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 (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-

import sys
input = sys.stdin.readline

from collections import deque

H, W = map(int, input().split())

start, goal = (1, 1), (H, W)
# 左右上下
directions = [[0,-1],[0,1],[-1,0],[1,0]]
# 四方に一回り大きいフィールドを作る
field = [['*'] * (W+2) for i in range(H+2)]
for i in range(1,H+1):
    row = list(input())[:-1]
    for j in range(1, W+1):
        field[i][j] = row[j-1]

# 移動距離メモ
memo = [[float('inf')] * (W+2) for i in range(H+2)]
memo[start[0]][start[1]] = 0
# 訪問済メモ
visited = [[0] * (W+2) for i in range(H+2)]
# 移動元メモ
prevs = [[None] * (W+2) for i in range(H+2)]

def bfs():
    que = deque()
    # スタート位置
    que.append(start)
    while len(que) != 0:
        cur = que.popleft()
        # 見終わった場所はもうやらない
        if visited[cur[0]][cur[1]] == 1:
            continue
        # 訪問済にする
        visited[cur[0]][cur[1]] = 1
        # 4方向見る
        for direction in directions:
            # 上下左右に1つずつ動かした座標
            nxt = list(map(lambda x,y: x+y, cur, direction))
            # 壁か黒マスはスキップ
            if field[nxt[0]][nxt[1]] == '*' or field[nxt[0]][nxt[1]] == '#':
                continue
            # 現在位置+1の距離を移動先に記録
            if field[nxt[0]][nxt[1]] == '.' and memo[nxt[0]][nxt[1]] > memo[cur[0]][cur[1]] + 1:
                memo[nxt[0]][nxt[1]] = memo[cur[0]][cur[1]] + 1
                # ここで移動元のマスを記録
                prevs[nxt[0]][nxt[1]] = (cur[0], cur[1])
                # キューに次のマスを足す
                que.append(nxt)

# 最短経路を出す
bfs()
# ゴールに辿り着けない場合
if memo[goal[0]][goal[1]] == float('inf'):
    print(-1)
    exit()
# 最短経路で使うマスに目印をつける
field[goal[0]][goal[1]] = '@'
nxt = prevs[goal[0]][goal[1]]
for _ in range(memo[goal[0]][goal[1]]):
    field[nxt[0]][nxt[1]] = '@'
    nxt = prevs[nxt[0]][nxt[1]]
# 残っている白マスが塗り替えられる場所
ans = 0
for i in range(1,H+1):
    for j in range(1, W+1):
        if field[i][j] == '.':
            ans += 1
print(ans)