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: Accepted)

class Position
  def initialize(x, y, count = 0)
    @x, @y = x, y
    @count = count
  end
  attr_accessor :x, :y, :count

  def up
    Position.new(x, y - 1, @count + 1)
  end

  def down
    Position.new(x, y + 1, @count + 1)
  end

  def left
    Position.new(x - 1, y, @count + 1)
  end

  def right
    Position.new(x + 1, y, @count + 1)
  end
end

class Matrix
  def initialize(map)
    @map    = map
  end

  def get(pos)
    @map[pos.y][pos.x]
  end
  
  def set(pos, newVal)
    @map[pos.y][pos.x] = newVal
  end

  def blank_count
    cnt = 0
    @map.each do |row|
      row.each do |e|
        cnt += 1 if e == Maze::BLANK || e == Maze::GOAL
      end
    end
    return cnt
  end
end

class Maze
  GOAL  = 'G'
  BLANK = '.'
  WALL  = '#'

  def initialize(maze, visited)
    @maze    = maze
    @visited = visited
  end

  def is_goal?(pos)
    @maze.get(pos) == GOAL
  end

  def available?(pos)
    @maze.get(pos) == BLANK && !@visited.get(pos)
  end
  
  def steps_to_goal
    q = [Position.new(1, 1)]
    @visited.set(q.first, true)
    while (s = q.shift)
      [s.up, s.down, s.left, s.right].each do |nxt|
        return nxt.count if is_goal?(nxt)
        if available?(nxt)
          @visited.set(nxt, true)
          q << nxt
        end
      end
    end
    return -1
  end

  def blank_count
    @maze.blank_count
  end

  def turnable_cell_count
    used_cell_count = steps_to_goal + 1
    return -1 if used_cell_count <= 0
    blank_count - used_cell_count
  end
end

H, W = STDIN.gets.split(' ').map(&:to_i)
maze = []
maze << Array.new(H + 2, '#')
H.times do
  maze << ['#'] + STDIN.gets.chomp.split('') + ['#']
end
maze << Array.new(H + 2, '#')
maze[H][W] = Maze::GOAL

map     = Matrix.new(maze)
visited = []
(H+2).times do
  visited << Array.new(W + 2, false)
end
visited = Matrix.new(visited)

puts Maze.new(map, visited).turnable_cell_count