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<algorithm>
#include<vector>
#include<string>
#define int long long
using namespace std;

int h, w;
int W, B;
bool a[400][400];//使ったか？
string b[400];
int dx[4] = { -1,0,0,1 }, dy[4] = { 0,-1,1,0 };
void saiki(int x, int y) {
	if (a[x][y])return;
	a[x][y] = true;
	if (b[x][y] == '#')B++;
	else W++;
	for (int i = 0; i < 4; i++) {
		if (x + dx[i] < h&&x + dx[i] >= 0 && y + dy[i] < w&&y + dy[i] >= 0 && b[x + dx[i]][y + dy[i]] != b[x][y]) {
			saiki(x + dx[i], y + dy[i]);
		}
	}
}
signed main() {
	cin >> h >> w;
	for (int i = 0; i < h; i++)cin >> b[i];
	int ans = 0;
	for (int i = 0; i < h; i++) {
		for (int j = 0; j < w; j++) {
			W = B = 0;
			saiki(i, j);
			ans += B*W;
		}
	}
	cout << ans << endl;
}