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;

int gox[4] = {1,-1,0,0};
int goy[4] = {0,0,1,-1};
typedef long long ll;

bool vis[410][410];
int n,m;
char a[410][410];

ll num1,num2;

void dfs(int x,int y,char f){
    vis[x][y] = 1;
    if(f=='#')
    num1++;
    else num2++;
    for(int i=0;i<4;i++){
        int nowx = x+gox[i];
        int nowy = y+goy[i];
        if(nowx<0||nowx>=n||nowy<0||nowy>=m||a[nowx][nowy]==f||vis[nowx][nowy])continue;
        dfs(nowx,nowy,a[nowx][nowy]);
    }
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=0;i<n;i++){
        scanf("%s",a[i]);
    }
    ll res = 0;
    for(int i=0;i<n;i++){
        for(int j=0;j<m;j++){
            num1 = num2 = 0;
            if(!vis[i][j]){
            dfs(i,j,a[i][j]);
            res+=num1*num2;
            }
        }
    }
    printf("%lld\n",res);
    return 0;
}