Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include<bits/stdc++.h>
#include<fstream>
using namespace std;

void winter_is_coming()
{
	std::ios_base::sync_with_stdio(0);
	cin.tie(NULL); cout.tie(NULL );
}

int n,m,clr=0,ans=0;
char ch[401][401];
int vis[401][401];
bool valid(int x,int y, char c)
{
    if(x>=0 && x<n && y>=0 && y<m && vis[x][y]!=clr && ch[x][y]!=c )return true;
    return false;
}
void dfs(int x,int y)
{
    //cout<<x<<"------------- "<<y<<"\n";
    if(valid(x+1,y,ch[x][y]))
    {
        vis[x+1][y]=clr,dfs(x+1,y); if(ch[x+1][y]=='#')ans++;
    }
    if(valid(x-1,y,ch[x][y]))
    {
        vis[x-1][y]=clr,dfs(x-1,y); if(ch[x-1][y]=='#')ans++;
    }
    if(valid(x,y+1,ch[x][y]))
    {
        vis[x][y+1]=clr,dfs(x,y+1); if(ch[x][y+1]=='#')ans++;
    }
    if(valid(x,y-1,ch[x][y]))
    {
        vis[x][y-1]=clr,dfs(x,y-1); if(ch[x][y-1]=='#')ans++;
    }
}
int main()
{
   winter_is_coming();

   cin>>n>>m;
   for(int i=0;i<n;i++) for(int j=0;j<m;j++) cin>>ch[i][j];


   for(int i=0;i<n;i++)
   {
      for(int j=0;j<m;j++)
      {
         clr++;
         vis[i][j]=clr;
        if(ch[i][j]=='.') dfs(i,j);
      }
   }
   cout<<ans<<"\n";


    return 0;
}