21822_CountCross

Given a MM×NN grid with different colors (black and white) on each cell, your task is to calculate the total amount of crosses of black color. We say there exists a black cross centered at the black cell (x, y) if there are four positive integer L, R, U, D that the cell (x, y-L), (x, y+R), (x-U, y), (x+D, y) are all black. Note that if two crosses have the same center but different L, R, U, D, we consider they are distinct. We use 1 to describe black.

For example

00100
00100
11111
00100
00100
00000

There are 16 black crosses.

The MM and NN are large, so we divide the matrix into M×N rectangle blocks. If two cells are in the same block, their colors are same.

So we can divide the sample into 4×3 blocks.

There are at most 100 cases.

In every case, there are two integers, M, N in the first line. ( 1 ≤ M, N ≤ 50 )

The next line contains M positive integers which are less than or equals to 50. The p-th integer describe the p-th row block's height.

The next line contains N positive integers which are less than or equals to 50. The p-th integer describe the p-th colomn block's width.

The following M lines each has a string which contain N digits.The q-th digit in the p-th line describe the color of the q-th colomn block in the p-th row.

Output the answer to each case.

4 3
2 1 2 1
2 1 2
010
111
010
000

16