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 <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int (i)=(0);(i)<(int)(n);++(i))
using ll = long long;
using P = pair<ll, ll>;
using namespace std;

template<class T> void vin(vector<T>& v, int n) {
    v.resize(n);
    for (int i = 0; i < n; ++i) {
        cin >> v[i];
    }
}

int ans[400*400+1];

struct UnionFind {
    vector<int> v;
    UnionFind(int N) :v(N, -1) {}
    int root(int x) {
        if (v[x] < 0) return x;
        else return v[x] = root(v[x]);
    }
    void unite(int x, int y) {
        x = root(x);
        y = root(y);
        if (x == y) return;
        if (v[x] > v[y]) swap(x, y);
        v[x] += v[y];
        v[y] = x;
    }
    int size(int x) {
        return -v[root(x)];
    }
};

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

bool ok(int h, int w, int x, int y) {
    return 0 <= x and x < w and 0 <= y and y < h;
}

ll kuro[400*400+2];
ll siro[400*400+2];

int main() {
    int H, W;
    cin >> H >> W;
    string s[500];
    rep(i, H) cin >> s[i];

    UnionFind uf(H*W);
    rep(r, H) rep(c, W) {
        if (s[r][c] == '#') {
            rep(d, 4) {
                int nr = r + dy[d], nc = c + dx[d];
                if (ok(H, W, nc, nr) and s[nr][nc] == '.') uf.unite(r*W+c, nr*W+nc);
            }
        }
    }

    //cout << uf.same(0, 2) << endl;

    rep(r, H) rep(c, W) {
        if (s[r][c] == '.') siro[uf.root(r*W+c)]++;
        else kuro[uf.root(r*W+c)]++;
    }

    ll ret = 0;
    rep(r, H) rep(c, W) {
        ret += siro[r*W+c]*kuro[r*W+c];
    }
    cout << ret << endl;
}