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<bits/stdc++.h>
using namespace std;
const int SZ = 405;
char graph[SZ][SZ];
int visit[SZ][SZ];
int n,m; 
long long b,w;
void dfs(int x, int y){
	visit[x][y]=1;
	if(graph[x][y]=='#') b++;
	else w++;
	int dx[4]={0,0,1,-1}; int dy[4]={1,-1,0,0};
	for(int i=0;i<4;i++){
		int nx = x+dx[i]; int ny = y+dy[i];
		if(nx<0 || nx>=n) continue;
		if(ny<0 || ny>=m) continue;
		if(graph[x][y]==graph[nx][ny]) continue;
		if(visit[nx][ny]==1) continue;
		dfs(nx,ny);
	}
}
int main(void){
	scanf("%d %d",&n,&m); getchar();
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++) graph[i][j]=getchar();
		getchar();
	}
	long long aa = 0;
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			b = 0; w = 0;
			if(visit[i][j]==1) continue;
			if(graph[i][j]=='#') dfs(i,j); 
			aa += b*w;
		}
	}
	printf("%lld",aa);
	return 0;
}