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;         
long long n,m,d[405][405],cnt,x,y;
char b[405][405];
void go(int i, int j)
{
    if(b[i][j]=='#') 
	{
		++x;
	}
    else 
	{
		++y;
	}
    d[i][j]=cnt;
    if(i>0 && d[i-1][j]==-1 && b[i-1][j]!=b[i][j])
	{
        go(i-1,j);
    }
    if(j>0 && d[i][j-1]==-1 && b[i][j-1]!=b[i][j])
	{
        go(i,j-1);
    }
    if(i<n-1 && d[i+1][j]==-1 && b[i+1][j]!=b[i][j])
	{
        go(i+1,j);
    }
    if(j<m-1 && d[i][j+1]==-1 && b[i][j+1]!=b[i][j])
	{
        go(i,j+1);
    }
}

int main() {
    cin>>n>>m;
    for(int i=0;i<n;i++)
	{
		for(int j=0;j<m;j++)
		{
			cin>>b[i][j];
		}
	}
    memset(d,-1,sizeof d);
    long long ans=0;
    for(int i=0;i<n;i++)
    {
    	for(int j=0;j<m;j++)
    	{
    		if(d[i][j]==-1)
			{
				x=0;
				y=0;
            	go(i,j);
            	cnt++;
            	ans+=x*y;
        	}
		}
	}
    cout<<ans<<endl;
    return 0;
}