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 Python (3.8.2) (judge verdict: Runtime Error)

from collections import deque

def bfs():
    # たどり着くまでにかかった回数をいれる多重リスト。
    d = [[float("inf")] * w for i in range(h)]
    # 1ノード降りるときにforで回せるようリスト化しておく
    dx = [1, 0, -1, 0]
    dy = [0, 1, 0, -1]
    # 接したポイントを取り込む用のqueを定義
    que = deque([])
    # スタート地点をqueに加える。探索の際はqueから取り出すループを回すので最初だけ先に入れておく
    que.append(sx,sy)
    # スタートからスタートにかかる距離は0なのでinfを0にかえる。
    d[sx][sy] = 0
    # queがあるかぎり続ける
    while que:
        p = que.popleft()
        # 取り出した点がゴールなら終了
        if p[0] == gy and p[1] == gx:
            break
        #　それ以外の時は，接している点を4方向順に取得。一つずつ処理する。
        for i in range(4):
            nx = p[0] + dx[i]
            ny = p[1] + dy[i]
            # 新しく取得した座標に対しての処理
            # 迷路内に存在する座標であり，壁ではなく，まだ通ったことがなくdがinfの点なら処理する = 新しく取得した道候補の1つ
            if 0 <= nx < r and 0 <= ny < c and maze[nx][ny] != "#" and d[nx][ny] == float("inf"):
                # 道候補をqueに加える。
                que.append((nx, ny))
                # その道候補への経路までにかかった経路をdに加える。
                d[nx][ny] = d[p[0]][p[1]] + 1
    return d[gy][gx]

h, w = map(int, input().split())
maze = [list(input()) for i in range(h)]
sx, sy = 0, 0
gx, gy = h - 1, w - 1

white = 0
for i in range(h):
    for j in range(w):
        if maze[i][j] == ".":
            white += 1

res = bfs()
if 0 < res < float("inf"):
    # 白いマスの数から最短経路でかかるコスト分を引く
    # ゴールを黒いマスに変えることはできないためその分も引く
    print(white - res - 1)
else:
    print(-1)