Problem:
Score: 400 points

Problem statement

We have an H \times W grid whose squares are painted black or white. The square at the i-th row from the top and the j-th column from the left is denoted as (i, j).

Snuke would like to play the following game on this grid. At the beginning of the game, there is a character called Kenus at square (1, 1). The player repeatedly moves Kenus up, down, left or right by one square. The game is completed when Kenus reaches square (H, W) passing only white squares.

Before Snuke starts the game, he can change the color of some of the white squares to black. However, he cannot change the color of square (1, 1) and (H, W). Also, changes of color must all be carried out before the beginning of the game.

When the game is completed, Snuke's score will be the number of times he changed the color of a square before the beginning of the game. Find the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed, that is, Kenus can never reach square (H, W) regardless of how Snuke changes the color of the squares.

The color of the squares are given to you as characters s_{i, j}. If square (i, j) is initially painted by white, s_{i, j} is .; if square (i, j) is initially painted by black, s_{i, j} is #.

Constraints

H is an integer between 2 and 50 (inclusive).

W is an integer between 2 and 50 (inclusive).

s_{i, j} is . or # (1 \leq i \leq H, 1 \leq j \leq W).

s_{1, 1} and s_{H, W} are ..

Input

Input is given from Standard Input in the following format:

H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}

Output

Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.

Sample Input 1

3 3
..#
#..
...

Sample Output 1

2

The score 2 can be achieved by changing the color of squares as follows:

Sample Input 2

10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................

Sample Output 2

209

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

# goal
h,w = gets.split(" ").map(&:to_i)

# 可能な限り黒(=壁)を増やしてクリア

$H = h -1
$W = w -1

class Node
  attr_accessor :status, :x, :y, :c_cost, :h_cost, :parent, :state

  def initialize(x,y,state)
    @status = :None
    @x = x
    @y = y
    @c_cost = 0
    @h_cost = 0 # dx+dy
    @score = -1

    @state = state

    @parent = nil
  end

  def get_score
    @score
  end

  def set_score(goal_x,goal_y, step)
    @c_cost = step
    @h_cost = goal_x - @x + goal_y - @y
    @score = @c_cost + @h_cost
  end

  def open_cell(step)
    @status = :Open
    set_score($W,$H,step)
  end

  def close(cells,step)

    target = []

    target << cells[@y][@x-1] if @x > 0
    target << cells[@y][@x+1] if @x < $W
    target << cells[@y-1][@x] if @y > 0
    target << cells[@y+1][@x] if @y < $H

    target.each do |cell|
      if cell.status == :None && cell.state == "."
        cell.open_cell(step)
        cell.parent = self
      end
    end

    @status = :Close

  end
end


cell = Array.new(h){Array.new(w)}
h.times do |i|
  gets.chomp.split("").each_with_index  do |c,j|
    cell[i][j] = Node.new(j,i,c)
#    cell[i][j].set_score(w-1,h-1)
  end
end

step = 1

cell[0][0].open_cell(0)
cell[0][0].close(cell,step)

#ループ
while true
  step += 1

  # Openステータスの中に終了座標に到達しているものを検索
  if cell[$H][$W].status == :Open
    break
  end

  target = nil
  min_score = 100000000
  cell.each do |c|
    c.each do |c|
      if c.status == :Open
        if c.get_score < min_score
          min_score = c.get_score
          target = c
        end
      end
    end
  end

  if target.nil?
#    puts "-1"
    break
#    exit
  end

  target.close(cell,step)

end


#puts "finish"
stack = cell[$H][$W]

if stack.get_score == -1
  puts "-1"
  exit
end

route = []

until stack.nil?
  route << {x: stack.x, y: stack.y}
  stack = stack.parent
end

#cell.flatten.each_with_index do |c,i|
#  print c.get_score
#  if (i+1)%w == 0
#    puts ""
#  end
#end

count = 0
h.times do |i|
  w.times do |j|
    unless route.include?({x:j,y:i})
      if cell[i][j].state == "."
        count += 1
      end
    end
  end
end

puts count