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 Scala (2.11.7) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer

import scala.collection.mutable
import scala.reflect.ClassTag

object Main {
  def main(args: Array[String]): Unit = {
    try {
      val (in, out) =
        if (isOnlineJudge) {
          (
            new FastScanner(new InputStreamReader(System.in)),
            new PrintWriter(System.out)
          )
        } else {
          (
            new FastScanner(new FileReader(new File("src/resource/problem.in"))),
            new PrintWriter(new File("src/resource/problem.out"))
          )
        }
      new Abc151(in, out).solve()
      out.flush()
      out.close()
    } catch {
      case e: IOException => e.printStackTrace()
    }
  }

  private[this] val isOnlineJudge = true

  class FastScanner(val streamReader: InputStreamReader) {
    private[this] val reader = new BufferedReader(streamReader, 32768)
    private[this] var tokenizer: StringTokenizer = _

    @inline private[this] final def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = Integer.parseInt(next())

    def nextLong(): Long = java.lang.Long.parseLong(next())

    def nextChar(): Char = next().charAt(0)

    def ni(): Int = nextInt()

    def nl(): Long = nextLong()

    def nc(): Char = nextChar()

    def ns(): String = next()

    def ns(n: Int): Array[Char] = ns().toCharArray

    def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)

    def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
      val A1, A2 = Array.ofDim[Int](n)
      REP(n) { i =>
        A1(i) = ni() + offset
        A2(i) = ni() + offset
      }
      (A1, A2)
    }

    def nm(n: Int, m: Int): Array[Array[Int]] = {
      val A = Array.ofDim[Int](n, m)
      REP(n) { i =>
        REP(m) { j =>
          A(i)(j) = ni()
        }
      }
      A
    }

    def nal(n: Int): Array[Long] = map(n)(_ => nl())

    def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n)(_ => ns(m))
  }

  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while (i < N) {
      f(i);
      i += 1
    }
  }

  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while (i >= offset) {
      f(i);
      i -= 1
    }
  }

  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from)(f)
  }

  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }

  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

class Abc151(fScanner: Main.FastScanner, out: java.io.PrintWriter) {

  import Main._
  import fScanner._

  def solve(): Unit = {
    H = ni()
    W = ni()
    maze = Array.ofDim[Boolean](H, W)
    REP(H) { i =>
      val s = ns(W)
      REP(W) { j =>
        s(j) match {
          case '.' => maze(i)(j) = true
          case _ => maze(i)(j) = false
        }
      }
    }
    var ans = -1
    REP(H) { i =>
      REP(W) { j =>
        if(maze(i)(j)) ans = Math.max(ans, bfs(i,j))
      }
    }
    out.println(ans)
  }

  var maze: Array[Array[Boolean]] = _
  var dx = Array(-1, 1, 0, 0)
  var dy = Array(0, 0, -1, 1)
  var H: Int = _
  var W: Int = _

  def bfs(gx: Int, gy: Int): Int = {
    val dist = Array.fill[Int](H, W)(-1)
    val q = new mutable.Queue[(Int, Int)]()
    q.enqueue((gx, gy))
    dist(gx)(gy) = 0
    while (q.nonEmpty) {
      val p = q.dequeue()
      val ax = p._1
      val ay = p._2

      REP(4) { i =>
        val nx = ax + dx(i)
        val ny = ay + dy(i)

        if(nx >=0 && nx < H && ny >= 0 && ny < W && maze(nx)(ny) && dist(nx)(ny) == -1) {
          dist(nx)(ny) = dist(ax)(ay) + 1
          q.enqueue((nx, ny))
        }
      }
    }
    dist.map(p => p.max).max
  }
}