AT_abc475_f.Rectangle Filling

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.

有一个 $H$ 行 $W$ 列的网格。记从上往下第 $i$ 行、从左往右第 $j$ 列的格子为格子 $(i, j)$。

网格中的每个格子被涂成白色或黑色：若字符串 $S_i$ 的第 $j$ 个字符为 .，则格子 $(i, j)$ 为白色；若为 #，则为黑色。

你最多可以执行一次以下操作：

• 选择一个矩形区域，并将该区域内所有格子涂成黑色。更准确地说，选择满足 $1 \leq h_1 \leq h_2 \leq H$ 和 $1 \leq w_1 \leq w_2 \leq W$ 的整数 $h_1, h_2, w_1, w_2$，并将所有满足 $h_1 \leq h \leq h_2$ 且 $w_1 \leq w \leq w_2$ 的格子 $(h, w)$ 涂成黑色。

求可得到的不同网格状态的总数。此处，若存在一对整数 $(i, j)$（其中 $1 \leq i \leq H$ 且 $1 \leq j \leq W$），使得在一种状态下格子 $(i, j)$ 为白色而在另一种状态下为黑色，则认为这两种网格状态不同。

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

$H$ $W$
$S_1$
$S_2$
$\vdots$
$S_H$

输入从标准输入中按以下格式给出：

$H$ $W$
$S_1$
$S_2$
$\vdots$
$S_H$

Output the answer.

输出答案。

Sample 1 Explanation:
The possible states of the grid obtainable by performing the operation at most once are the following seven:

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 #.

样例 1 解释：
最多执行一次操作所能得到的网格可能状态如下所示，共七种：

约束条件

• $1 \leq H, W$
• $H \times W \leq 2 \times 10^5$
• $H$ 和 $W$ 均为整数。
• $S_i$ 是一个长度为 $W$ 的字符串，仅由字符 . 和 # 组成。