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;
ll h,w,cb=0,cw=0,ans=0;
char s[410][410];
bool b[410][410];

void search_area(int i,int j){
    b[i][j]=true;
    if(s[i][j]=='#') cb ++;
    if(s[i][j]=='.') cw ++;
    if(j<w-1&&s[i][j]!=s[i][j+1]&&!b[i][j+1]) search_area(i,j+1);
    if(j>0&&s[i][j]!=s[i][j-1]&&!b[i][j-1]) search_area(i,j-1);
    if(i<h-1&&s[i][j]!=s[i+1][j]&&!b[i+1][j]) search_area(i+1,j);
    if(i>0&&s[i][j]!=s[i-1][j]&&!b[i-1][j]) search_area(i-1,j);
    return;
}

int main(){
    cin >> h >> w;
    for(int i = 0;i < h;i ++){
        for(int j = 0;j < w;j ++){
            cin >> s[i][j];
        }
    }
    for(int i = 0;i < h;i ++){
        for(int j = 0;j < w;j ++){
            cb=0;
            cw=0;
            if(!b[i][j]){
                search_area(i,j);
                ans += cb*cw;
            }
        }
    }
    cout << ans << endl;
    return 0;
}