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 <algorithm>
#include <vector>
#define mp make_pair 
#define x first
#define y second
#define ll long long
using namespace std;

ll h,w,sum,ans,a[405][405],ct,ww,sz;
char s[405][405];
vector <pair<int,int>  > v; 
void clear(int last){
	sz=v.size(); ww+=sz;
	for (int i=last;i<sz;i++){
		a[v[i].x][v[i].y]=0;
	}
}
void dfs (int x,int y,char d){
	if (a[x][y] == 0 && s[x][y] == '.')
	sum+=1;
	else
	if (a[x][y] == 0 && s[x][y] == '#'){
		ct+=1;
		s[x][y]='B';
	}
	
	a[x][y]=1;
	if (y-1 > 0 && s[x][y-1] != d && s[x][y-1] != 'B' && a[x][y-1] == 0)
	dfs(x,y-1,s[x][y-1]);
	if (x-1 > 0 && s[x-1][y] != d && s[x-1][y] != 'B' && a[x-1][y] == 0)
	dfs(x-1,y,s[x-1][y]);
	if (x+1 <= h && s[x+1][y] != d && s[x+1][y] != 'B' && a[x+1][y] == 0)
	dfs(x+1,y,s[x+1][y]);
	if (y+1 <= w && s[x][y+1] != d&& s[x][y+1] != 'B'  && a[x][y+1] == 0)
	dfs(x,y+1,s[x][y+1]);
} 
int main(){
	scanf("%lld%lld\n",&h,&w);
	for (int i=1;i<=h;i++){
		for (int j=1;j<=w;j++){
			scanf("%c",&s[i][j]);
		}
		if (i < h)
		scanf("\n");
	}
	for (int i=1;i<=h;i++){
		for (int j=1;j<=w;j++){
			if (s[i][j] == '#'){
				sum=0; ct=0;
				clear(ww);
				dfs(i,j,s[i][j]);
				ans+=sum*ct;
			}
		}
	}
	printf("%lld\n",ans);
	return 0;
}