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 Ruby (2.3.3) (judge verdict: Wrong Answer)

ARG_H, ARG_W = gets.split.map(&:to_i)
map = Array.new(ARG_H+2)
(ARG_H+2).times do |i|
  if i == 0 || i == ARG_H+1
    map[i] = Array.new(ARG_W+2, false)
    next
  end
  line = Array.new(ARG_W+2)
  line[0] = false
  line[ARG_W+1] = false
  str = gets.chomp.split('')
  j = 1
  str.each do |chr|
    line[j] = chr == '#' ? false : true
    j+=1
  end
  map[i] = line
end

first_found = false
first_point = [-1,-1]
map.each_with_index do |line, h|
  line.each_with_index do |point, w|
    if point
      first_point = [h, w]
      first_found = true
      break
    end
  end
  break if first_found
end

dxylist = [[0,1], [0,-1], [1,0], [-1,0]]
prev_distance = -1
max_distance=0
max_distance_point=nil
while(max_distance != prev_distance) do
  distance = {
    first_point => 0
  }
  prev_distance = max_distance
  max_distance = 0
  q = [first_point]
  while(q.size > 0) do
    point = q.shift
    dxylist.each do |dxy|
      new_point = [point[0]+dxy[0], point[1]+dxy[1]]
      next unless map[new_point[0]][new_point[1]]
      next if distance[new_point]
      q.push new_point
      new_distance = distance[point] + 1
      distance[new_point] = new_distance
      if new_distance > max_distance
        max_distance = new_distance
        max_distance_point = new_point
      end
    end
  end
  first_point = max_distance_point
end

puts max_distance