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; 
char C[410][410] = {}; 
int A[410][410] = {}; 
int a; 
void dfs(int x, int y, int a){
	if(A[x][y] > 0) return; 
	A[x][y] = a; 
	if(x < H && C[x][y] != C[x+1][y]) dfs(x+1, y, a); 
	if(x > 0 && C[x][y] != C[x-1][y]) dfs(x-1, y, a); 
	if(y < W && C[x][y] != C[x][y+1]) dfs(x, y+1, a); 
	if(y > 0 && C[x][y] != C[x][y-1]) dfs(x, y-1, a); 
}
int main(){
    cin >> H >> W; 
	for(int i = 0; i < H; i++){
		for(int j = 0; j < W; j++){
			cin >> C[i][j]; 
		}
	}
	a = 1; 
	for(int i = 0; i < H; i++){
		for(int j = 0; j < W; j++){
			dfs(i, j, a); 
			a++;
		}
	}
	long long int X[160010][2] = {}; 
	for(int i = 0; i < H; i++){
		for(int j = 0; j < W; j++){
			X[A[i][j]][(i + j) % 2] ++;
		}
	}
	long long int ans = 0; 
	for(int i = 1; i <= H * W; i++){
		ans += X[i][0] * X[i][1];
	}
	cout << ans << endl; 
}