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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.Sequence   as S
import qualified Data.Map.Strict as M
import qualified Control.Monad   as C
import Data.Sequence ((><))
import Data.Map.Strict ((!))
 
import Data.Maybe
import Debug.Trace
 
type Queue  = S.Seq
 
main :: IO ()
main = do
    [h, w] <- map read . words <$> getLine :: IO [Int]
    let (sy, sx) = (1, 1)
    let (gy, gx) = (h, w)
 
    -- ここは入力を受け取っているだけなので気にしないで
    input <- C.replicateM h getLine :: IO [[Char]]
    let c = map (\(y, line) ->
                map (\(x, c) ->
                    if c == '#' then ((y, x), Nothing) else ((y, x), Just 1000000)
                    ) (zip [1..] line) 
            ) (zip [1..] input)

    let shortestPath = bfs (M.insert (sy, sx) (Just 0) . M.fromList $ concat c) 
                              (h,w)
                            $ S.fromList [(sy, sx)]
    let cnt = (foldr (\a b -> (if a=='.' then 1 else 0) + b) 0 $ concat input)
    let p = fromJust $ shortestPath ! (gy, gx)
    print $ if p/=1000000 then cnt - (fromJust $ shortestPath ! (gy, gx)) - 1
                          else -1
 
-- 幅優先探索
bfs :: M.Map (Int, Int) (Maybe Int) -- 地図
    -> (Int, Int)
    -> Queue (Int, Int)
    -> M.Map (Int, Int) (Maybe Int)
bfs c (h,w) queue 
    | S.null queue = c
    | otherwise    = let
        (y, x) = queue `S.index` 0
        q = S.tails queue `S.index` 1
        -- qはqueueの追加分, cは地図の変更分
        (q', c') = unzip . concat . flip map (destinations y x) $ \(ny, nx) ->
            if 1<=ny && ny<=h && 1<=nx && nx<=w then
                case (c!(y,x), c!(ny,nx)) of
                    (Just a, Just b) -> if (a+1 >= b) then [] else [((ny, nx) ,((ny, nx), Just $ a+1))]
                    _                -> []
                else []
        in bfs (override c $ M.fromList c') (h,w) (q >< S.fromList q')
    where
    -- Keyが重複していれば二つ目の引数のMapで一つ目のMapを上書き
    override :: (Ord k) => M.Map k a -> M.Map k a -> M.Map k a
    override = M.unionWith (\a b -> b)
    -- この問題では四方に動けるので、その行き先を作っている
    destinations y x = [(y+1, x), (y-1, x),(y, x+1),(y, x-1)]