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 n,m,vis[500*500],bcnt;
vector<int> edge[500*500];
char s[500][500];

int getnode(int x,int y)
{
	return (x-1)*m+y;
}

int dfs(int u)
{
	int res=1;
	if(s[(u-1)/m+1][(u-1)%m+1]=='.')++bcnt;
	vis[u]=true;
	for(auto v : edge[u])
	{
		if(!vis[v])res+=dfs(v);
	}
	return res;
}

int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;++i)
	{
		scanf("%s",s[i]+1);
	}
	for(int i=1;i<=n;++i)
	{
		for(int j=1;j<=m;++j)
		{
			if(i<n && s[i][j]!=s[i+1][j])
			{
				edge[getnode(i,j)].push_back(getnode(i+1,j));
				edge[getnode(i+1,j)].push_back(getnode(i,j));
			}
			if(j<m && s[i][j]!=s[i][j+1])
			{
				edge[getnode(i,j)].push_back(getnode(i,j+1));
				edge[getnode(i,j+1)].push_back(getnode(i,j));
			}
		}
	}
	long long ans=0;
	for(int i=1;i<=n*m;++i)
	{
		if(!vis[i])
		{
			bcnt=0;
			int res=dfs(i);
			ans+=(long long)(res-bcnt)*bcnt;
		}
	}
	printf("%lld\n",ans);
}