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>
#define ll long long
#define fort(i,n) for (int i = 1; i <= n; ++i)
#define pi pair<int,int>
#define vi vector<int>
#define pb push_back
#define sz size()
#define er erase
#define fr first
#define sc second
#define rc(x) return cout << x, 0
using namespace std;

ll h,w,v[405][405],ans,a,b;
char c[405][405];

void go(int i, int j)
{
    if (v[i][j]) return;
    v[i][j]=1;
    if (c[i][j]=='#') ++a;
    else ++b;
    if (i>1&&c[i-1][j]!=c[i][j]) go(i-1,j);
    if (j>1&&c[i][j-1]!=c[i][j]) go(i,j-1);
    if (i<h&&c[i+1][j]!=c[i][j]) go(i+1,j);
    if (j<w&&c[i][j+1]!=c[i][j]) go(i,j+1);
}

int32_t main()
{
    ios_base :: sync_with_stdio(0); cin.tie(); cout.tie();
    cin >> h >> w;
    fort (i,h)
        fort (j,w)
            cin >> c[i][j];
    fort (i,h)
        fort (j,w)
        {
            a=0,b=0;
            go(i,j);
            ans+=a*b;
        }
    cout << ans;
}