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>

using namespace std;

int H, W;
bool map[400][400], isused[400][400];
long long cttr, ctfl;//探索してる部分グラフでのノードでの　true falseの数のカウント
int vx[4] = { 1,0,-1,0 }, vy[4] = { 0,1,0,-1 };

void search(int i, int j) {
	isused[i][j] = true;
	if (map[i][j])cttr++;
	else ctfl++;
	for (int k = 0; k < 4; k++) {
		int nx = i + vx[k], ny = j + vy[k];
		if (nx < 0 || ny < 0 || nx >= H || ny >= W)continue;
		if (isused[nx][ny] || map[nx][ny] == map[i][j])continue;
		search(nx, ny);
	}
}

int main() {
	cin >> H >> W;
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			char c;
			cin >> c;
			if (c == '#')map[i][j] = true;
			else map[i][j] = false;
		}
	}
	long long ans = 0;
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			if (isused[i][j] || !map[i][j])continue;
			cttr = 0, ctfl = 0;
			search(i, j);
			ans += (cttr * ctfl);
		}
	}
	cout << ans << endl;
	return 0;
}