Problem:
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

Output

Print the answer.

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

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int H, W;
char text[400][401];
int buf[400][400];
int ans = 0;

void loop(int x1, int y1, int last){
  if(x1 < 0 || x1 >= W|| y1 < 0 || y1 >= H){
    return;
  }
  if(text[y1][x1] == last || buf[y1][x1]){
  	return;
  }
  if(text[y1][x1] == '#'){
    ans++;
  }
  buf[y1][x1] = 1;
  loop(x1 + 1, y1, text[y1][x1]);
  loop(x1 - 1, y1, text[y1][x1]);
  loop(x1, y1 + 1, text[y1][x1]);
  loop(x1, y1 - 1, text[y1][x1]);
}

void reset(){
  int x, y;
  for(y = 0; y < H; y++){
    for(x = 0; x < W; x++){
      buf[y][x] = 0;
    }
  }
}

int main(void){
  scanf("%d %d", &H, &W);
  int x, y;
  reset();
  for(y = 0; y < H; y++){
    scanf("%s", text[y]);
  }
  for(y = 0; y < H; y++){
    for(x = 0; x < W; x++){
      reset();
      if(text[y][x] == '.'){
        loop(x, y, 'x');
      }
    }
  }
  printf("%d\n", ans);
  return 0;
}