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;

#define ll long long
#define INF 10e10
#define rep(i,n) for(int i=0; i<n; i++)
#define repr(i,n,m) for(int i=m; i<n; i++)
#define MAX 100
#define MOD 1000000007
#define pb push_back
#define debug(x) cout << x << endl;
#define END cout << endl;
#define sorti(x) sort(x.begin(), x.end())

int d[401][401];
ll ans = 0;
int h,w;
char s[401][401];

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

void dfs(int x, int y, char now, int t) {
  if (t > 0) ans += 1;
  d[x][y] = 1;
  for (int i = 0; i < 4; ++i) {
    int nx = x + dx[i], ny = dy[i] + y;
    if (nx >= 0 and nx < h and ny >= 0 and ny < w and d[nx][ny] == 0) {
      if (now == '#') {
        if (s[nx][ny] != '#') {
          dfs(nx,ny,'.',1);
        }
      } else {
        if (s[nx][ny] != '.') {
          dfs(nx,ny,'#',1);
        }
      }
    }
  }
  d[x][y] = 0;
}

int main() {
  cin >> h >> w;

  vector<pair<int,int> > p;
  rep(i,h) rep(j,w){
    cin >> s[i][j];
  }
  ll cnt1 = 0;
  for (int tt = 0; tt < h; ++tt) {
    for (int i = 0; i < w; ++i) {
      // kuromasukara
      if (s[tt][i] == '#') {
        dfs(tt,i,'#',0);
      }
    }
  }

  cout << ans / 2 << endl;
}