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>
long long a,b,c,h,w,k[]={0,0,-1,1,0,0},i;
char s[405][405];
void d(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+k[i]][y+k[i+2]]+t==81)d(x+k[i],y+k[i+2]);
}
int main(){
  scanf("%d%d",&h,&w);
  for(;i<=h;)scanf("%s",s[++i]+1);
  for(;h;--h)for(i=w;i;--i)if(s[h][i])a=b=0,d(h,i),c+=a*b;
  printf("%lld\n",c);
}