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;
typedef long long ll;
int n,m,cnt,fa[404*404],sh[404*404],sb[404*404],id[404][404],vis[404][404];
ll ans;
char mp[404][404];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++)
	{
		scanf("%s",mp[i]+1);
		for(int j=1;j<=m;j++)id[i][j]=++cnt,fa[cnt]=cnt;
	}
	for(int i=1;i<=n;i++)
	for(int j=1;j<=m;j++)
	if(mp[i][j]=='.')sb[id[i][j]]=1;
	else sh[id[i][j]]=1;
	for(int i=1;i<=n;i++)
	for(int j=1;j<=m;j++)
	{
		if(i<n&&mp[i+1][j]!=mp[i][j])
		{
			int u=find(id[i][j]),v=find(id[i+1][j]);
			if(u!=v)
			{
				fa[u]=v;
				sh[v]+=sh[u],sb[v]+=sb[u];
				sh[u]=sb[u]=0;
			}
		}
		if(j<m&&mp[i][j+1]!=mp[i][j])
		{
			int u=find(id[i][j]),v=find(id[i][j+1]);
			if(u!=v)
			{
				fa[u]=v;
				sh[v]+=sh[u],sb[v]+=sb[u];
				sh[u]=sb[u]=0;
			}
		}
	}
	for(int i=1;i<=n*m;i++)if(sh[i]&&sb[i])ans+=1ll*sh[i]*sb[i];
	cout<<ans<<endl;
}