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 Rust (1.15.1) (judge verdict: Accepted)

extern crate core;

use std::io::{self, Read};

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = run(input.trim().to_string());
    println!("{}", output);
}

fn run(input: String) -> String {
    let list = input
        .split("\n")
        .skip(1)
        .map(|x| {
            x.chars()
                .map(|x| if x == '.' { true } else { false })
                .collect::<Vec<_>>()
        })
        .collect::<Vec<_>>();

    let path = bfs(&list);
    //白の数
    let count = list.into_iter().flat_map(|x| x).filter(|x| *x).count();
    if let Some(len) = path.map(|x| x.len()) {
        (count - len).to_string()
    } else {
        "-1".to_string()
    }
}

#[test]
fn test() {
    let tests = vec![
        (
            "3 3
..#
#..
...",
            "2",
        ),
        (
            "10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................",
            "209",
        ),
    ];
    for (i, (input, output)) in tests.into_iter().enumerate() {
        println!("test:{}", i);
        assert_eq!(run(input.to_string()), output.to_string());
    }
}

#[derive(PartialEq, Debug, Clone)]
enum Cell {
    Wall,
    Empty,
    Visited(usize, usize),
}
fn bfs(m: &Vec<Vec<bool>>) -> Option<Vec<(usize, usize)>> {
    let mut m = m.iter()
        .map(|x| {
            x.iter()
                .map(|&x| if x { Cell::Empty } else { Cell::Wall })
                .collect::<Vec<_>>()
        })
        .collect::<Vec<_>>();
    let goal = (m.len() - 1, m[0].len() - 1);
    let mut n: (usize, usize) = (0, 0);
    // Queue に初期値を積む
    let mut queue = vec![n];
    while queue.len() > 0 {
        // queueから取り出す
        n = queue[0];
        queue.remove(0);
        // 行けるセルとをチェック
        for d in vec![(1i32, 0i32), (0i32, 1i32), (-1i32, 0i32), (0i32, -1i32)] {
            let next_x = (n.0 as i32) + d.0;
            let next_y = (n.1 as i32) + d.1;
            if next_x >= 0 && next_x <= (goal.0 as i32) && next_y >= 0 && next_y <= (goal.1 as i32)
            {
                let next_x = next_x as usize;
                let next_y = next_y as usize;

                if m[next_x][next_y] == Cell::Empty {
                    m[next_x][next_y] = Cell::Visited(n.0, n.1);
                    // Queueに積む
                    queue.push((next_x, next_y))
                }

                if (next_x, next_y) == goal {
                    m[0][0] = Cell::Empty;
                    let mut path = vec![(goal.0, goal.1)];
                    let mut c = &m[goal.0][goal.1];
                    while let &Cell::Visited(x, y) = c {
                        path.push((x, y));
                        c = &m[x][y];
                    }
                    path.reverse();
                    return Some(path);
                }
            }
        }
    }
    None
}