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 <iostream>
#include <queue>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <cmath>
#include <iomanip>

using namespace std;

#define REP(i,n) for(ll (i) = (0); (i) < (n); ++i)
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define ALL(v) v.begin(),v.end()
#define INF 1100000000
#define LLINF 1000000000000000000LL
#define MOD 1000000007
#define Decimal fixed << setpresicion(20)


typedef long long ll;
typedef pair<ll, ll> P;

int mp[500][500];
pair<int, int> par[500][500];
int kosu[500][500];
bool used[500][500];
int main()
{
  int H, W;
  cin >> H >> W;
  vector<pair<int, int>> pB;
  REP(i, H) REP(j, W) {
    char c; cin >> c;
    if (c == '#') {
      mp[i][j] = 1;
      pB.PB(MP(i, j));
    } else mp[i][j] = -1;
  }

  int dx[] = {-1, 0, 1, 0};
  int dy[] = {0, -1, 0, 1};
  int ans = 0;
  REP(i, 500) REP(j, 500) par[i][j] = MP(i, j);

  REP(i, pB.size()) {
    if (used[pB[i].FI][pB[i].SE]) {
      pair<int, int> pos = par[pB[i].FI][pB[i].SE];
      ans += kosu[pos.FI][pos.SE];
      continue;
    }
    queue<pair<int, int>> q;
    q.push(MP(pB[i].FI, pB[i].SE));
    used[pB[i].FI][pB[i].SE] = true;
    int cnt = 0;
    while (! q.empty()) {
      pair<int, int> pos = q.front(); q.pop();
      int y = pos.FI;
      int x = pos.SE;
      REP(j, 4) {
        int ny = y + dy[j];
        int nx = x + dx[j];
        if (0 <= ny && ny < H && 0 <= nx && nx < W
            && !used[ny][nx]
            && mp[y][x] * mp[ny][nx] == -1) {
          par[ny][nx] = MP(pB[i].FI, pB[i].SE);
          used[ny][nx] = true;
          q.push(MP(ny, nx));
          if (mp[ny][nx] == -1) cnt++;
        }
      }
    }
    ans += cnt;
    kosu[pB[i].FI][pB[i].SE] = cnt;
  }
  cout << ans << endl;
  return 0;
}