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;
int H, W;
vector<string> S;
complex<int> f(int i, int j, char c) {
	if (!(0 <= i && i < H && 0 <= j && j < W)) return 0;
	if (S[i][j] != c) return 0;
	S[i][j] = '*';
	complex<int> r;
	if (c == '.') r.real(1); else r.imag(1);
	char cc = c == '.' ? '#' : '.';
	r += f(i+1,j,cc);
	r += f(i-1,j,cc);
	r += f(i,j+1,cc);
	r += f(i,j-1,cc);
	return r;
}
int main() {
	cin >> H >> W;
	S.resize(H);
	for (auto& x : S) cin >> x;
	long long r = 0;
	for (int i = 0; i < H; ++ i) for (int j = 0; j < W; ++ j) if (S[i][j] != '*') {
		auto n = f(i,j,S[i][j]);
		r += (long long)n.real() * n.imag();
	}
	cout << r << endl;
}