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 <bits/stdc++.h>
using namespace std;

//https://atcoder.jp/contests/aising2019/tasks/aising2019_c

int h, w, dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 };
long long c[2], ans = 0;
bool b[400][400], visited[400][400];
void dfs(int x, int y) {
	c[b[x][y]]++;
	for (int i = 0; i < 4; i++) {
		int nx = x + dx[i];
		int ny = y + dy[i];
		if (nx < 0 || nx >= h || ny < 0 || ny >= w)
			continue;
		if (visited[nx][ny] || b[nx][ny] == b[x][y])
			continue;
		visited[nx][ny] = 1;
		dfs(nx, ny);
	}
}

int main() {
	cin >> h >> w;
	for (int i = 0; i < h; i++) {
		string s;
		cin >> s;
		for (int j = 0; j < w; j++)
			b[i][j] = s[j] == '#';
	}
	for (int i = 0; i < h; i++)
		for (int j = 0; j < w; j++) {
			if (visited[i][j])
				continue;
			visited[i][j] = 1;
			c[0] = 0, c[1] = 0;
			dfs(i, j);
			ans += c[0] * c[1];
		}
	cout << ans << endl;
}