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, black, white, d[400][400];
char s[400][400];
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};

void dfs(int x, int y){
	d[x][y] = 1;
	if(s[x][y] == '#'){
		black++;
	}else{
		white++;
	}
	for(int i=0; i<4; i++){
		int nx = x + dx[i], ny = y + dy[i];
		if(0<=nx && nx<H && 0<=ny && ny<W && s[nx][ny] != s[x][y] && d[nx][ny] != 1){
			dfs(nx, ny);
		}
	}
}

int main(){
	long long ans = 0;
	cin >> H >> W;
	for(int i=0; i<H; i++){
		for(int j=0; j<W; j++){
			cin >> s[i][j];
		}
	}
	for(int i=0; i<H; i++){
		for(int j=0; j<W; j++){
			black = 0, white = 0;
			if(!d[i][j]){
				dfs(i, j);
			}
			ans += (long long)black*white;
		}
	}
	cout << ans << endl;
	return 0;
}