0
0
4
2
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
3
1
1
1
1
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
5
0
2
1
0
3
0
0
1
0
1
0
0
2
1
0
1
0
0
3
1
0
2
0
2
0
0
3
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
0
6
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
3
1
2
1
0
1
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
2
12
1
6
0
1
0
0
0
0
1
1
0
0
0
0
4
1
1
0
1
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
2
9
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
3
0
0
1
9
1
0
1
0
0
1
0
6
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
6
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
4
2
0
1
2
0
1
0
0
0
3
0
1
2
3
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
5
1
1
0
1
1
0
0
1
0
0
3
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
4
0
0
0
0
0
3
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
1
2
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
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
1
4
0
0
1
0
1
8
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
3
1
0
0
0
1
0
2
1
0
0
2
1
1
0
2
1
1
5
0
1
1
2
1
1
1
3
0
0
0
1
2
1
0
5
1
1
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
6
0
0
1
1
3
0
0
0
0
0
1
0
2
0
2
0
3
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
1
4
1
0
28
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
1
1
0
8
0
0
1
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
1
1
0
10
1
0
0
0
2
0
0
1
1
1
3
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
2
0
0
0
2
0
1
1
0
1
1
0
0
4
3
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
0
1
1
0
0
4
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
2
0
0
1
0
1
1
0
0
2
2
1
5
1
1
0
1
0
4
0
1
1
0
3
0
0
2
2
1
1
6
3
1
1
2
3
0
2
0
1
0
0
0
0
0
1
1
3
1
4
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
3
1
0
0
1
0
1
1
1
1
2
0
0
0
4
1
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
1
1
0
2
1
1
0
0
0
0
1
0
0
5
0
1
0
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
2
2
0
0
0
1
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
0
0
0
6
0
0
1
0
1
0
1
1
0
3
4
1
1
1
2
5
0
0
0
0
7
0
0
0
0
1
1
0
0
6
0
1
1
2
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
1
1
0
0
0
1
2
0
0
0
1
0
0
0
3
2
0
1
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
2
1
1
1
3
1
0
0
0
0
1
0
3
0
1
0
1
2
3
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
3
1
1
2
0
0
0
1
2
5
1
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
3
0
2
1
0
0
0
1
3
0
0
0
1
0
1
3
0
1
0
2
1
1
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
1
0
1
0
0
3
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
1
1
1
0
2
2
0
0
0
0
0
0
3
0
2
1
4
0
1
1
0
0
0
3
2
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
2
1
0
3
0
0
1
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
3
1
3
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
2
0
0
1
0
1
0
1
1
1
3
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
1
3
5
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
3
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
3
0
0
0
2
3
1
0
1
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
3
1
0
1
0
2
1
0
1
1
0
0
11
0
0
0
0
2
0
1
2
0
0
0
1
0
1
2
2
5
1
0
1
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
6
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
3
0
1
1
3
0
1
1
0
0
0
0
0
5
0
2
1
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
3
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
3
4
1
1
0
0
0
0
1
4
0
1
4
1
1
5
1
3
0
1
1
1
0
0
0
0
0
1
6
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
3
1
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
7
0
0
0
0
0
2
1
1
2
1
0
1
1
1
0
0
0
0
1
1
1
0
6
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
3
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
9
3
0
0
0
1
1
1
1
0
1
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
39
2
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
2
5
0
0
0
0
4
2
0
0
0
2
5
0
0
0
1
4
1
0
1
5
0
0
0
1
0
0
1
1
4
2
0
1
2
2
0
1
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
1
2
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
1
0
0
0
0
1
3
0
0
0
1
0
1
0
9
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
1
2
2
1595
1
0
1
8
0
1
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
3
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
5
0
1
0
0
0
0
0
0
3
0
1
0
0
4
1
0
1
0
3
0
0
8
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
3
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
7
0
2
1
2
1
9
0
1
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
1
1
0
1
1
0
0
1
1
0
0
1
0
1
2
0
1
1
0
3
2
3
1
2
1
0
1
0
2
1
1
8
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
7
0
0
0
0
0
0
1
0
1
8
1
0
1
0
0
1
1
0
1
0
0
2
1
0
0
3
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
3
1
1
1
0
2
0
2
0
0
0
1
3
0
3
0
0
2
0
1
0
2
1
3
2
0
0
0
0
1
0
3
1
0
0
3
1
0
1
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
3
1
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
1
1
0
0
2
0
2
0
0
0
1
0
0
6
1
4
0
1
0
0
2
3
2
1
0
1
0
2
0
0
0
4
0
0
0
0
1
0
2
1
1
0
0
0
3
0
6
1
1
2
0
0
1
0
1
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
4
2
2
0
0
1
1
1
0
0
1
1
3
0
0
1
2
0
1
0
1
0
0
1
1
0
0
1
1
0
4
0
3
1
2
3
1
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
5
0
0
4
1
1
0
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
2
4
0
6
0
0
4
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
0
2
1
4
1
1
0
1
0
0
0
4
1
0
1
5
0
1
1
0
1
0
1
0
5
3
0
1
0
19
0
1
0
1
1
7
0
1
0
0
0
0
1
0
0
1
0
0
1
1
4
3
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
1
0
2
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
5
1
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
5
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
0
2
0
1
0
0
1
2
2
0
0
1
0
1
2
0
1
0
1
0
1
1
4
0
0
4
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
2
10
0
0
0
5
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
36
1
0
2
2
1
0
2
2
1
1
1
0
2
0
1
0
0
0
0
5
0
1
0
1
0
0
5
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
1
3
0
0
3
0
5
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
10
0
0
3
1
0
0
0
1
0
1
2
0
0
1
0
0
6
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
3
0
1
1
0
2
3
0
1
0
0
0
2
0
0
0
3
0
0
3
0
1
4
0
2
1
0
0
0
2
2
2
1
2
0
0
0
0
2
0
0
0
0
0
12
0
1
0
3
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
7
0
5
3
2
1
0
0
1
2
2
1
6
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
4
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
4
1
0
1
3
0
1
1
0
0
3
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
1
8
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
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
5
2
2
2
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
1
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
6
0
0
2
1
0
0
1
3
1
0
1
7
0
2
0
0
0
0
0
1
0
0
0
0
4
12
5
0
3
2
0
1
0
1
3
5
0
0
0
1
0
5
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
5
7
0
0
0
0
1
0
1
1
1
0
5
1
0
6
0
0
0
0
2
0
1
1
0
0
0
4
0
2
0
2
0
0
1
3
0
0
1
3
0
0
7
0
1
1
0
0
2
3
1
1
0
0
0
0
0
1
7
3
0
0
1
1
1
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
2
4
3
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
1
0
1
1
1
1
2
116
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
2
1
1
0
0
0
2
2
3
2
1
4
1
1
4
0
1
1
0
0
0
3
0
1
0
0
0
2
0
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
3
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
5
2
2
0
0
1
1
0
1
0
4
1
0
0
0
0
2
0
1
0
1
1
1
0
1
1
1
1
1
7
0
2
1
0
4
7
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
3
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
5
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
3
1
0
2
1
0
0
2
0
0
0
0
0
1
0
1
6
7
0
2
1
2
1
0
3
0
2
0
2
2
0
5
0
1
1
3
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
2
1
3
0
1
0
0
0
1
2
1
0
5
3
1
0
3
1
0
0
1
2
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
2
1
0
0
0
1
0
6
0
6
0
4
2
1
1
1
0
0
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
0
2
0
1
0
1
0
3
1
0
1
1
2
0
0
1
0
0
2
1
1
1
1
1
0
0
0
2
5
0
0
0
1
1
1
0
1
0
0
0
0
1
1
4
0
0
0
0
2
1
0
3
3
0
1
0
1
2
0
74
1
0
1
0
1
1
0
1
0
3
3
0
0
1
0
1
1
7
0
2
1
0
0
1
0
1
0
0
2
0
5
4
0
1
2
0
0
0
0
1
0
3
3
0
1
1
1
1
0
2
0
0
0
5
0
0
0
0
0
0
5
1
0
3
1
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
2
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
5
1
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
1
1
4
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
1
0
0
1
0
3
0
0
2
1
0
0
1
14
0
1
2
3
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
1
0
0
17
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
2
1
1
6
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
3
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
3
1
1
3
2
3
0
1
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
8
0
2
0
0
3
1
1
0
1
0
0
2
0
1
0
1
0
1
1
3
1
2
0
4
0
0
0
0
5
0
2
2
0
0
1
4
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
4
3
2
0
1
1
0
0
0
0
0
2
3
1
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
1
3
4
0
6
0
0
0
6
0
1
0
0
2
1
2
0
0
0
2
0
4
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
1
0
0
1
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
3
4
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
16
0
0
0
0
2
3
0
4
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
29
2
1
0
0
0
0
1
1
4
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
1
0
2
4
0
0
0
0
1
3
0
0
3
2
0
0
1
2
0
2
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
5
3
0
0
0
0
4
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
1
5
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
1
1
0
3
0
1
0
1
3
0
1
1
1
1
1
0
2
4
1
0
0
2
1
0
0
1
2
5
0
2
1
3
2
1
0
3
0
1
0
1
1
2
1
0
2
0
1
0
1
0
0
2
0
0
1
3
2
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
0
6
0
1
1
0
0
3
0
0
0
0
1
4
0
24
0
0
0
2
0
1
1
5
0
2
1
0
0
1
0
0
2
0
2
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
5
0
0
1
1
1
0
3
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
4
0
2
1
0
0
4
0
0
0
1
0
1
1
0
0
0
1
6
1
1
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
6
0
2
1
0
0
1
0
0
3
4
0
0
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
1
1
0
1
1
2
1
0
0
2
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
1
1
0
2
1
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
5
3
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
3
1
1
3
1
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
5
4
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
1
1
1
1
1
0
7
3
0
0
1
0
0
0
0
1
3
1
0
4
0
0
2
3
0
0
1
1
0
0
21
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
3
1
2
1
1
3
0
2
0
1
0
0
0
2
1
1
2
0
2
3
2
5
5
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
3
2
0
0
1
0
4
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
3
0
0
0
0
2
0
1
0
0
0
9
0
0
2
1
0
1
2
1
0
0
0
1
0
1
0
2
0
1
2
0
5
0
0
2
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
7
1
2
2
0
0
0
1
0
1
5
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
3
0
1
0
0
5
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
1
1
1
0
1
0
0
1
1
0
0
0
3
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
140
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
1
0
1
2
1
0
0
2
0
1
0
2
1
0
1
0
2
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
3
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
5
0
0
1
0
5
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
16
1
0
0
2
1
0
2
0
0
0
0
6
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
1
1
3
3
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
1
2
0
0
1
0
1
0
1
2
1
1
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
7
0
0
0
2
0
0
0
0
0
0
5
0
0
1
3
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
6
2
0
1
0
0
0
3
0
1
1
1
2
1
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
4
0
2
0
1
0
1
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
3
0
1
10
1
4
0
0
0
0
3
0
1
1
2
2
0
0
1
3
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
2
1
1
0
4
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
3
0
1
2
0
1
0
3
3
0
0
0
1
0
0
0
1
0
0
0
0
2
3
1
0
2
0
1
2
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
4
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
1
2
0
3
0
1
1
1
0
2
0
1
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
4
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
1
0
2
2
1
1
1
0
0
0
5
0
0
2
0
0
0
0
3
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
5
0
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
2
0
1
1
1
1
10
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
8
0
0
10
0
0
0
1
0
3
2
2
2
0
1
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
2
0
3
0
1
0
3
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
3
0
1
0
0
1
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
5
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
2
0
3
0
0
3
0
1
2
3
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
3
1
0
1
4
0
0
1
0
3
2
2
0
1
0
1
0
0
2
4
0
4
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
4
4
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
2
1
1
1
2
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
1
2
1
3
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
3
1
56
3
0
0
0
0
0
0
2
0
2
0
5
0
0
4
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
4
1
0
0
0
0
2
0
1
3
1
0
4
0
3
1
0
0
4
1
0
1
1
1
0
2
0
0
0
0
0
1
0
1
3
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
5
1
3
1
0
0
0
1
0
0
0
1
2
0
8
2
0
0
0
1
0
0
0
0
3
1
1
1
0
5
0
1
2
2
0
0
0
1
1
1
0
0
1
1
0
0
1
2
4
0
1
3
0
3
0
0
1
0
1
0
1
17
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
2
9
0
0
1
0
0
0
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
5
0
2
2
3
2
0
0
0
3
1
4
1
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
6
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
4
0
1
0
1
1
0
2
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
2
0
0
2
0
0
4
2
3
0
0
3
0
0
0
0
0
0
2
0
0
0
3
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
1
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
1
2
3
1
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
3
3
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
1
0
0
2
2
2
0
0
0
3
0
1
3
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
1
2
1
3
0
2
3
1
0
0
3
2
0
0
1
0
0
0
1
0
0
0
3
3
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
5
2
0
0
2
1
0
1
1
1
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
2
0
4
0
2
1
0
2
1
0
2
2
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
4
0
0
0
2
3
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
0
0
0
0
2
0
1
6
0
1
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
64
0
2
1
0
0
0
3
0
1
0
1
0
0
0
6
1
1
0
1
1
0
0
1
2
3
1
1
0
0
0
0
0
3
0
4
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
3
0
1
0
2
0
1
0
2
0
0
3
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
4
0
0
0
0
1
2
1
4
0
4
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
0
1
4
1
0
0
0
0
1
0
1
2
0
2
0
0
2
7
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
3
0
1
1
0
2
0
1
1
0
0
1
1
1
0
1
0
3
5
1
0
0
0
0
2
1
0
0
3
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
2
1
4
0
1
6
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
7
0
0
1
5
0
1
0
0
0
1
1
0
1
0
0
4
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
2
1
0
0
3
3
0
0
1
0
0
1
0
1
0
0
0
3
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
2
3
0
1
0
0
1
0
1
0
6
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
0
50
0
0
0
2
3
1
1
0
1
1
0
0
2
2
0
1
3
0
0
0
1
0
0
1
0
0
0
3
1
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
70
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
4
2
0
0
0
0
3
3
0
1
1
1
1
2
0
1
2
0
0
2
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
27
0
0
1
0
2
0
0
2
1
0
0
3
3
0
0
0
1
1
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
4
1
1
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
3
0
0
0
0
1
0
1
2
0
1
1
0
1
2
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
3
0
0
3
1
1
1
1
1
2
0
0
4
0
0
0
1
1
2
1
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
3
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
21
0
3
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
5
3
1
1
1
2
0
2
2
0
3
0
3
0
2
1
0
0
2
0
0
1
0
2
5
1
0
0
5
1
0
0
3
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
2
1
3
0
0
2
0
1
0
1
0
0
1
0
4
3
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
1
0
1
0
1
1
0
1
0
2
3
0
0
0
1
0
3
0
0
5
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
1
0
1
60
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
3
0
0
1
0
0
0
0
1
2
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
2
1
0
1
1
1
1
1
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
5
0
0
0
0
1
2
0
1
0
0
1
0
4
0
0
0
0
0
5
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
5
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
3
1
0
1
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
8
1
0
0
0
0
4
0
1
0
1
1
2
1
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
7
0
1
0
2
0
1
1
1
0
1
0
0
2
0
0
0
3
2
0
0
3
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
4
3
0
1
1
0
4
1
3
3
1
3
0
0
0
0
0
4
0
1
1
1
0
0
0
0
1
3
0
0
0
1
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
2
0
1
0
1
1
1
2
0
2
0
0
3
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
1
0
3
0
0
1
1
1
0
0
1
1
3
0
0
1
0
1
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
1
3
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
2
0
0
0
1
0
0
0
1
2
3
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
4
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
3
0
1
1
0
2
0
2
3
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
1
0
3
0
1
2
0
1
0
0
0
0
0
0
0
6
1
0
3
2
0
2
0
2
0
3
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
3
0
1
0
4
24
1
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
3
2
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
1
1
3
0
0
2
2
0
0
0
2
0
1
1
0
0
5
0
0
0
0
1
3
1
0
0
0
1
4
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
1
3
0
0
1
0
1
2
0
0
1
1
0
4
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
3
1
0
1
0
1
0
2
0
2
2
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
5
0
0
3
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
4
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
6
0
0
0
0
1
0
0
0
3
3
2
1
0
3
0
2
1
2
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
5
1
1
1
0
0
0
1
2
1
0
0
0
0
6
0
0
0
0
0
3
0
1
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
2
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
1
1
0
1
0
1
3
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
1
0
0
1
1
1
1
3
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
5
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
0
1
0
1
3
1
3
2
0
2
0
0
0
1
0
1
0
4
0
1
2
0
1
0
0
0
0
0
3
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
1
4
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
3
0
0
6
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
4
3
1
1
2
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
7
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
4
1
0
0
0
1
3
1
0
1
3
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
3
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
1
2
1
0
1
1
3
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
4
0
1
1
0
1
0
1
0
1
0
4
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
1
0
0
3
1
1
0
0
0
0
2
0
0
0
1
3
2
0
0
2
0
1
2
0
0
1
1
0
1
3
0
1
0
7
0
1
3
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
2
1
0
0
0
4
1
1
0
1
0
1
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
4
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
3
2
2
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
3
1
3
2
0
1
0
1
2
3
0
0
0
3
1
0
2
4
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
1
3
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
7
1
0
0
4
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
3
1
0
0
2
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
3
1
0
0
3
0
2
0
1
0
0
0
1
2
1
0
0
0
1
1
1
1
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
6
1
0
0
0
0
0
1
0
4
0
0
6
1
0
1
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
1
2
0
1
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
1
1
0
1
0
0
2
0
404
0
3
0
0
0
3
0
0
2
0
0
1
1
0
0
0
1
1
1
1
0
0
5
0
1
0
0
0
0
0
0
0
1
1
3
2
0
0
1
0
2
7
0
0
1
1
0
0
0
2
0
3
1
0
0
0
0
1
0
1
0
0
2
2
7
0
1
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
1
2
1
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
1
3
3
0
1
2
3
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
3
0
0
0
0
0
0
5
2
0
1
0
3
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
1
1
1
2
0
1
1
0
2
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
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
1
0
0
0
1
3
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
3
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
5
0
0
0
2
0
2
0
0
3
0
0
2
0
15
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
15
0
4
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
4
0
0
0
1
0
0
0
3
0
0
0
0
0
5
1
0
4
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
3
0
2
0
3
2
3
0
1
2
0
0
0
0
2
0
5
1
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
1
0
1
1
1
0
0
6
1
2
2
2
0
2
1
1
0
0
1
0
0
1
0
0
0
1
8
0
1
0
0
0
0
1
0
0
2
4
0
0
1
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
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
1
0
0
0
0
1
2
0
0
2
1
0
3
0
1
0
0
1
1
1
1
0
1
0
0
0
6
1
1
0
1
0
0
5
0
0
1
1
0
0
2
0
5
0
0
0
0
1
1
0
1
3
0
0
6
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
1
1
0
2
0
0
4
0
1
0
1
0
0
1
1
0
0
0
1
2
1
0
2
2
0
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
0
0
1
2
0
0
0
0
3
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
3
2
1
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
0
1
1
1
3
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
4
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
3
0
0
2
1
0
0
1
0
5
0
1
0
3
3
0
1
1
2
3
0
2
5
1
1
0
1
0
1
2
0
0
0
3
0
10
5
0
0
2
1
0
0
1
6
1
0
1
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
36
0
0
0
0
0
0
1
0
1
0
0
3
7
0
0
0
0
0
0
0
0
1
0
3
0
3
0
1
2
0
1
3
0
0
0
0
0
1
0
0
0
1
1
1
0
0
3
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
1
0
3
3
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
4
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
2
4
2
0
2
0
3
0
0
1
2
2
0
2
0
0
2
1
0
3
1
1
1
0
0
2
1
1
0
0
5
0
0
0
1
0
1
0
0
0
2
0
3
0
0
1
0
1
3
0
0
2
1
0
0
1
0
0
0
3
2
1
0
1
1
0
0
21
0
1
0
7
0
1
2
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
8
0
12
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
1
0
2
0
0
0
1
1
0
3
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
2
0
3
0
0
4
4
0
0
1
0
1
0
0
1
1
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
2
1
1
0
5
1
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
1
0
1
0
1
0
0
3
0
1
1
4
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
4
2
0
0
0
1
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
7
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
6
3
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
2
0
0
1
4
0
1
1
0
0
3
0
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
6
1
0
0
0
0
1
1
0
0
0
0
0
0
1
33
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
5
0
3
1
0
0
1
0
2
2
0
6
1
0
4
0
0
1
0
2
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
1
1
1
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
1
2
1
0
4
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
3
1
1
2
0
0
0
0
1
1
0
0
0
1
3
0
0
5
0
1
2
0
4
0
1
1
1
3
1
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
4
0
0