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;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int H,W;
string S[444];
vector<vector<int>> G(444*444);
int color[444*444];
int visit[444*444];
ll whi,bla;

void bfs(int v){
  visit[v]=1;
  if(color[v]) bla++;
  else whi++;
  for(int u:G[v]) if(!visit[u]){
    bfs(u);
  }
}

int main(){
  cin>>H>>W;
  rep(i,H) cin>>S[i];
  rep(i,H) rep(j,W){
    int cur=i*W+j,d=(i+1)*W+j, r=i*W+j+1;
    color[cur]=(S[i][j]=='#');
    if(S[i][j]!=S[i+1][j]&&i+1<H){
      G[cur].push_back(d);
      G[d].push_back(cur);
    }
    if(S[i][j]!=S[i][j+1]&&j+1<W){
      G[cur].push_back(r);
      G[r].push_back(cur);
    }
  }
  ll ans=0;
  rep(i,H*W) if(!visit[i]){
    whi=0,bla=0;
    bfs(i);
    ans+=whi*bla;
  }
  cout<<ans<<endl;
  return 0;
}