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>
#define int long long
using namespace std;

int h,w;
string s[400];
int f[411][411];
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};

int white,black,ans;

void dfs(int x,int y,char ch){
    f[x][y]=1;
    if(s[x][y]=='.')white++;
    else black++;
    
    for(int i=0;i<4;i++){
        int kx=x+dx[i],ky=y+dy[i];
        if(kx>=0 && ky>=0 && kx<h && ky<w && s[kx][ky]!=ch && f[kx][ky]!=1){
        	if(ch=='.')dfs(kx,ky,'#');
        	else dfs(kx,ky,'.');
        }
    }
    
    
    
    return ;
}

signed 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++){
            if(s[i][j]=='#'){
                dfs(i,j,'#');
                ans+=black*white;
                //cout<<ans<<endl;
            }
            black=0;white=0;
        }
    }
    cout<<ans<<endl;
}