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

$1\le N,M\le 1000$