input:

3 10
^>^<^^^^>^
<v^v^^v^v>
<>vvvvvvvv
10 1
v
^
<
<
v
<
v
>
<
<
5 4
<^^^
<vvv
<<^>
vv^v
<vvv
2 9
^^^^^^^^^
vvvvvvvvv
9 10
^>^^<^<^<>
<^<<><<<<>
v^v^^<>^<^
^<vvv<><<>
<v>>><^v^>
^^^^>^^<<v
v^v>v^v^<>
v^vvv>v^<^
vvvvv><>v>
8 8
^^^^<^<^
<>^<v>v^
<v<v>^v>
v>v<vv<>
^<^>>v<>
<v^v^<<>
^v^^>v<>
<vv<vv<>
2 2
...

output:

3
0
2
4
5
7
0
2
3
2
5
0
5
2
0
2
1
2
2
0
0
0
0
2
3
3
2
3
2
4
2
0
3
3
9
5
0
3
0
9
5
2
3
2
2
5
5
1
4
0
0
4
0
2
3
3
2
4
5
2
0
5
3
7
4
3
4
0
3
0
4
3
4
6
0
7
3
0
2
0
0
7
8
4
2
3
6
3
2
3
0
0
0
3
3
2
2
0
0
5
4
4
4
3
3
5
4
3
0
3
4
0
9
0
4
5
5
3
3
0
0
2
4
4
3
4
2
6
4
0
0
3
3
4
0
4
3
4
2
0
3
6
1
3
4
4
6
3
4
2
...

result: