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: Time Limit Exceeded)

require 'pp'

@h, @w = gets.strip.split.map(&:to_i)
maze = []

@h.times do
  maze << gets.strip.split('')
end

# 元の白マスの個数
# pp maze
num_whites = 0
@h.times do |i|
  @w.times do |j|
    # puts "maze[i][j] = #{maze[i][j]}"
    if maze[i][j] == '.'
      num_whites += 1
    end
  end
end

def bfs(maze)
  q = [[0, 0]]
  path = []
  @h.times do |i|
    path << []
    @w.times do |j|
      path[i] << nil
    end
  end
  # path = [[nil] * @w] * @h # 経路復元用

  until q.empty? do
    now_x, now_y = q.shift

    # puts "(now_x, now_y) = (#{now_x}, #{now_y})"
    # 次のマスに到達した
    # ここはゴールか？
    if now_x == @w - 1 && now_y == @h - 1
      break
    end

    # ゴールではないので探索済みのチェックを付けて次のマスに進む
    maze[now_y][now_x] = '#'

    dirs = [
      [now_x - 1, now_y],
      [now_x + 1, now_y],
      [now_x, now_y - 1],
      [now_x, now_y + 1]
    ]
    dirs.each do |d|
      x, y = d
      if x < 0 || @w <= x || y < 0 || @h <= y
        next
      end
      cell = maze[y][x]
      if cell == '#'
        next
      end

      # 進めるマスがあった
      # 経路復元用のメモ
      if path[y][x] == nil
        path[y][x] = [now_x, now_y]
      end

      # キューに入れる
      q << [x, y]
    end
  end

  # 経路を返して探索終わり
  path
end

def path_length(path)
  len = 0
  x, y = @w - 1, @h - 1
  until (x == 0 && y == 0)
    # puts ("x, y = #{x}, #{y}")
    len += 1
    x, y = path[y][x]
  end
  len
end

path = bfs(maze)
# pp path
if path[@h - 1][@w - 1] == nil
  # ゴールにたどり着けない
  puts -1
else
  # puts "num_whites = #{num_whites}"
  # 元の白マスの個数 - 経路の長さ - 1 個塗って良い
  puts num_whites - path_length(path) - 1
end