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.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1 };
        static readonly int[] dJ = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var input = cin.ReadSplitInt();
            int H = input[0];
            int W = input[1];

            var map = new char[H][];
            for(var i = 0; i < H; i++)
            {
                map[i] = Console.ReadLine().ToCharArray();
            }
            var d = new long[H * W, H * W];
            int num = H * W;
            for(var i = 0; i < num; i++)
            {
                for(var j = 0; j < num; j++)
                {
                    d[i, j] = i == j ? 0 : INF;
                }
            }
            for(var i = 0; i < H; i++)
            {
                for(var j = 0; j < W; j++)
                {
                    if (map[i][j] == '#') { continue; }
                    int id = i * W + j;
                    if (i < H - 1 && map[i + 1][j] == '.')
                    {
                        d[id, (i + 1) * W + j] = 1;
                        d[(i + 1) * W + j, id] = 1;
                    }
                    if (j < W - 1 && map[i][j + 1] == '.')
                    {
                        d[id, i * W + j + 1] = 1;
                        d[i * W + j + 1, id] = 1;
                    }
                }
            }
            Warshall_floyd(num, d);
            long ans = 0;
            for(var i = 0; i < num; i++)
            {
                for(var j = 0; j < num; j++)
                {
                    if (d[i, j] != INF)
                    {
                        ans = Max(ans, d[i, j]);
                    }
                }
            }
            Console.WriteLine(ans);

            //Console.Out.Flush();
        }
        public static void Warshall_floyd(int n, long[,] dist)
        {
            for (var k = 0; k < n; k++)
            {
                for (var i = 0; i < n; i++)
                {
                    for (var j = 0; j < n; j++)
                    {
                        dist[i, j] = Min(dist[i, j], dist[i, k] + dist[k, j]);
                    }
                }
            }
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }

    public class Scanner
    {
        public int[] ReadSplitInt()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitLong()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplit_Double()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
    class Modulo
    {
        private const int M = 1000000007;
        private readonly int[] m_facs;
        public int Mul(int a, int b)
        {
            return (int)(Math.BigMul(a, b) % M);
        }
        public Modulo(int n)
        {
            m_facs = new int[n + 1];
            m_facs[0] = 1;
            for (int i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public int Fac(int n)
        {
            return m_facs[n];
        }
        public int Pow(int a, int m)
        {
            switch (m)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    int p1 = Pow(a, m / 2);
                    int p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public int Div(int a, int b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public int Ncr(int n, int r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            int res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
        public Modulo() { }
    }
}