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>
#define int long long
#define f(i,n) for(int i=0;i<n;i++)
#define F first
#define S second
#define mod 1000000007
#define P pair<int,int>
using namespace std;
string s[400];
int x[400][400],a,b,vx[160000],vy[160000];
void mutu(int y,int z){
	if(y&&s[y-1][z]!=s[y][z]&&!x[y-1][z]){
		x[y-1][z]=x[y][z];
		mutu(y-1,z);
	}
	if(z&&s[y][z-1]!=s[y][z]&&!x[y][z-1]){
		x[y][z-1]=x[y][z];
		mutu(y,z-1);
	}
	if(y<a-1&&s[y+1][z]!=s[y][z]&&!x[y+1][z]){
		x[y+1][z]=x[y][z];
		mutu(y+1,z);
	}
	if(z<b-1&&s[y][z+1]!=s[y][z]&&!x[y][z+1]){
		x[y][z+1]=x[y][z];
		mutu(y,z+1);
	}
	return ;
}
signed main(){
	int z=1,ans=0;
	cin>>a>>b;
	f(i,a){
		cin>>s[i];
	}
	f(i,a){
		f(j,b){
			if(!x[i][j]){
				x[i][j]=z;
				mutu(i,j);
				z++;
			}
			if(s[i][j]=='.') vx[x[i][j]]++;
			else vy[x[i][j]]++;
		}
	}
	f(i,z){
		ans+=vx[i]*vy[i];
	}
	cout<<ans<<endl;
	return 0;
}