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;
using ll = long long;
const ll mod = 998244353;

int dx[4] = {1,0,-1,0};
int dy[4] = {0,-1,0,1};
const int limit = 410;
using pint = pair<int,int>;

int h,w;
vector<string>s;

ll numb=0,numw=0;
bool paint[limit][limit];
void dfs(int x, int y){
  paint[x][y]=true;
  if(s[x][y]=='#') numb++;
  else numw++;
  
  for(int i=0; i<4; i++){
    int nx = x+dx[i];
    int ny = y+dy[i];
    
    if(nx<0 || nx>=h || ny<0 || ny>=w) continue;
    if(s[x][y] == s[nx][ny])continue;
    if(paint[nx][ny]) continue;
    
    dfs(nx,ny);
  }  
}

int main(){
  cin >> h >> w;
  s.resize(h);
  for(int i=0; i<h; i++) cin >> s[i];
  
  ll ans=0;
  for(int x=0; x<h; x++){
   for(int y=0; y<w; y++){
     if(paint[x][y]) continue;
     numb = numw = 0;
     dfs(x,y);
     ans+= numb*numw;
   }
  }
  
  
  cout << ans << endl;
  
  
  return 0;
  
  
  
}