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)

#region いつもの
#pragma warning disable
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using static AtCoderProject.Global;

namespace AtCoderProject
{
    static class Global
    {
        private class ComparerReverseImpl<T> : Comparer<T> where T : IComparable<T> { public override int Compare(T y, T x) => x.CompareTo(y); public override bool Equals(object obj) => obj != null && GetType() == obj.GetType(); public override int GetHashCode() => GetType().GetHashCode(); }
        public static IComparer<T> ComparerReverse<T>() where T : IComparable<T> => new ComparerReverseImpl<T>();
        public static BigInteger ParseBigInteger(string s)
        {
            // MonoのBigInteger.Parseが遅いので自前実装
            var res = BigInteger.Zero;
            var splited = new string[(s.Length + 7) / 8];
            for (int i = 0; i < splited.Length - 1; i++)
            {
                splited[i] = s.Substring(8 * i, 8);
            }
            splited[splited.Length - 1] = s.Substring(8 * (splited.Length - 1));
            foreach (var sp in splited)
            {
                res *= (int)Math.Pow(10, sp.Length);
                res += int.Parse(sp);
            }
            return res;
        }
        public static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        public static string AllJoin<T>(IEnumerable<T> source) => string.Join(" ", source);
    }
    static class Ext
    {
        public static T[][] Chunk<T>(this T[,] source)
        {
            var len0 = source.GetLength(0);
            var len1 = source.GetLength(1);
            var res = new T[len0][];
            for (int i = 0; i < len0; i++)
            {
                res[i] = new T[len1];
                for (int j = 0; j < len1; j++)
                {
                    res[i][j] = source[i, j];
                }
            }
            return res;
        }

        public static Tuple<TSource, TMax> MaxBy<TSource, TMax>
            (this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector)
            where TMax : IComparable<TMax>
        {
            TMax max;
            TSource maxByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            maxByItem = e.Current;
            max = maxBySelector(maxByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = maxBySelector(item);
                if (max.CompareTo(next) < 0)
                {
                    max = next;
                    maxByItem = item;
                }
            }
            return Tuple.Create(maxByItem, max);
        }
        public static Tuple<TSource, TMin> MinBy<TSource, TMin>
            (this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector)
            where TMin : IComparable<TMin>
        {
            TMin min;
            TSource minByItem;

            var e = source.GetEnumerator();
            e.MoveNext();
            minByItem = e.Current;
            min = minBySelector(minByItem);
            while (e.MoveNext())
            {
                var item = e.Current;
                var next = minBySelector(item);
                if (min.CompareTo(next) > 0)
                {
                    min = next;
                    minByItem = item;
                }
            }
            return Tuple.Create(minByItem, min);
        }
        public static IComparer<T> Reverse<T>(this IComparer<T> comparer) => Comparer<T>.Create((x, y) => comparer.Compare(y, x));
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public int Int0 => Int - 1; public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public string[] String => this.Select(cr => cr.String).ToArray(); public int[] Int => this.Select(cr => cr.Int).ToArray(); public int[] Int0 => this.Select(cr => cr.Int - 1).ToArray(); public long[] Long => this.Select(cr => cr.Long).ToArray(); public double[] Double => this.Select(cr => cr.Double).ToArray(); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    public class Program
    {
        [System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] private ConsoleReader cr;
        public Program(ConsoleReader consoleReader) { this.cr = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc());

        #endregion
        public object Calc()
        {
            var H = cr.Int;
            var W = cr.Int;
            var s = cr.Repeat(H).Select(cr => cr.String.Select(c => c == '.').ToArray()).ToArray();
            var gb = new GraphBuilder(H * W, false);
            var walls = new List<int>();

            for (int h = 0; h < H; h++)
                for (int w = 0; w < W; w++)
                {
                    if (s[h][w])
                    {
                        if (w + 1 < W && s[h][w + 1])
                            gb.Add(h * W + w, h * W + w + 1);

                        if (h + 1 < H && s[h + 1][w])
                            gb.Add(h * W + w, (h + 1) * W + w);
                    }
                    else walls.Add(h * W + w);
                }

            var res = WarshallFloyd(gb.ToArray());

            return res.Cast<long>().Where(l => l < int.MaxValue).Max();
        }
        public static long[,] WarshallFloyd(Node[] graph)
        {
            var res = new long[graph.Length, graph.Length];
            for (var i = 0; i < graph.Length; i++)
            {
                for (var j = 0; j < graph.Length; j++)
                {
                    res[i, j] = long.MaxValue / 2;
                }
                res[i, i] = 0;
                foreach (var next in graph[i].children)
                    res[i, next] = 1;
            }
            for (var k = 0; k < graph.Length; k++)
                for (var i = 0; i < graph.Length; i++)
                    for (var j = 0; j < graph.Length; j++)
                        if (res[i, j] > res[i, k] + res[k, j])
                            res[i, j] = res[i, k] + res[k, j];
            return res;
        }
    }

    class GraphBuilder
    {
        private List<int>[] roots;
        private List<int>[] children;
        public GraphBuilder(int count, bool isOriented = true)
        {
            this.roots = new List<int>[count];
            this.children = new List<int>[count];
            for (var i = 0; i < count; i++)
            {
                if (isOriented)
                {
                    this.roots[i] = new List<int>();
                    this.children[i] = new List<int>();
                }
                else
                {
                    this.roots[i] = this.children[i] = new List<int>();
                }
            }
        }
        public GraphBuilder(int count, ConsoleReader cr, int edgeCount, bool isOriented = true) : this(count, isOriented)
        {
            for (var i = 0; i < edgeCount; i++)
                this.Add(cr.Int - 1, cr.Int - 1);
        }
        public void Add(int from, int to)
        {
            children[from].Add(to);
            roots[to].Add(from);
        }
        public TreeNode[] ToTree(int root)
        {
            if (this.roots[0] != this.children[0]) throw new Exception("木には無向グラフをしたほうが良い");
            var res = new TreeNode[this.children.Length];
            res[root] = new TreeNode(root, -1, this.children[root].ToArray());

            var queue = new Queue<int>();
            foreach (var child in res[root].children)
            {
                res[child] = new TreeNode(child, root, Array.Empty<int>());
                queue.Enqueue(child);
            }

            while (queue.Count > 0)
            {
                var from = queue.Dequeue();
                if (res[from].root == -1)
                    res[from].children = this.children[from].ToArray();
                else
                {
                    var children = new List<int>(this.children[from].Count);
                    foreach (var c in this.children[from])
                        if (c != res[from].root)
                            children.Add(c);

                    res[from].children = children.ToArray();
                }

                foreach (var child in res[from].children)
                {
                    res[child] = new TreeNode(child, from, Array.Empty<int>());
                    queue.Enqueue(child);
                }
            }

            return res;
        }

        public Node[] ToArray() =>
            Enumerable
            .Zip(roots, children, (r, c) => Tuple.Create(r, c))
            .Select((t, i) => new Node(i, t.Item1.ToArray(), t.Item2.ToArray()))
            .ToArray();
    }
    public class TreeNode : IEquatable<TreeNode>
    {
        public TreeNode(int i, int root, int[] children)
        {
            this.index = i;
            this.root = root;
            this.children = children;
        }
        public int index;
        public int root;
        public int[] children;

        public override string ToString() => $"children: {string.Join(",", children)}";
        public override bool Equals(object obj)
        {
            if (obj is TreeNode)
                return this.Equals((TreeNode)obj);
            else
                return false;
        }
        public bool Equals(TreeNode other) => this.index == other.index;
        public override int GetHashCode() => this.index;
    }
    public class Node : IEquatable<Node>
    {
        public Node(int i, int[] roots, int[] children)
        {
            this.index = i;
            this.roots = roots;
            this.children = children;
        }
        public int index;
        public int[] roots;
        public int[] children;

        public override string ToString() => $"children: {string.Join(",", children)}";
        public override bool Equals(object obj)
        {
            if (obj is Node)
                return this.Equals((Node)obj);
            else
                return false;
        }
        public bool Equals(Node other) => this.index == other.index;
        public override int GetHashCode() => this.index;
    }

}