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>
#define rep(i,n) for(int i = 0; i < n; i++)
#define pb push_back
using namespace std;
typedef long long ll;

const int dx[4]={0,0,1,-1};
const int dy[4]={1,-1,0,0};

int h,w;  
vector<string> s;
vector<vector<int>> seen;
ll res;
ll res2;

void dfs(int y,int x){
  seen[y][x]=1;
  if(s[y][x]=='.') res++;
  else if(s[y][x]=='#') res2++;
  rep(i,4){
    int nx=x+dx[i]; int ny=y+dy[i];
    if(nx>=w||nx<0||ny>=h||ny<0) continue;
    if(s[y][x]==s[ny][nx]) continue;
    if(seen[ny][nx]!=0) continue;
    dfs(ny,nx);
  }
}

int main(){
  cin>>h>>w;
  s.resize(h);
  rep(i,h) cin>>s[i]; 
  
  ll ans=0;
  seen.assign(h,vector<int>(w));
  rep(i,h)rep(j,w){
    if(seen[i][j]==0){
      res=0;
      res2=0;
      dfs(i,j);
      ans+=res*res2;
    }
  }
  cout<<ans<<endl;
}