Contest Duration: - (local time) (120 minutes)
C - Alternating Path /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

HW 列のマス目があり、各マスは黒または白に塗られています。

• 上下左右に隣り合うマスへの移動を繰り返してマス c_1 からマス c_2 へ行く方法であって、通るマスの色が黒、白、黒、白・・・と交互になっているものが存在する。

### 制約

• 1 \leq H, W \leq 400
• |S_i| = W (1 \leq i \leq H)
• i (1 \leq i \leq H) に対して、文字列 S_i は文字 # と文字 . だけからなる。

### 入力

H W
S_1
S_2
:
S_H


### 入力例 1

3 3
.#.
..#
#..


### 出力例 1

10


### 入力例 2

2 4
....
....


### 出力例 2

0


### 入力例 3

4 3
###
###
...
###


### 出力例 3

6


Score : 300 points

### Problem Statement

There is a grid with H rows and W columns, where each square is painted black or white.

You are given H strings S_1, S_2, ..., S_H, each of length W. If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is #; if that square is painted white, the j-th character in the string S_i is ..

Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

• There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

### Constraints

• 1 \leq H, W \leq 400
• |S_i| = W (1 \leq i \leq H)
• For each i (1 \leq i \leq H), the string S_i consists of characters # and ..

### Input

Input is given from Standard Input in the following format:

H W
S_1
S_2
:
S_H


### Sample Input 1

3 3
.#.
..#
#..


### Sample Output 1

10


Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

### Sample Input 2

2 4
....
....


### Sample Output 2

0


### Sample Input 3

4 3
###
###
...
###


### Sample Output 3

6