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 <iostream>
using namespace std;
string s[400];
int dp[400][400];
long long h,w,t[]={-1,0,0,1},u[]={0,-1,1,0},a,b,ans,x,y;
void f(int i,int j,int k){
    for(int ii=0;ii<4;ii++){
        x=t[ii],y=u[ii];
        if(i+x>=0&&i+x<h&&j+y>=0&&j+y<w&&dp[i+x][y+j]==0){
            if(k==0&&s[i+x][y+j]=='.'){dp[i+x][y+j]=1;b++;f(i+x,y+j,1);}
            else if(k==1&&s[i+x][y+j]=='#'){dp[i+x][y+j]=1;a++;f(i+x,y+j,0);}
        }
    }
    return ;
}
int main(void){
    cin>>h>>w;
    for(int i=0;i<h;i++){
        cin>>s[i];
    }
    for(int i=0;i<h;i++){
        for(int j=0;j<w;j++){
            a=0,b=0;
            if(s[i][j]=='#'&&dp[i][j]==0){
                a++;
                dp[i][j]=1;
                f(i,j,0);
                ans+=a*b;
            }
        }
    }
    cout<<ans<<endl;
}