Description

Mr. Malnar wants to put up a picture of himself on the wall. The wall can be represented as a matrix with $n$ rows and $m$ columns. Since he has placed his picture on the wall many times before, some positions still have nails embedded in them. Such positions are marked with the symbol "$\texttt{\#}$", while empty spots are marked with the symbol "$\texttt{.}$".

The picture has a rectangular shape with arbitrary dimensions and is placed on the wall in a way that it covers a rectangular area. The picture can be placed on the wall if it covers at most one position that contains a nail.

Help Mr. Malnar calculate the number of ways he can place his picture on the wall.

Input Format

The first line of input contains $n$ and $m$ ($1 ≤ n,m ≤ 500$), the dimensions of the wall.

In each of the next $n$ lines, there are $m$ characters $c_{ij}$ , describing the wall. Each character will be either "$\texttt{.}$" or "$\texttt{\#}$" (without quotes).

Output Format

In a single line of output, print the number of possible ways to place the picture on the wall.

3 3
...
...
..#

36

4 4
....
.#..
#...
#.#.

76

5 5
.....
#..#.
..#.#
.....
..#..

154

Hint

Clarification of the first example:

Each placement of the picture is valid as long as it covers at most one nail.

Clarification of the second example:

The picture cannot be placed in a way that it covers positions $(3, 1)$ and $(4, 1)$ simultaneously.

Scoring