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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using Graph_c = vector<vector<char>>;
using ll=long long;
// 幅優先探索
struct Z{
  ll y;
  ll x;
  bool black;
};

ll H,W,y,x,ans=0;
vector<ll> y_vec={1,0,-1,0};
vector<ll> x_vec={0,1,0,-1};
Graph_c A,B;
queue<Z> q;
bool black;
ll bfs(){
  while(!q.empty()){
    Z now=q.front(); q.pop();
    y=now.y, x=now.x, black=now.black;
    for(int k=0; k<4; k++){
      if(black==true){
        Z next={y+y_vec[k], x+x_vec[k], false};
        if(A[next.y][next.x]=='.'){
          A[next.y][next.x]='0';
          ans++;
          q.push(next);
        }
      }
      else{
        Z next={y+y_vec[k], x+x_vec[k], true};
        if(A[next.y][next.x]=='#'){
          A[next.y][next.x]='0';
          q.push(next);
        }
      }
    }
  }
  return 0;
}

int main(){
  cin>>H>>W;
  A.assign(H+2, vector<char>(W+2, '0'));
  for(int i=1; i<=H; i++){
    string S; cin>>S;
    for(int j=1; j<=W; j++){
      A[i][j]=S[j-1];
    }
  }
  B=A;
  for(int i=1; i<=H; i++){
    for(int j=1; j<=W; j++){
      if(A[i][j]!='#') continue;
      black=true;
      A[i][j]='0';
      Z start={i,j,black};
      q.emplace(start);
      bfs();
      A=B;
    }
  }
  cout<<ans<<endl;
}