Problem Statement

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

Each cell of the grid is painted white or black: cell $(i, j)$ is white if the $j$-th character of $S_i$ is ., and black if it is #.

You can perform the following operation at most once.

• Choose a rectangular region, and paint all cells within that region black. More formally, choose integers $h_1, h_2, w_1, w_2$ satisfying $1 \leq h_1 \leq h_2 \leq H$ and $1 \leq w_1 \leq w_2 \leq W$, and paint cell $(h, w)$ black for every pair of integers $(h, w)$ satisfying $h_1 \leq h \leq h_2$ and $w_1 \leq w \leq w_2$.

Find the number of possible states of the grid that can be obtained. Here, two states of the grid are considered different if there exists a pair of integers $(i, j)$ satisfying $1 \leq i \leq H$ and $1 \leq j \leq W$ such that cell $(i, j)$ is painted white in one state and painted black in the other state.

Constraints

• $1 \leq H, W$
• $H \times W \leq 2 \times 10^5$
• $H$ 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.

2 3
#..
.##

7

The possible states of the grid obtainable by performing the operation at most once are the following seven:

#.. ##. #.# ### #.. ##. ###
.## .## .## .## ### ### ###

4 1
#
#
#
#

1

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

96

• Source: AtCoder ABC 475 F