You are given a tiled chart paper of $$N$$ rows and $$M$$ columns. There are a total of $$N \times M$$ tiles in it. Each tile is colored either black or white. Now, you need to count how many ways are there to cut valid chessboards of size $$8 \times 8$$ out of this chart paper. 

Notes

$$1$$. One chessboard is different from another if either of them contains at least one tile which is different from another chessboard.
$$2$$. The chess board formation should have distinct colors of adjacent cells i.e. Black$$/$$White alternative (regular chessboard rules apply).

Input Format

The first line contains two space-separated integers $$N$$ and $$M$$ as input.
In the next $$N$$ lines, you are given a string of $$M$$ characters. Each character is either $$0$$ or $$1$$. If it is $$0$$ then the tile color is white, if it is $$1$$ then the tile color is black.

Output Format

In the output, you need to print an integer that denotes the required count as stated in the problem statement.

Constraints

$$1 \le N , M \le 1000$$