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 N=400+10;
typedef long long LL;
const int dx[]={-1,0,1,0};
const int dy[]={0,1,0,-1};
int n,m;
char mp[N][N];
bool vis[N][N];
LL black,white;
 
void dfs(int x,int y) {
	vis[x][y]=1;
	if (mp[x][y]=='#') black++; else white++;
	for (int i=0;i<4;i++) {
		int nx=x+dx[i],ny=y+dy[i];
		if (nx<1 || nx>n || ny<1 || ny>m || vis[nx][ny] || mp[x][y]==mp[nx][ny]) continue;
		dfs(nx,ny);
	}
}

int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=n;i++) scanf("%s",mp[i]+1);
	
	LL ans=0;
	memset(vis,0,sizeof(vis));
	for (int i=1;i<=n;i++)
		for (int j=1;j<=m;j++)
			if (!vis[i][j] && mp[i][j]=='#') {
				black=0; white=0;
				dfs(i,j);
				ans+=black*white;
			}
	cout<<ans;		
	return 0;
}