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 n,m;
long long a=0,b=0,ans=0;
char s[407][407];
int vis[407][407];
const int dir[4][2]={{1,0},{0,1},{-1,0},{0,-1}};
void dfs(int x,int y){
    vis[x][y]=1;
    if(s[x][y]=='#')
        b++;
    else if(s[x][y]=='.')
        a++;
    for(int i=0;i<4;i++)
        if(x+dir[i][0]>0&&x+dir[i][0]<=n&&y+dir[i][1]<=m&&y+dir[i][1]>0&&!vis[x+dir[i][0]][y+dir[i][1]]&&s[x+dir[i][0]][y+dir[i][1]]!=s[x][y])
            dfs(x+dir[i][0],y+dir[i][1]);
}
int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
        scanf("%s",s[i]+1);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=m;j++)
            if(!vis[i][j])
                a=b=0,dfs(i,j),ans+=a*b;
    printf("%lld",ans);
    return 0;
}