Problem: 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.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio>
using namespace std;
typedef long long ll;
ll h, w, ca, cb, ans;
bool v[405][405];
char a[405][405];

void f(ll p, ll q) {
	if(p<1 || q<1 || p>h || q>w || v[p][q]) return;
	v[p][q] = 1;
	if(a[p][q]=='#') ca++; else cb++;
	if(a[p][q] != a[p+1][q]) f(p+1, q);
	if(a[p][q] != a[p-1][q]) f(p-1, q);
	if(a[p][q] != a[p][q+1]) f(p, q+1);
	if(a[p][q] != a[p][q-1]) f(p, q-1);
}

int main() {
	ll i, j;
	cin>>h>>w;
	for(i=1; i<=h; i++) scanf("%s", &a[i][1]);
	for(i=1; i<=h; i++) for(j=1; j<=w; j++) {
		if(!v[i][j]) {
			ca = cb = 0;
			f(i, j);
			ans += ca * cb;
		}
	}
	cout<<ans<<endl;
	return 0;
}