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 LuaJIT (2.0.4) (judge verdict: Wrong Answer)

local mma = math.max
local h, w = io.read("*n", "*n", "*l")
local map = {}
for i = 1, h do
  local s = io.read()
  for j = 1, w do
    map[(i - 1) * w + j] = s:sub(j, j) == "."
  end
end


local function getlength(start_idx, dst_idx)
  local taskstate = {}
  for i = 1, h * w do taskstate[i] = false end
  local tasks = {}
  local tasknum = 0
  local done = 0

  local len = {}
  local inf = -1
  for i = 1, h * w do len[i] = inf end
  len[start_idx] = 0

  local function addtask(idx)
    if not taskstate[idx] then
      taskstate[idx] = true
      tasknum = tasknum + 1
      tasks[tasknum] = idx
    end
  end
  addtask(start_idx)

  local function walk(src, dst)
    if map[dst] then
      if len[dst] == inf or len[src] + 1 < len[dst] then
        len[dst] = len[src] + 1
        addtask(dst)
      end
    end
  end

  while done < tasknum do
    done = done + 1
    local idx = tasks[done]
    taskstate[idx] = false
    local tmp = {}

    if w < idx then walk(idx, idx - w) end
    if idx <= (h - 1) * w then walk(idx, idx + w) end
    if 1 < w then
      if idx % w ~= 0 then walk(idx, idx + 1) end
      if idx % w ~= 1 then walk(idx, idx - 1) end
    end
  end
  local ret = 0
  for i = 1, h * w do
    if 0 < len[i] then
      ret = mma(ret, len[i])
    end
  end
  return ret
end
local totret = 0
for i = 1, h * w do
  totret = mma(totret, getlength(i))
end
print(totret)