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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.LinkedList;
import java.util.NoSuchElementException;
import java.util.Queue;

public class Main{
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int ROW;
	static int COL;
	static int [][] field;
	static final int[] dx = {0,1,0,-1};
	static final int[] dy = {-1,0,1,0};
	static int max_d;
	static int max_x;
	static int max_y;
	
	public static void main(String[] args) {
		ROW = sc.nextInt();
		COL = sc.nextInt();
		char [][] map = new char[ROW][COL];
		field = new int [ROW][COL];
		
		for (int i=0; i<ROW; i++) 
			map[i]=sc.next().toCharArray();
		
		int sx = 0;
		int sy = 0;
		boolean flag = false;
		for (int i=0; i<ROW; i++) {
			for (int j=0; j<COL; j++) {
				if (map[i][j]=='.') {
					sx = i;
					sy = j;
					flag = true;
					break;
				}
			}
			if (flag)
				break;
		}
		
		Point start = new Point (sx, sy);
		BFS(map, start);
		
		int cur = max_d;
		
		while (true) {
			Point start_ = new Point (max_x, max_y);
			BFS(map, start_);
			
			int next = max_d;
			if (next==cur)
				break;
			
			cur = next;
		}
		
		out.println(max_d);
		out.flush();
		
	}
		
		static boolean isValid(int row, int col) { 
			return (row >= 0) && (row < ROW) && 
				(col >= 0) && (col < COL); 
		} 

		static class Point { 
			int x; 
			int y; 

			public Point(int x, int y) { 
				this.x = x; 
				this.y = y; 
			} 
		}
		
		static class queueNode { 
			Point pt; 
			int dist; 

			public queueNode(Point pt, int dist) { 
				this.pt = pt; 
				this.dist = dist; 
			} 
		}
		
		static void BFS(char map[][], Point src) { 
		 
			boolean [][] visited = new boolean[ROW][COL]; 
			visited[src.x][src.y] = true; 
			field [src.x][src.y] = 0; 

			Queue<queueNode> q = new LinkedList<>(); 

			queueNode s = new queueNode(src, 0); 
			q.add(s); 
			
			max_d=0;

			while (!q.isEmpty()) { 
				queueNode curr = q.peek(); 
				Point pt = curr.pt; 

				q.remove(); 

				for (int i = 0; i < 4; i++) { 
					int row = pt.x + dx[i]; 
					int col = pt.y + dy[i]; 

					if (isValid(row, col) && map[row][col] == '.' && !visited[row][col]) { 
						visited[row][col] = true; 	
						field [row][col] = field [row-dx[i]][col-dy[i]]+1;
						curr.dist++;
						if (curr.dist>max_d) {
							max_x = row;
							max_y = col;
							max_d = curr.dist;
						}
						queueNode Adjcell = new queueNode(new Point(row, col), curr.dist); 
						q.add(Adjcell); 
					} 
				} 
			}
		} 
	
		static class FastScanner {
		    private final InputStream in = System.in;
		    private final byte[] buffer = new byte[1024];
		    private int ptr = 0;
		    private int buflen = 0;

		    private boolean hasNextByte() {
		      if (ptr < buflen) {
		        return true;
		      } else {
		        ptr = 0;
		        try {
		          buflen = in.read(buffer);
		        } catch (IOException e) {
		          e.printStackTrace();
		        }
		        if (buflen <= 0) {
		          return false;
		        }
		      }
		      return true;
		    }

		    private int readByte() {
		      if (hasNextByte()) return buffer[ptr++];
		      else return -1;
		    }

		    private static boolean isPrintableChar(int c) {
		      return 33 <= c && c <= 126;
		    }

		    private void skipUnprintable() {
		      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		    }

		    public boolean hasNext() {
		      skipUnprintable();
		      return hasNextByte();
		    }

		    public String next() {
		      if (!hasNext()) throw new NoSuchElementException();
		      StringBuilder sb = new StringBuilder();
		      int b = readByte();
		      while (isPrintableChar(b)) {
		        sb.appendCodePoint(b);
		        b = readByte();
		      }
		      return sb.toString();
		    }

		    public long nextLong() {
		      if (!hasNext()) throw new NoSuchElementException();
		      long n = 0;
		      boolean minus = false;
		      int b = readByte();
		      if (b == '-') {
		        minus = true;
		        b = readByte();
		      }
		      if (b < '0' || '9' < b) {
		        throw new NumberFormatException();
		      }
		      while (true) {
		        if ('0' <= b && b <= '9') {
		          n *= 10;
		          n += b - '0';
		        } else if (b == -1 || !isPrintableChar(b)) {
		          return minus ? -n : n;
		        } else {
		          throw new NumberFormatException();
		        }
		        b = readByte();
		      }
		    }

		    public int nextInt() {
		      return (int) nextLong();
		    }

		    public int[] nextIntArray(int N, boolean oneBased) {
		      if (oneBased) {
		        int[] array = new int[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      } else {
		        int[] array = new int[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      }
		    }

		    public long[] nextLongArray(int N, boolean oneBased) {
		      if (oneBased) {
		        long[] array = new long[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      } else {
		        long[] array = new long[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      }
		    }
		  }

		}