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: Accepted)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>

#define REP(i, a, b) for (int i = int(a); i < int(b); i++)
#define dump(val) cerr << __LINE__ << ":\t" << #val << " = " << (val) << endl

using namespace std;

typedef long long int ll;

template<typename T>
vector<T> make_v(size_t a, T b) {
    return vector<T>(a, b);
}

template<typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

class UnionFind {
public:
    vector<int> par;
    vector<ll> white;
    UnionFind(int n) {
        par.resize(n);
        white.resize(n, 0);
        REP(i, 0, n) {
            par[i] = i;
        }
    }
    int Find(int n) {
        return (n == par[n] ? n : par[n] = Find(par[n]));
    }
    bool Union(int a, int b, bool at, bool bt) {
        a = Find(a);
        b = Find(b);
        if (a == b) return false;
        par[a] = b;
        if (at && white[a] == 0) {
            white[a]++;
        }
        if (bt && white[b] == 0) {
            white[b]++;
        }
        white[a] += white[b];
        white[b] = white[a];
        return true;
    }
    ll getWhite(int n) {
        return white[Find(n)];
    }
};

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int H, W;
    cin >> H >> W;
    auto mp = make_v(H, W, ' ');
    REP(i, 0, H) {
        REP(j, 0, W) {
            cin >> mp[i][j];
        }
    }
    UnionFind uf(H * W);
    int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
    REP(i, 0, H) {
        REP(j, 0, W) {
            REP(k, 0, 4) {
                int nx = j + dx[k], ny = i + dy[k];
                if (nx < 0 || nx >= W || ny < 0 || ny >= H || mp[ny][nx] == mp[i][j]) continue;
                uf.Union(i * W + j, ny * W + nx, mp[i][j] == '.', mp[ny][nx] == '.');
            }
        }
    }

    ll ans = 0;
    REP(i, 0, H) {
        REP(j, 0, W) {
            if (mp[i][j] == '#') {
                ans += uf.getWhite(i * W + j);
            }
        }
    }

    cout << ans << endl;

    return 0;
}