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>
#define N 405
using namespace std;

typedef long long ll;
ll h, w, s, c1, c2;
ll dy[4] = {-1, 0, 1, 0};
ll dx[4] = {0, 1, 0, -1};
bool v[N][N];
char a[N][N];

void f(ll p, ll q) {
	ll i;
	if (v[p][q]) return;
	v[p][q] = 1;
    if (a[p][q] == '#') c1++;
    else c2++;
    for (i = 0; i < 4; i++) {
		if (a[p][q] != a[p + dy[i]][q + dx[i]]) f(p + dy[i], q + dx[i]);
    }
}

int main()
{
	ll i, j;
	cin >> h >> w;
	for (i = 0; i <= h + 1; i++) for (j = 0; j <= w + 1; j++) v[i][j] = 1;
	for (i = 1; i <= h; i++) for (j = 1; j <= w; j++) v[i][j] = 0;
	for (i = 1; i <= h; i++) {
		scanf("%s", &a[i][1]);
	}
	for (i = 1; i <= h; i++) {
		for (j = 1; j <= w; j++) {
			c1 = c2 = 0;
			f(i, j);
			s += c1 * c2;
		}
	}
    cout << s << endl;
    return 0;
}