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 MAX=1e6+5;
int dir[4][2]={0,1,0,-1,1,0,-1,0};
int n,m;
char mmp[500][500];
bool vis[500][500];
void dfs(int i,int j,int tag,ll &x,ll &y)
{
    if(vis[i][j])return;
    vis[i][j]=1;

    if(mmp[i][j]=='#')x++;
    else y++;
    for(int k=0;k<4;k++)
    {
        int di=i+dir[k][0];
        int dj=j+dir[k][1];
        if(di<1||dj<1||di>n||dj>m)continue;
        int t=mmp[di][dj]=='#';
        if(t!=tag)dfs(di,dj,t,x,y);
    }
}
int main()
{
    while(cin>>n>>m)
    {
        memset(vis,0,sizeof(vis));
        for(int i=1;i<=n;i++)
            scanf("%s",mmp[i]+1);
        ll ans=0;
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=m;j++)if(mmp[i][j]=='#'&&!vis[i][j])
            {
                ll x=0,y=0;
                dfs(i,j,1,x,y);
                ans+=x*y;
            }
        }
        cout<<ans<<endl;
    }
}