Problem:
Score : 400 points

Problem Statement

Takahashi has a maze, which is a grid of H \times W squares with H horizontal rows and W vertical columns.

The square at the i-th row from the top and the j-th column is a "wall" square if S_{ij} is #, and a "road" square if S_{ij} is ..

From a road square, you can move to a horizontally or vertically adjacent road square.

You cannot move out of the maze, move to a wall square, or move diagonally.

Takahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.

Aoki will then travel from the starting square to the goal square, in the minimum number of moves required.

In this situation, find the maximum possible number of moves Aoki has to make.

Constraints

1 \leq H,W \leq 20

S_{ij} is . or #.

S contains at least two occurrences of ..

Any road square can be reached from any road square in zero or more moves.

Input

Input is given from Standard Input in the following format:

H W
S_{11}...S_{1W}
:
S_{H1}...S_{HW}

Output

Print the maximum possible number of moves Aoki has to make.

Sample Input 1

3 3
...
...
...

Sample Output 1

4

If Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.

Sample Input 2

3 5
...#.
.#.#.
.#...

Sample Output 2

10

If Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace BFS2
{
    class Program
    {
        public class DoneTile
        {
            public DoneTile(int[] thisPos,DoneTile from,int order)
            {
                ThisPos = thisPos;
                From = from;
                Order = order;
            }

            public int[] ThisPos { get; }
            public DoneTile From { get; }
            public int Order;
        }

        static void Main(string[] args)
        {
            int H,W;
            char[][] map = ReadMap(out H,out W);

            List<int[]> roadPoses = new List<int[]>();

            //一度選んだstart goal のペア
            //[S[0]][S[1]][G[0]][G[1]] = 0 or 1
            int[][][][] withExperience = new int[H][][][];

            //通れるタイルを探す(と同時にwithEcperienceを初期化)
            for (int i = 0; i < H; i++)
            {
                withExperience[i] = new int[W][][];
                for (int j = 0; j < W; j++)
                {
                    withExperience[i][j] = new int[H][];
                    for (int k = 0; k < H; k++)
                    {
                        withExperience[i][j][k] = new int[W];
                    }
                    if (map[i][j] == '.')
                    {
                        roadPoses.Add(new int[2] { i, j });
                    }
                }
            }



            int[][] deltas = { new int[2] { 0, 1 }, new int[2] { 1, 0 }, new int[2] { 0, -1 }, new int[2] { -1, 0 } };

            DoneTile currentTile = null;


            int maxCount = 0;

            //startとgoalの位置を動かす
            for (int i = 0; i < roadPoses.Count-1; i++)
            {
                for (int j = i+1; j < roadPoses.Count; j++)
                {

                    int[] startPos = new int[3] { roadPoses[i][0], roadPoses[i][1], 0 };
                    int[] goalPos = roadPoses[j];

                    //startとgoalの位置が実験済みなら飛ばす
                    if (withExperience[startPos[0]][startPos[1]][goalPos[0]][goalPos[1]]==0)
                    {

                        Queue<DoneTile> queue = new Queue<DoneTile>();
                        DoneTile startDoneTile = new DoneTile(startPos, null, 0);

                        //計算済みのタイルを記憶する配列(とその初期化)
                        int[][] done = new int[H][];
                        for (int k = 0; k < H; k++)
                        {
                            done[k] = new int[W];
                        }

                        //スタート地点は計算済み
                        done[startDoneTile.ThisPos[0]][startDoneTile.ThisPos[1]] = 1;

                        //スタートタイルから計算を初める
                        queue.Enqueue(startDoneTile);
                        while (true)
                        {
                            currentTile = queue.Dequeue();

                            //ゴールの位置に等しいなら
                            if (currentTile.ThisPos[0] == goalPos[0] && currentTile.ThisPos[1] == goalPos[1])
                            {
                                //スタートまで逆走する
                                //その過程で踏んだタイルは、絶対にmax(答え)にはならない
                                DoneTile returnTile = currentTile;
                                while (returnTile != startDoneTile)
                                {
                                    withExperience[startDoneTile.ThisPos[0]][startDoneTile.ThisPos[1]][returnTile.ThisPos[0]][returnTile.ThisPos[1]] = 1;
                                    returnTile = returnTile.From;
                                }
                                break;
                            }

                            //通れるなら
                            if (map[currentTile.ThisPos[0]][currentTile.ThisPos[1]] == '.')
                            {
                                //この次に議論するタイルを選ぶ
                                foreach (var delta in deltas)
                                {
                                    int[] aroundPos = new int[] { currentTile.ThisPos[0] + delta[0], currentTile.ThisPos[1] + delta[1] };
                                    if (aroundPos[0] >= 0 && aroundPos[0] < H && aroundPos[1] >= 0 && aroundPos[1] < W)
                                    {
                                        if (done[aroundPos[0]][aroundPos[1]] == 0)
                                        {
                                            DoneTile next = new DoneTile(aroundPos, currentTile, currentTile.Order + 1);
                                            queue.Enqueue(next);
                                            done[aroundPos[0]][aroundPos[1]] = 1;
                                        }
                                    }
                                }
                            }
                        }
                    }
                    maxCount = Math.Max(maxCount, currentTile.Order);

                }

            }

            Console.WriteLine(maxCount);
            Console.ReadLine();
        }

        static private char[][] ReadMap(out int H,out int W)
        {
            string[] HW = Console.ReadLine().Split(' ');
            H = int.Parse(HW[0]);
            W = int.Parse(HW[1]);

            char[][] map = new char[H][];
            for (int i = 0; i < H; i++)
            {
                map[i] = Console.ReadLine().ToArray();
            }
            return map;
        }
    }
}