Count H-Shaped Patterns

You are given an $n \times m$ grid consisting of white and black cells. A cell is white if it is denoted by a dot ('.') and black if it is denoted by a hash ('#').

An H-shape is defined by selecting four integers $x_1$, $x_2$, $y_1$, $y_2$ satisfying the following conditions:

1. $1\le x_1<x_2\le n$ and $1\le y_1<y_2\le m$.
2. $x_1+x_2$ is even.

Let $mid=\frac{x_1+x_2}{2}$ (which is an integer by condition 2). The three segments that form an H-shape are:

• The left vertical segment: from $(x_1,y_1)$ to $(x_2,y_1)$, i.e. all cells in column $y_1$ from row $x_1$ to row $x_2$.
• The right vertical segment: from $(x_1,y_2)$ to $(x_2,y_2)$, i.e. all cells in column $y_2$ from row $x_1$ to row $x_2$.
• The middle horizontal segment: from $(mid, y_1)$ to $(mid,y_2)$, i.e. all cells in row $mid$ from column $y_1$ to column $y_2$.

An H-shape is valid if every cell on these three segments is white. Two H-shapes are considered the same if and only if their values of $x_1$, $x_2$, $y_1$, and $y_2$ are identical.

Your task is to count the number of different valid H-shapes in the grid.

inputFormat

The first line contains two integers $n$ and $m$ ($2\le n, m\le 300$) --- the number of rows and columns of the grid.

Each of the next $n$ lines contains a string of length $m$ consisting only of characters . and #, where . represents a white cell and # represents a black cell.

It is guaranteed that the grid dimensions allow at least one possible H-shape selection (though it might not pass the white condition).

outputFormat

Output a single integer, the number of valid H-shapes in the grid.

sample

3 3
...
...
...

3