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: Accepted)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace エイシングプログラミングコンテスト2019C
{
    class Program
    {
        static void Main(string[] args)
        {
            var H = RInt;
            var W = RInt;

            char[,] map = new char[H + 2, W + 2];
            for (int i = 0; i < H; i++)
            {
                var input = Console.ReadLine();
                for (int j = 0; j < W; j++)
                {
                    map[i + 1, j + 1] = input[j];
                }
            }

            bool[,] accessed = new bool[H + 2, W + 2];
            Queue<int> queR = new Queue<int>();
            Queue<int> queC = new Queue<int>();

            int[] dr = new int[4] { 1, 0, -1, 0 };
            int[] dc = new int[4] { 0, -1, 0, 1 };

            UnionFind uf = new UnionFind(H * W);
            for (int i = 1; i <= H; i++)
            {
                for (int j = 1; j <= W; j++)
                {
                    if (accessed[i, j]) continue;
                    queR.Enqueue(i);
                    queC.Enqueue(j);

                    while (queR.Count > 0)
                    {
                        int r = queR.Dequeue();
                        int c = queC.Dequeue();
                        accessed[r, c] = true;

                        for (int t = 0; t < 4; t++)
                        {
                            int nr = r + dr[t];
                            int nc = c + dc[t];
                            if (accessed[nr, nc]) continue;
                            if ((map[nr, nc] == '#' && map[r, c] == '.') || (map[nr, nc] == '.' && map[r, c] == '#'))
                            {
                                accessed[nr, nc] = true;
                                queR.Enqueue(nr);
                                queC.Enqueue(nc);

                                uf.Unite(Ind(r, c, W), Ind(nr, nc, W));
                            }
                        }
                    }
                }
            }

            int[] countA = new int[H * W];
            int[] countB = new int[H * W];
            for (int i = 0; i < H; i++)
            {
                for (int j = 0; j < W; j++)
                {
                    int f = uf.Find(i * W + j);
                    if (map[i + 1, j + 1] == '#') countA[f]++;
                    if (map[i + 1, j + 1] == '.') countB[f]++;
                }
            }

            long ans = 0;
            for (int i = 0; i < H * W; i++)
            {
                ans += (long)countA[i] * countB[i];
            }

            Console.WriteLine(ans);
        }

        static int Ind(int i, int j, int W)
        {
            return (i - 1) * W + j - 1;
        }
    }


    /// <summary>
    /// UnionFind
    /// </summary>
    class UnionFind
    {
        int[] par;
        int[] rank;
        int[] count;

        public UnionFind(int n)
        {
            Init(n);
        }

        void Init(int n)
        {
            par = new int[n];
            rank = new int[n];
            count = new int[n].Select(x => 1).ToArray();

            for (int i = 0; i < n; i++)
            {
                par[i] = i;
            }
        }

        public int Find(int x)
        {
            if (par[x] == x)
            {
                return x;
            }
            else
            {
                return par[x] = Find(par[x]);
            }
        }

        public bool Unite(int x, int y)
        {
            x = Find(x);
            y = Find(y);
            if (x == y) return false; //すでに要素を追加済みの場合、falseを返す。

            if (rank[x] < rank[y])
            {
                par[x] = y;
                count[y] += count[x];
            }
            else
            {
                par[y] = x;
                count[x] += count[y];
                if (rank[x] == rank[y]) rank[x]++;
            }
            return true;
        }
        public bool Same(int x, int y)
        {
            return Find(x) == Find(y);
        }

        public int Size(int x)
        {
            return count[Find(x)];
        }
    }
}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a % mod, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}