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 <iostream> // cin, cout, cerr
#include <algorithm> // minmax, sort, swap
#include <numeric> // iota
#include <cstdio> // printf, scanf
#include <string> // string, stoi, to_string
#include <vector> // vector
#include <queue> // queue, priority_queue
#include <deque> // deque
#include <map> // key-value pairs sorted by keys
#include <set> // set
#include <iomanip> // cout<<setprecision(n)
#include <functional> // function<void(int)>
#include <cmath>

#ifdef DEBUG
#include "debug.hpp"
#else
#define debug(...)
#endif

#define int long long // at least int64 > 9*10^18
#define ENDL '\n'
#define rep(i,n) for(int i = 0; i < (n); i++)
#define print(i) std::cout << (i) << '\n'
#define all(v) (v).begin(), (v).end()
/* libraries */

struct UnionFind
{
  int n;
  std::vector<int> par,size;
  UnionFind(int sz) : n(sz), par(sz,0), size(sz,1) {
    std::iota(par.begin(),par.end(),0);
  }
  int find(int x) {
    if(par[x]==x) return x;
    return par[x] = find(par[x]);
  }
  void unite(int x, int y) {
    x=find(x);y=find(y);
    if(x==y) return;
    if(size[x]<size[y]) std::swap(x,y);
    size[x]+=size[y];
    par[y]=x;
  }
};

int convert(int x, int y, int w) {
	return x*w+y;
}

signed main() {
	int h,w;
	std::cin >> h >> w;
	std::vector<std::string> g(h);
	rep(i,h) std::cin >> g[i];
	UnionFind uf(h*w);
	rep(x,h) {
		rep(y,w) {
			for(int dx=-1;dx<=1;dx++) {
				for(int dy=-1;dy<=1;dy++) {
					if(dx*dy!=0) continue;
					if(dx==0&&dy==0) continue;
					if(x+dx<0||x+dx>=h) continue;
					if(y+dy<0||y+dy>=w) continue;
					if(g[x][y]!=g[x+dx][y+dy]) uf.unite(convert(x,y,w),convert(x+dx,y+dy,w));
					debug(uf.par);
				}
			}
		}
	}
	std::map<int,int> mapw;
	std::map<int,int> mapb;
	debug(h,w);
	rep(i,h*w) {
		if(g[i/w][i%w]=='.') mapw[uf.find(i)]++;
		else mapb[uf.find(i)]++;
	}
	debug(mapw,mapb);
	debug(uf.par);
	int count = 0;
	for(auto x:mapw) {
		count+=x.second*mapb[x.first];
	}
	print(count);

	return 0;
}