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 <stdio.h>
#include <string>
#include <iostream>
#include <iomanip>
#include <map>
#include <algorithm>
#include <vector>
#include <math.h>
#define MOD 1000000007
using namespace std;

long long h,w,ans=0,black,white;
char temp;
int grid[404][404];
int visit[404][404];

void check(int i, int j, int iswhite){
    if(i<0 || h<=i || j<0 || w<=j);
    else if(visit[i][j]==1);
    else  if(grid[i][j]==iswhite){
        if(iswhite)white++;
        else black++;
        visit[i][j]=1;
        check(i,j+1,!iswhite);
        check(i+1,j,!iswhite);
        check(i,j-1,!iswhite);
        check(i-1,j,!iswhite);
    }
}
int main(void){
    cin >> h >> w;
    for(int i=0; i<h; i++){
        for(int j=0; j<w; j++){
            cin >> temp;
            if(temp=='#')grid[i][j]=0;
            else grid[i][j]=1;
        }
    }
    for(int i=0; i<h; i++){
        for(int j=0; j<w; j++){
            black=0;white=0;
            check(i,j,0);
            ans+=black*white;
        }
    }
    cout << ans << endl;
    return 0;
}