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

int h,w;
vector<string> s;

void dfs(int y, int x, vector<vector<int>> &seen, int &p, int &q){
  if(seen[y][x] == 1)
    return;
  seen[y][x] = 1;
  if (s[y][x] == '#') p++;
  if (s[y][x] == '.') q++;

  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[ny][nx] == s[y][x]) continue;
    dfs(ny,nx,seen,p,q);
  }
  return;
}

int main(){
  cin>>h>>w;
  s.resize(h);
  rep(i,h) cin>>s[i];

  vector<vector<int>> seen(h,vector<int>(w,0));
  ll ans = 0;
  int p,q;
  rep(i,h)rep(j,w){
      p = 0;
      q = 0;
      dfs(i,j,seen,p,q);
      ans += (ll)p*q;
  }
  cout<<ans<<endl;
}