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<iostream>
#include<cstdio>

using namespace std;

const int dir[4][2]={{1,0},{0,1},{-1,0},{0,-1}};
long long b,a,h,w,ans;
char str[401][401];
bool vis[401][401];

void dfs(int x,int y){
	vis[x][y]=true;
	if(str[x][y]=='#')++b;else ++a;
	for(int i=0;i<4;++i){
		int xx=x+dir[i][0],yy=y+dir[i][1];
		if(xx>0&&yy>0&&xx<=h&&yy<=w&&!vis[xx][yy]&&str[xx][yy]!=str[x][y])dfs(xx,yy);
	}
}

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