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

string s[410];
int Y, X;

int dx[4] = {1,0,-1,0};
int dy[4] = {0,1,0,-1};

void calc(int y, int x, int &black, int &white, char pre) {
    if (y < 0 || x < 0 || x>=X || y>=Y) return;
    if (s[y][x] == '!' || s[y][x] == pre) return;
    if (s[y][x] == '#') black++;
    if (s[y][x] == '.') white++;
    char cur = s[y][x];
    s[y][x] = '!';
    rep(i,4){
        calc(y+dy[i], x+dx[i], black, white, cur);
    }
}

int main(void){
    cin >> Y >> X;
    rep(y,Y) cin >> s[y];

    int res = 0;
    rep(y,Y) rep(x,X){
        int black = 0;
        int white = 0;
        calc(y, x, black, white, '!');
        res += black * white;
    }
    cout << res << endl;
    return 0;
}