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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <list>
#include <deque>
#include <string>
#include <algorithm>
#include <cmath>
#include <ctype.h>
using namespace std;
#define dump(a) cout << (a) << '\n';
typedef long long Int;
Int mod = 1e9+7;
Int MOD = 998244353;

Int H, W;
Int b, w;
bool visited[500][500];

void dfs(vector<string> s, Int x, Int y) {
    if (visited[y][x]) return;
    visited[y][x] = true;
    if (s[y][x] == '#') b++;
    else if (s[y][x] == '.') w++;
    if (y > 0 && s[y][x] != s[y-1][x]) dfs(s, x, y-1);
    if (y < H-1 && s[y][x] != s[y+1][x]) dfs(s, x, y+1);
    if (x > 0 && s[y][x] != s[y][x-1]) dfs(s, x-1, y);
    if (x < W-1 && s[y][x] != s[y][x+1]) dfs(s, x+1, y);
}

int main() {
    ios::sync_with_stdio(false);
    cin >> H >> W;
    vector<string> s(H);
    for (Int i = 0; i < H; i++) cin >> s[i];
    Int res = 0;
    for (Int i = 0; i < H; i++) {
        for (Int j = 0; j < W; j++) {
            b = w = 0;
            dfs(s, j, i);
            //cout << b << " " << w << '\n';
            res += b*w;
        }
    }
    dump(res);
    return 0;  
}