Problem Statement

There is a grid with $H$ rows and $W$ columns. The cell at the $i$-th row from the top and $j$-th column from the left is denoted as cell $(i, j)$.

Each cell of the grid is colored white or black. The information of the grid is given by $H$ strings $S_1, S_2, \ldots, S_H$ each of length $W$: cell $(i, j)$ is white if the $j$-th character of $S_i$ is ., and black if it is #.

Find the number of rectangular regions of the grid that are point-symmetrically colored.

More formally, find the number of integer tuples $(h_1, h_2, w_1, w_2)$ satisfying all of the following conditions:

• $1 \leq h_1 \leq h_2 \leq H$
• $1 \leq w_1 \leq w_2 \leq W$
• For all integers $i, j$ satisfying $h_1 \leq i \leq h_2$ and $w_1 \leq j \leq w_2$, cell $(i, j)$ and cell $(h_1 + h_2 - i, w_1 + w_2 - j)$ have the same color.

Constraints

• $1 \leq H, W \leq 10$
• $H$ and $W$ are integers.
• $S_i$ is a string of length $W$ consisting of . and #.

Input

The input is given from Standard Input in the following format:

H W
S_1
S_2
\vdots
S_H

Output

Output the answer.