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: Accepted)

            
import java.util.*;import java.io.*;import java.math.*;

public class Main
{
    static int dp[][];
    static boolean visited[][];
    static class Node{
        int r,c,dist;
        public Node(int r,int c,int dist){
            this.r=r;
            this.c=c;
            this.dist=dist;
        }
    }

    static boolean isValid(int i,int j,int h,int w){
        if(i<1 || i>h || j<1 || j>w || visited[i][j])
            return false;
        return true;
    }

    static void find_path(int sr,int sc,int h,int w,char grid[][]){
        Queue<Node> q=new LinkedList<>();
        q.add(new Node(sr,sc,0));
        visited[sr][sc]=true;
        for(int i=1;i<=h;i++)
            for(int j=1;j<=w;j++)
                if(grid[i][j]=='#')
                    visited[i][j]=true;

        while(!q.isEmpty()){
            Node n=q.poll();
            int r=n.r,c=n.c,dist=n.dist;

            dp[r][c]=Math.max(dp[r][c], dist);

            dist++;
            if(isValid(r+1,c,h,w)){
                q.add(new Node(r+1,c,dist));
                visited[r+1][c]=true;
            }

            if(isValid(r-1,c,h,w)){
                q.add(new Node(r-1,c,dist));
                visited[r-1][c]=true;
            }

            if(isValid(r,c+1,h,w)){
                q.add(new Node(r,c+1,dist));
                visited[r][c+1]=true;
            }

            if(isValid(r,c-1,h,w)){
                q.add(new Node(r,c-1,dist));
                visited[r][c-1]=true;
            }
        }
    }
    public static void process()throws IOException
    {
        int h=ni(),w=ni();
        dp=new int[h+1][w+1];
        visited=new boolean[h+1][w+1];
        for(int row[] : dp)
            Arrays.fill(row,-1);

        char grid[][]=new char[h+1][w+1];
        for(int i=1;i<=h;i++) grid[i]=(" "+nln()).toCharArray();

        for(int i=1;i<=h;i++){
            for(int j=1;j<=w;j++){
                if(grid[i][j]=='#')
                    continue;
                find_path(i,j,h,w,grid);

                for(boolean row[] : visited)
                    Arrays.fill(row,false);
            }
        }

        int res=0;
        for(int i=1;i<=h;i++)
            for(int j=1;j<=w;j++)
                res=Math.max(res, dp[i][j]);

        pn(res);
    }


    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

       // oj = System.getProperty("ONLINE_JUDGE") != null;
        if(!oj) sc=new AnotherReader(100);

        long s = System.currentTimeMillis();
        int t=1;
        //t=ni();
        while(t-->0)
            process();
        out.flush();
        if(!oj)
            System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;
    static long mod=(long)1e9+7l;
    static long mpow(long x, long n) {
        if(n == 0)
            return 1;
        if(n % 2 == 0) {
            long root = mpow(x, n / 2);
            return root * root % mod;
        }else {
            return x * mpow(x, n - 1) % mod;
        }
    }
    static long mcomb(long a, long b) {
        if(b > a - b)
            return mcomb(a, a - b);
        long m = 1;
        long d = 1;
        long i;
        for(i = 0; i < b; i++) {
            m *= (a - i);
            m %= mod;
            d *= (i + 1);
            d %= mod;
        }
        long ans = m * mpow(d, mod - 2) % mod;
        return ans;
    }
/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}