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)


#if 1
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <array>
#include <deque>
#include <algorithm>
#include <utility>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <list>

auto& in = std::cin;
auto& out = std::cout;
#define all_range(C) std::begin(C), std::end(C)
const double PI = 3.141592653589793238462643383279502884197169399375105820974944;

int32_t H,W;
char map[400][410];
bool passed[400][400];
std::pair<int64_t, int64_t> func(int i, int j)
{
	assert(passed[i][j] == false);
	passed[i][j] = true;

	std::pair<int64_t, int64_t> res;
	if (map[i][j] == '#') {
		res.first += 1;
	}
	else {
		res.second += 1;
	}
	const int diff[] = { -1,0,1,0,-1 };
	for (size_t d = 0; d < 4; d++)
	{
		int ni = diff[d] + i;
		int nj = diff[d+1] + j;
		if (0 <= ni && ni < H && 0 <= nj && nj < W && passed[ni][nj] == false && map[ni][nj] != map[i][j]) {
			auto t =func(ni, nj);
			res.first += t.first;
			res.second += t.second;
		}
	}
	return res;
}

int main()
{
	using std::endl;
	in.sync_with_stdio(false);
	out.sync_with_stdio(false);
	in.tie(nullptr);
	out.tie(nullptr);

	in >> H>>W;
	for (size_t i = 0; i < H; i++)
	{
		in >> map[i];
	}
	
	int64_t res = 0;
	for (size_t i = 0; i < H; i++)
	{
		for (size_t j = 0; j < W; j++)
		{
			if (passed[i][j] == false)
			{
				auto tmp = func(i, j);
				res += tmp.first * tmp.second;
			}
		}
	}
	out << res << endl;

	return 0;
}
#endif