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>
using namespace std;
typedef long long ll;
const int N=400+10;
int h, w, g[N][N], vis[N][N], d[5][5];
ll cb, cw, ans=0;
inline void dfs( int x, int y )
{
	vis[x][y]=1; 
	if ( g[x][y] ) ++cb;
	else ++cw;
	for ( int i=1; i<=4; i++ )
	{
		int dx=x+d[i][1], dy=y+d[i][2];
		if ( !vis[dx][dy]&&g[dx][dy]!=g[x][y]&&dx>=1&&dx<=h&&dy>=1&&dy<=w ) dfs( dx, dy );
	}
}
int main()
{
	scanf( "%d%d\n", &h, &w );
	for ( int i=1; i<=h; i++ )
	{
		char s[N];
		scanf( "%s", &s );
		for ( int j=1; j<=w; j++ ) 
		  if ( s[j-1]=='#' ) g[i][j]=1;
		  else g[i][j]=0;
	}
	d[1][1]=1, d[2][1]=-1, d[3][2]=1, d[4][2]=-1;
	for ( int i=1; i<=h; i++ )
	  for ( int j=1; j<=w; j++ )
	  {
	  	  if ( vis[i][j] ) continue;
		  cb=cw=0;
		  dfs( i, j );
		  ans+=cb*cw;
	  }
	printf( "%lld", ans );
	return 0;
}