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>
#include<iostream>
#include<algorithm>
using namespace std;
char str[405][405];
bool vis[405][405];
const int ne[4][2]={{-1,0},{1,0},{0,1},{0,-1}};
long long a,b,ans=0,h,w;
void dfs(int i,int j){
	vis[i][j]=true;
	if(str[i][j]=='#')++a;else ++b;
	for(int k=0;k<4;k++){
		int xx=i+ne[k][0],yy=j+ne[k][1];
		if(xx>0&&yy>0&&xx<=h&&yy<=w&&!vis[xx][yy]&&str[i][j]!=str[xx][yy])
			dfs(xx,yy);
	}
}
int main(){
	cin>>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+=a*b;
			printf("%lld",ans);
}