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 <vector>
#include <algorithm>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <array>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

int main()
{
    ll H, W;
    string Si;
    cin >> H >> W;
    int S[H][W];
    for(int i=0;i<H;i++){
        cin >> Si;
        for(int j=0;j<W;j++){
            S[i][j] = Si[j]=='#'? 1:0;
        }
    }
    int cmap[H][W];
    for(int i=0;i<H;i++){
        for(int j=0;j<W;j++){
            cmap[i][j]=-1;
        }
    }
    int imax=0;
    for(int i=0;i<H;i++){
        for(int j=0;j<W;j++){
            if(cmap[i][j]!=-1) continue;
            cmap[i][j] = ++imax;
            queue<array<int,2>> q;
            q.push(array<int,2>{i,j});
            while(!q.empty()){
                auto ij = q.front(); q.pop();
                auto x = ij[0];
                auto y = ij[1];
                if(y-1>=0 && cmap[x  ][y-1]==-1 && S[x][y] + S[x  ][y-1] == 1){ q.push(array<int,2>{x  ,y-1});cmap[x  ][y-1] = imax;}
                if(y+1< W && cmap[x  ][y+1]==-1 && S[x][y] + S[x  ][y+1] == 1){ q.push(array<int,2>{x  ,y+1});cmap[x  ][y+1] = imax;}
                if(x-1>=0 && cmap[x-1][y  ]==-1 && S[x][y] + S[x-1][y  ] == 1){ q.push(array<int,2>{x-1,y  });cmap[x-1][y  ] = imax;}
                if(x+1< H && cmap[x+1][y  ]==-1 && S[x][y] + S[x+1][y  ] == 1){ q.push(array<int,2>{x+1,y  });cmap[x+1][y  ] = imax;}
            }
        }
    }
    map<int, array<int,2>> group;
    for(int i=0;i<H;i++){
        for(int j=0;j<W;j++){
            if(group.count(cmap[i][j])==0) group[cmap[i][j]] = array<int,2>{0,0};
            if(S[i][j]) group[cmap[i][j]][0]++;
            else        group[cmap[i][j]][1]++;
        }
    }
    ll count = 0;
    for(auto m : group){
        count += m.second[0] * m.second[1];
    }



    cout<<count<<endl;

    return 0;
}