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;

typedef long long ll;

const int MAXN = 4e2 + 5;

const int dx[] = {0, 0, -1, 1};
const int dy[] = {-1, 1, 0, 0};

int N, M;
char mat[MAXN][MAXN];
bool bio[MAXN][MAXN];

void load() {
	scanf("%d%d", &N, &M);
	for (int i = 0; i < N; i++)
		scanf("%s", mat[i]);
}

void dfs(int x, int y, int &b, int &w) {
	bio[x][y] = true;
	if (mat[x][y] == '#')
		b++;
	else
		w++; 
	for (int i = 0; i < 4; i++) {
		int nx = x + dx[i];
		int ny = y + dy[i];
		if (nx < 0 || ny < 0 || nx >= N || ny >= M)
			continue;
		if (!bio[nx][ny] && mat[nx][ny] != mat[x][y])
			dfs(nx, ny, b, w);
	}
}

ll solve() {
	ll sol = 0;
	for (int i = 0; i < N; i++)
		for (int j = 0; j < M; j++)
			if (!bio[i][j]) {
				int black = 0, white = 0;
				dfs(i, j, black, white);
				sol += (ll)black * white;
			}
	return sol;
}

int main() {
	load();
	printf("%lld\n", solve());
	return 0;
}