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)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

class Maze
  ROOT='.'; WALL='#'; START='1'; GOAL='2'

  def initialize(map=nil, vec=nil)
    self.parseMap(map) if map
    unless vec
      vec = []
      for i in 0..3
        j = i%3==0 ? 1 : -1
        vec[i] = { :x=>(i+1)%2*j, :y=>i%2*j }
      end
    end
    @vec = vec
  end

  # マップ文字列を展開する
  def parseMap(map)
    @map = map.split("\n").map{|line| line.split }
    @size = Hash[*[[:x,:y],@map.shift.map{|val|val.to_i}].transpose.flatten]
    @map.each_with_index do |line,i|
      line.each_with_index do |val,j|
        @start = {:x=>j, :y=>i} if val==START
        @goal  = {:x=>j, :y=>i} if val==GOAL
      end
    end
  end

  # 探索開始
  def search()
    self.openNode(nil, pos=@start, cost=0)
    loop do
      cost += 1
      @vec.each do |vec|
        newPos = { :x=>pos[:x]+vec[:x], :y=>pos[:y]+vec[:y] }
        self.openNode(@map[pos[:y]][pos[:x]], newPos, cost)
        return true if newPos==@goal
      end
      self.closeNode(pos)
      return false unless pos=self.getNextPos()
    end
  end

  # OPENノードからコストが最小のノードを選ぶ
  def getNextPos()
    minScore = nil
    minNode = []
    for j in 0..@size[:y]-1
      for i in 0..@size[:x]-1
        if @map[j][i].is_a?(AStar) && @map[j][i].status===true then
          if !minScore || minScore>@map[j][i].score then
            minScore = @map[j][i].score
            minNode = [{ :x=>i, :y=>j }]
          elsif minScore==@map[j][i].score then
            minNode.push({ :x=>i, :y=>j })
          end
        end
      end
    end
    return minNode.length ? minNode[rand(minNode.length)] : false
  end

  # ノードを開く
  def openNode(parent, pos, cost)
    x=pos[:x]; y=pos[:y]
    return false if x<0 || y<0 || x>=@size[:x] || y>=@size[:y]
    return false if @map[y][x].is_a?(AStar) || @map[y][x]==WALL
    @map[y][x] = AStar.new(parent, cost, self.calcHeuristic(pos), pos)
    return true
  end

  # ノードを閉じる
  def closeNode(pos)
    @map[pos[:y]][pos[:x]].status = false
  end

  # ヒューリスティックコストを計算する
  def calcHeuristic(pos)
    x = pos[:x] - @goal[:x]
    y = pos[:y] - @goal[:y]
    return Math.sqrt(x*x+y*y).to_i
  end

  # スタートからゴールまでの道筋を辿る
  def getRoot()
    root=[]; node=@map[@goal[:y]][@goal[:x]]
    loop do
      return root.reverse unless node
      return false unless node.is_a?(AStar)
      root.push(node.pos)
      node = node.parent
    end
  end

  def getMap()
  	@map
  end
end

class AStar
  attr_accessor :status, :cost, :heuristic, :pos, :score, :parent

  def initialize(parent, cost, heuristic, pos)
    @status = true
    @parent=parent; @cost=cost; @heuristic=heuristic; @pos=pos
    self.calcScore()
  end

  def calcScore
    @score = @cost + @heuristic
  end
end

INT_MAX = 1000000001

H,W=gets.chomp.split(' ').map{|n| n.to_i}
S=Array.new(H){Array.new(W){0}}
0.upto(H-1){|i|
	S[i]=gets.chomp.split('').map{|n| n}
}
dp=Array.new(H){Array.new(W){INT_MAX }}

# 「.」のマス数
sum = 0
0.upto(H-1){|i|
	sum += (S[i].count{|i|i=="."})
}
# puts sum

S[0][0]=1
S[H-1][W-1]=2
map = <<EOM
#{W} #{H}
#{S.map{|a|a.join(" ")}.join("\n")}
EOM
#p map
maze = Maze.new(map)
# p maze.getMap()
maze.search()
path = maze.getRoot()
if(!path)
	puts "-1"
else
	p sum - path.size
end