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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;


namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] In = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            h = In[0];
            w = In[1];
            M = new char[h, w];
            for(int i=0; i < h; i++)
            {
                string In2 = Console.ReadLine();
                for(int j = 0; j < w; j++)
                {
                    M[i, j] = In2[j];
                }
            }
            ans = 0;
            //始める点(#)
            for(int i = 0; i < h; i++)
            {
                for(int j=0; j < w; j++)
                {
                    if (M[i, j] == '.') continue;
                    //終える点(.)
                    for (int x = 0; x < h; x++)
                    {
                        for(int y = 0; y < w; y++)
                        {
                            if (M[x, y] == '#') continue;
                            B = new bool[h, w];
                            dis = (int)(Math.Abs(i - x) + Math.Abs(j - y));
                            Chk(i, j, x, y, 0);
                        }
                    }
                }
            }
            Console.WriteLine(ans);
        }
        static public int h, w;
        static public int ans;
        static public char[,] M;
        static public bool[,] B;
        static public int dis;
        static public void Chk(int x1,int y1, int x2, int y2, int cnt)
        {
            if (cnt % 2 == 0) if (M[x1, y1] == '.') return;
            if (cnt % 2 == 1) if (M[x1, y1] == '#') return;
            if (dis == cnt)
            {
                if (x1 == x2 && y1 == y2 && !B[x1,y1]) { ans++; B[x1,y1]=true; }
                return;
            }
            cnt++;
            //上
            if (0 <= x1 - 1) Chk(x1 - 1, y1, x2, y2, cnt);
            //下
            if (x1 + 1 <  h) Chk(x1 + 1, y1, x2, y2, cnt);
            //左
            if (0 <= y1 - 1) Chk(x1, y1 - 1, x2, y2, cnt);
            //右
            if (y1 + 1 <  w) Chk(x1, y1 + 1, x2, y2, cnt);

        }

    }
}