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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int nextInt();
int dif(int a, int b){return a<b?b-a:a-b;}

int H, W, S[400][401], i, j, f, g, l;
int par[160000], rank[160000];
int num[160000][2];
long long int ans;

void init(int n){
	for(int i=0; i<n; i++){
		par[i] = i;
		rank[i] = 0;
	}
}

int find(int x){
	if(par[x] == 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(rank[x] < rank[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if(rank[x] == rank[y]){rank[x]++;}
	}
}

int main(){
	H = nextInt();
	W = nextInt();
	for(i=0; i<H; i++){
		for(j=0; j<W; j++){
			S[i][j] = getchar();
		}
		getchar();
	}
	init(W*H);
	for(i=0; i<H; i++){
		for(j=0; j<W; j++){
			if(i>0){
				if(S[i][j]!=S[i-1][j]){unite(W*i+j, W*(i-1)+j);}
			}
			if(j>0){
				if(S[i][j]!=S[i][j-1]){unite(W*i+j, W*i+(j-1));}
			}
		}
	}
	for(i=0; i<H; i++){
		for(j=0; j<W; j++){
			f = W*i+j;
			g = find(f);
			if((dif(i, g/W)+dif(j, g%W)) & 1){
				num[g][1]++;
			}else{
				num[g][0]++;
			}
		}
	}
	for(i=0, l=W*H; i<l; i++){
		ans += num[i][0]*num[i][1];
	}
	printf("%lld\n", ans);
	return 0;
}

int nextInt(){
	int f=0; char c=getchar();
	while((c<'0')||('9'<c)){c=getchar();}
	while((c>='0')&&(c<='9')){f=f*10+(c-'0'); c=getchar();}
	return f;
}