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;
#define ll long long
ll h,w;
char s[400][400];
bool used[400][400];
ll dcnt = 0;
ll dx[] = {1,0,-1,0}, dy[] = {0, 1, 0 ,-1};
ll dfs(ll x, ll y){
  if(used[x][y]) return 0;
  ll ret = 0;
  used[x][y] = true;
  if(s[x][y] == '.') ret++;
  else dcnt++;
  for(ll i=0;i<4;i++){
    if(x+dx[i] < 0 || y+dy[i] < 0 || x+dx[i] >=h || y+dy[i] >= w) continue;
    if(s[x+dx[i]][y+dy[i]] != s[x][y])
      ret += dfs(x+dx[i], y+dy[i]);
  }
  return ret;
}

int main(){
  cin >> h >> w;
  
  for(ll x=0;x<h;x++){
    for(ll y=0;y<w;y++){
      cin >> s[x][y];
      used[x][y] = false;
    }
  }
  ll ans = 0;
  for(ll x=0;x<h;x++){
    for(ll y=0;y<w;y++){
      if(s[x][y] == '#'){
        // cout << "x: " << x << " y: " << y << " start" << endl;
        dcnt = 0;
        ll tmp = dfs(x,y);
        ans += tmp*dcnt;
      }
    }
  }

  cout << ans << endl;

}