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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
 
public class AchieveTheGoal {
    public enum Direction : int
    {
        Right = 0,
        Left,
        Up,
        Down
    };
    public static int H, W;
    
    public static void Main(){
        string[] line = Console.ReadLine().Split(' ');
        H = int.Parse(line[0]);
        W = int.Parse(line[1]);
        
        int maxCount = 0;
        // マップが二次ではなく一次になるとき
        if (H == 1)
        {
            char[] newline = Console.ReadLine().ToCharArray();
            maxCount = GetMaxCountLine(newline, W);
        }
        else if (W == 1)
        {
            char[] newline = new char[H];
            for (int i = 0 ; i < H; i++)
            {
                newline[i] = Console.ReadLine().ToCharArray()[0];
            }
            maxCount = GetMaxCountLine(newline, H);
        }
        // マップが二次になるとき
        else
        {
            char[,] map = new char[H, W];
    
            // Mapの構築
            for (int i = 0; i < H ; i++ )
            {
                string newline = Console.ReadLine();
                for (int j = 0; j < W ; j++ )
                {
                    map[i, j] = newline.ToCharArray()[j];
                }
            }
            
            // 全通り探索する
            // 探索方法は、幅優先探索
            for (int i = 0; i < H ; i++ )
            {
                for (int j = 0; j < H ; j++ )
                {
                    //Console.WriteLine(i +", "+j+":");
                    int treeDepth = GetMaxDepth(map, new Point(i,j));
                    if (maxCount < treeDepth)
                    {
                        maxCount = treeDepth;
                    }
                }
            }
        }
        
        Console.WriteLine(maxCount);
    }
    
    private static int GetMaxCountLine(char[] line, int length)
    {
        int maxCount = 0;
        for (int i = 0 ; i < length ; i++ )
        {
            int currentLength = 0;
            while ((i < length) && (line[i] == '.'))
            {
                currentLength++;
                i++;
            }
            if (maxCount < currentLength-1)
            {
                maxCount = currentLength-1;
            }
        }
        return maxCount;
    }
    
    private static int GetMaxDepth(char[,] map, Point startPoint)
    {
        // スタート地点が壁の場合
        if (map[startPoint.y, startPoint.x] == '#')
        {
            // 長さを0で返す
            return 0;
        }
        
        int maxTreeDepth = 0;
        startPoint.treeDepth = 0;
        Queue<Point> queue = new Queue<Point>();
        queue.Enqueue(startPoint);
        // startPointは既訪問
        Dictionary<string, bool> hasAlreadyVisited = new Dictionary<string, bool>();
        string pointID = startPoint.x.ToString() + startPoint.y.ToString();
        
        while (queue.Count > 0)
        {
            int nextSearchCount = queue.Count;
            for (int i = 0; i < nextSearchCount ; i++)
            {
                Point next = queue.Dequeue();
                pointID = next.x.ToString() + next.y.ToString();
                //Console.WriteLine(next.x +" "+next.y);
                // 未訪問の場合のみ続行
                if (!hasAlreadyVisited.ContainsKey(pointID))
                {
                    hasAlreadyVisited[pointID] = true;
                    VisitNextPoint(map, next, queue);
                    maxTreeDepth = next.treeDepth;
                    //Console.WriteLine(maxTreeDepth);
                }
            }
        }
        return maxTreeDepth;
    }
    
    private static void VisitNextPoint(char[,] map, Point p, Queue<Point> queue)
    {
        if (MoveCheck(map, p, (int)Direction.Right)) 
        {
            Point rightPoint = new Point(p.x+1, p.y);
            rightPoint.treeDepth = p.treeDepth + 1;
            queue.Enqueue(rightPoint);
        }
        if (MoveCheck(map, p, (int)Direction.Left))
        {
            Point leftPoint = new Point(p.x-1, p.y);
            leftPoint.treeDepth = p.treeDepth + 1;
            queue.Enqueue(leftPoint);
        }
        if (MoveCheck(map, p, (int)Direction.Up))
        {
            Point upPoint = new Point(p.x, p.y-1);
            upPoint.treeDepth = p.treeDepth + 1;
            queue.Enqueue(upPoint);
        }
        if (MoveCheck(map, p, (int)Direction.Down))
        {
            Point downPoint = new Point(p.x, p.y+1);
            downPoint.treeDepth = p.treeDepth + 1;
            queue.Enqueue(downPoint);
        }
    }
    
    private static bool MoveCheck(char[,] map, Point p, int dir)
    {
        if (dir == (int)Direction.Right)
        {
            if (p.x+1 >= W) 
            {
                return false;
            }
            else
            {
                if (map[p.y, p.x+1] == '.')
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }
        else if (dir == (int)Direction.Left)
        {
            if (p.x-1 < 0) 
            {
                return false;
            }
            else
            {
                if (map[p.y, p.x-1] == '.')
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }
        else if (dir == (int)Direction.Up)
        {
            if (p.y-1 < 0) 
            {
                return false;
            }
            else
            {
                if (map[p.y-1, p.x] == '.')
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }
        else if (dir == (int)Direction.Down)
        {
            if (p.y+1 >= H) 
            {
                return false;
            }
            else
            {
                if (map[p.y+1, p.x] == '.')
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }
        return false;
    }
}

public class Point {
    public int x, y;
    public int treeDepth;
    public Point(int x, int y)
    {
        this.x = x;
        this.y = y;
    }
}