Problem: 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.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in CPP):

Solution:
#include <cstdio>

int h, w, dx[] = {0,0,-1,1}, dy[] = {1,-1,0,0};
long long a, b, ans;
char s[405][405], t;

void dfs(int x, int y){
  char t;
  ((t = s[x][y]) == '#' ? a : b)++;
  s[x][y] = 0;
  for(int i = 0; i < 4; i++) if((s[x+dx[i]][y+dy[i]] | t) > t) dfs(x+dx[i], y+dy[i]);
}

int main(){
  scanf("%d %d\n", &h, &w);
  for(int i = 1; i <= h; i++){scanf("%s", s[i]+1);s[i][w+1] = 0;}
  for(int i = 1; i <= h; i++) for(int j = 1; j <= w; j++)
    if(s[i][j]) a = b = 0, dfs(i,j), ans += a*b;
  printf("%lld\n", ans);
}