Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

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

int h,w;  
vector<string> s;
vector<vector<int>> seen;
int res;
int res2;

void dfs(int y,int x){
  seen[y][x]=1;
  if(s[y][x]=='.') res++;
  else if(s[y][x]=='#') res2++;
  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[y][x]==s[ny][nx]) continue;
    if(seen[ny][nx]!=0) continue;
    dfs(ny,nx);
  }
}

int main(){
  cin>>h>>w;
  s.resize(h);
  rep(i,h) cin>>s[i]; 
  
  int ans=0;
  seen.assign(h,vector<int>(w));
  rep(i,h)rep(j,w){
    if(s[i][j]=='#'&&seen[i][j]==0){
      res=0;
      res2=0;
      dfs(i,j);
      ans+=res*res2;
    }
  }
  cout<<ans<<endl;
}