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.*;
import java.util.*;

class Node implements Comparable<Node> {
  final int i, j, cost;
  
  Node(int i, int j, int cost) {
    this.i = i;
    this.j = j;
    this.cost = cost;
  }
  
  public int compareTo(Node node) {
    return this.cost - node.cost;
  }
}

class Solver {
  private final int[] DI = new int[]{1, 0, -1, 0};
  private final int[] DJ = new int[]{0, 1, 0, -1};
  
  final int h, w;
  final char[][] sm;
  
  Solver(int h, int w, char[][] sm) {
    this.h = h;
    this.w = w;
    this.sm = sm;
  }
  
  private int dijkstra(int i0, int j0) {
    boolean[][] visited = new boolean[h][w];
    PriorityQueue<Node> queue = new PriorityQueue<>();
    queue.add(new Node(i0, j0, 0));
    int maxCost = 0;
    while (!queue.isEmpty()) {
      Node node = queue.poll();
      int i = node.i;
      int j = node.j;
      int cost = node.cost;
      if (visited[i][j]) {
        continue;
      }
      visited[i][j] = true;
      maxCost = Math.max(maxCost, cost);
      for (int k = 0; k < 4; k++) {
        int nextI = i + DI[k];
        int nextJ = j + DJ[k];
        if (nextI < 0 || h <= nextI || nextJ < 0 || w <= nextJ || visited[nextI][nextJ] || sm[nextI][nextJ] == '#') {
          continue;
        }
        queue.add(new Node(nextI, nextJ, cost + 1));
      }
    }
    return maxCost;
  }
  
  public int solve() {
    int answer = 0;
    for (int i = 0; i < h; i++) {
      for (int j = 0; j < w; j++) {
        answer = Math.max(answer, dijkstra(i, j));
      }
    }
    return answer;
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int h = reader.nextInt();
    int w = reader.nextInt();
    char[][] sm = reader.nextCharArray(h);
    out.println(new Solver(h, w, sm).solve());
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}