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;

vector<int> dx={1,0,0,-1};
vector<int> dy={0,1,-1,0};

int h,w;
bool seen[410][410];
char a[410][410];

long long countw,countb;
void dfs(int i,int j){
	seen[i][j]=true;
	if(a[i][j]=='#') countb++;
	else if(a[i][j]=='.') countw++;
	for(int k=0;k<4;k++){
		int nx=i+dx[k];
		int ny=j+dy[k];
		if(nx<0||nx>=h||ny<0||ny>=w) continue;
		if(a[i][j]==a[nx][ny]) continue;
		if(seen[nx][ny]) continue;
		dfs(nx,ny);
	}
}

int main() {
	cin >> h >> w;
	for(int i=0;i<h;i++){
		string s;
		cin >> s;
		for(int j=0;j<w;j++){
			a[i][j]=s[j];
		}
	}
	long long res=0;
	for(int i=0;i<h;i++){
		for(int j=0;j<w;j++){
			if(a[i][j]=='.') continue;
			if(seen[i][j]) continue;
			countw=0;
			countb=0;
			dfs(i,j);
			res+=countw*countb;
		}
	}
	cout << res << endl;
}