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;

int h,w;
vector<string>f(405);
int ans[405][405]={0};
long long res[200000][2]={0};
int cnt=1;

int dx[]={1,0,-1,0};
int dy[]={0,-1,0,1};

void dfs(int x, int y){
	for(int i = 0; i < 4; i++){
		int nx = x+ dx[i];
		int ny = y + dy[i];
		if(ans[nx][ny]==0&&0<=nx&&nx<h&&0<=ny&&ny<w&&f[nx][ny]!=f[x][y]){
			ans[nx][ny]=cnt;
			if(f[nx][ny]=='#') res[cnt][0]++;
			else res[cnt][1]++;
			dfs(nx,ny);
		}
	}
	return;
}


int main(){
	cin >> h >> w;
	for(int i = 0; i < h; i++) cin >> f[i];
	for(int i = 0; i < h; i++){
		for(int j = 0; j < w; j++){
			if(ans[i][j] == 0){
				ans[i][j]=cnt;
				if(f[i][j]=='#') res[cnt][0]++;
				else res[cnt][1]++;
				dfs(i,j);
				cnt++;
			}
		}
	}
	long long sum = 0;
	for(int i = 0; i < 200000;i++) sum += res[i][0]*res[i][1];
	cout << sum << endl;
	return 0;
}