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>
#define INF 2147483647
#define INF_LL 9223372036854775807
#define MOD 1000000007
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

int main() {
	int H, W;
	cin >> H >> W;
	vector<string> m(H);
	for (int i = 0; i < H; i++) {
		cin >> m[i];
	}
	ll ans = 0;
	for (int i = 0; i < H; i++)for (int j = 0; j < W; j++) {
		if (m[i][j] == '#') {
			if (i != 0) {
				if (m[i - 1][j] == '.') ans++;
			}
			if (i != H - 1) {
				if (m[i + 1][j] == '.')ans++;
			}
			if (j != 0) {
				if (m[i][j-1] == '.') ans++;
			}
			if (j != W-1) {
				if (m[i][j + 1] == '.') ans++;
			}
		}
	}
	cout << ans << endl;
	return 0;
}