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>
using namespace std;
using Graph = vector<vector<int>>;
#define rep(i,n) for (int i = 0; i < (n); i++)
typedef pair<int,int> P;
const int INF = 100000000;

int W,H;
int sy, sx, gy, gx;

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

bool movable(vector<vector<char>> &c, vector<vector<int>> &mat, int h, int w, int hb, int wb) {
  if ((h<0) || (h>=H) || (w<0) || (w>=W)) {
    return false;
  }
  else if (mat[h][w]!=INF || (c[h][w]==c[hb][wb])) {
    return false;
  }
  else {
    return true;
  }
}


int bfs(vector<vector<char>> &c, vector<vector<int>> &mat, pair<int,int> &q) {
  int r = 0;
  int k,s;
  k=s=0;
  k = 1;
  queue<P> que;
  que.push(q);
  
  if (mat[q.first][q.second] != INF) return 0;
  else (mat[q.first][q.second] = 0);

  while(que.size()) {
    P p = que.front();
    que.pop();

    rep(i,4){
      if (movable(c,mat,p.first+dy[i],p.second+dx[i],p.first,p.second)) {
        que.push(P(p.first+dy[i],p.second+dx[i]));
        mat[p.first+dy[i]][p.second+dx[i]]=mat[p.first][p.second]+1;
        if (c[p.first+dy[i]][p.second+dx[i]]=='.') s++;
        else k++;
      }
    }
  }
  return k*s;
}

int main() {
  int black = 0;
  cin >> H >> W;

  vector<vector<char>> c(H,vector<char> (W));
  vector<pair<int,int>> P;
  rep(h,H) {
      string s;
      cin >> s;
    rep(w,W) {
      c[h][w] = s[w];
      if (s[w]=='#') {
          P.push_back(make_pair(h,w));
      }
    }
  }
  vector<vector<int>> mat(H,vector<int> (W, INF));
  int ans = 0;
  for (auto p: P) {
    int tmp = bfs(c,mat,p);
    ans += tmp;

  }
    cout << ans << endl;
}