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;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,int> pli;
typedef pair<int,ll> pil;

const int INF = 1e9 ;
const int maxN = 1e3 + 5;

int n,h,w;
char a[maxN][maxN];
int dx[4] = {1,-1,0,0};
int dy[4] = {0,0,1,-1};
ll ans = 0;
int vis[maxN][maxN]; 
int flag = 0;
int bl = 0,wt = 0;
void check(int x,int y)
{
	vis[x][y] = 1;
	if(a[x][y] == '#')
	{
		bl++;
	}
	else
	{
		wt++;
	}
	for(int i=0;i<4;i++)
	{
		int tx = x + dx[i];
		int ty = y + dy[i];
		if(tx<1 || tx >h || ty<1 || ty >w) continue;
		if(vis[tx][ty]) continue;
		if(a[x][y] != a[tx][ty])
		{
			check(tx,ty);
		}
	}
}
int main()
{
	scanf("%d%d",&h,&w);
	for(int i=1;i<=h;i++)
	{
		scanf("%s",a[i]+1);
	}
	for(int i=1;i<=h;i++)
	{
		for(int j=1;j<=w;j++)
		{
			bl=0,wt=0;
			if(!vis[i][j])
			{
				check(i,j);
			}
			ans += ((ll)wt*bl);
		}
	}
	cout<<ans<<endl;
	return 0;
}