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 ll = long long;
using namespace std;
const int INFint = 1e9+1;
const ll INFll = (ll)1e18+1;
ll MOD=1e9+7;

int H,W;
string s[500];
bool pathed[500][500] = {0};
ll cntw(0),cntb(0);
int th[4]= {1,-1,0,0};
int tw[4]= {0,0,1,-1};

void dfs(int h,int w){
  //cout << h <<  " " << w << endl;
  pathed[h][w] = true;
  if(s[h][w] == '.') cntw++;
  else cntb++;
  for(int i(0);i<4;i++){
    int nh = h+th[i],nw = w + tw[i];
    if(nh < H && nh >= 0 && nw < W && nw >= 0 && pathed[nh][nw] == false && s[h][w] != s[nh][nw]){
      dfs(nh,nw);
    }
  }
}
int main(){
  cin>>H>>W;
  for(int i(0);i<H;i++){
    cin>>s[i];
  } 
  ll cnt(0);
  for(int i(0);i<H;i++){
    for(int j(0);j<W;j++){
      if(pathed[i][j] == false){
        cntw = 0;
        cntb = 0;
        dfs(i,j);
        cnt += cntb*cntw;
      }
    }
  }
  cout << cnt << endl;
  return 0;
}