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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <algorithm>
#include <vector>
#include <cassert>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define mod 1000000007
#define fi first
#define sc second
#define rep(i,x) for(int i=0;i<x;i++)
#define repn(i,x) for(int i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())
int h,w;
string s[405];
int par[200005],ran[200005];
void init(){ for(int i=0;i<200005;i++) par[i] = i; }
int find(int x){ if(x == par[x]) return x; else return par[x] = find(par[x]); }
void unite(int x,int y){
	x = find(x); y = find(y); if(x==y) return;
	if(ran[x] < ran[y]) par[x] = y;
	else{
		par[y] = x;
		if(ran[x] == ran[y]) ran[x]++;
	}
}
bool same(int x,int y){ return find(x)==find(y); }
int cnt[200005][2];
int main(){
	cin>>h>>w;
	int n = h, m = w;
	rep(i,h){
		cin>>s[i];
	}
	init();
	rep(i,h){
		rep(j,w){
			int dx[4]={0,1,0,-1};
			int dy[4]={1,0,-1,0};
			rep(k,4){
				int nx = i+dx[k];
				int ny = j+dy[k];
				if(0<=nx&&nx<n&&0<=ny&&ny<m&&s[i][j] != s[nx][ny]){
					unite(i*401+j,nx*401+ny);
				}
			}
		}
	}
	rep(i,h){
		rep(j,w){
			cnt[find(i*401+j)][(s[i][j]=='#')] ++;
		}
	}
	ll ans = 0;
	for(int i=0;i<200005;i++) ans+=1LL*cnt[i][0]*cnt[i][1];
	cout<<ans<<endl;
}