Problem:
Score : 400 points

Problem Statement

Takahashi has a maze, which is a grid of H \times W squares with H horizontal rows and W vertical columns.

The square at the i-th row from the top and the j-th column is a "wall" square if S_{ij} is #, and a "road" square if S_{ij} is ..

From a road square, you can move to a horizontally or vertically adjacent road square.

You cannot move out of the maze, move to a wall square, or move diagonally.

Takahashi will choose a starting square and a goal square, which can be any road squares, and give the maze to Aoki.

Aoki will then travel from the starting square to the goal square, in the minimum number of moves required.

In this situation, find the maximum possible number of moves Aoki has to make.

Constraints

1 \leq H,W \leq 20

S_{ij} is . or #.

S contains at least two occurrences of ..

Any road square can be reached from any road square in zero or more moves.

Input

Input is given from Standard Input in the following format:

H W
S_{11}...S_{1W}
:
S_{H1}...S_{HW}

Output

Print the maximum possible number of moves Aoki has to make.

Sample Input 1

3 3
...
...
...

Sample Output 1

4

If Takahashi chooses the top-left square as the starting square and the bottom-right square as the goal square, Aoki has to make four moves.

Sample Input 2

3 5
...#.
.#.#.
.#...

Sample Output 2

10

If Takahashi chooses the bottom-left square as the starting square and the top-right square as the goal square, Aoki has to make ten moves.

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

// -*- coding:utf-8-unix -*-

#[macro_use]
extern crate lazy_static;
extern crate num_bigint; // 0.2.2
extern crate num_traits; // 0.2.8
use num_bigint::BigInt;
use num_traits::Pow;

// use proconio::derive_readable;
use proconio::fastout;
use proconio::input;
// use std::convert::TryInto;
use ascii::{AsciiChar, AsciiString};
use itertools::concat;
use lazy_static::lazy_static;
use proconio::marker::Chars;
use std::cmp::*;
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::*;
use std::ops::Range;
use std::str::FromStr;
use std::sync::Mutex;
use superslice::*;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// lazy_static! {
//     static ref H: Mutex<Vec<i32>> = Mutex::default();
//     static ref W: Mutex<Vec<i32>> = Mutex::default();
// }

//abc147-C
// #[fastout]
fn main() {
    input![h: usize, w: usize, s: [Chars; h]];

    // let s: Vec<_> = s
    //     .into_iter()
    //     .map(|s: String| AsciiString::from_str(&s[..]).unwrap())
    //     .collect();

    // let mut maze = vec![vec!['#'; w + 2]; h + 2];
    // eprintln!("before init");

    // for hh in 1..(h + 1) {
    //     for ww in 1..(w + 1) {
    //         maze[hh][ww] = s[hh - 1][ww - 1];
    //         if maze[hh][ww] == '#' {
    //             // is_visit[hh - 1][ww - 1] = true;
    //         }
    //     }
    // }

    // eprintln!("after init");
    let del_h = [-1, 1, 0, 0];
    let del_w = [0, 0, -1, 1];
    let mut is_visit = vec![false; w * h];
    let mut ans = -1;
    let mut q = VecDeque::new();

    // let a = is_visit[0][1];

    for hh in 0..h {
        for ww in 0..w {
            if s[hh][ww] == '#' {
                continue;
            }

            {
                for hh in 0..h {
                    for ww in 0..w {
                        is_visit[hh * w + ww] = false;
                    }
                }
            }

            // let mut is_visit: Vec<_> = is_visit.iter().map(|v| v.clone()).collect();
            // let mut dist = vec![vec![1000; w]; h];
            let mut new_ans = -1;
            //hh, wwをスタートにして、幅優先探索をする
            q.clear();
            q.push_back((hh, ww, 0));
            while let Some((hh, ww, d)) = q.pop_front() {
                let mut is_comp = true;
                {
                    for hh in 0..h {
                        for ww in 0..w {
                            if !is_visit[hh * w + ww] && s[hh][ww] != '#' {
                                is_comp = false;
                            }
                        }
                    }
                    if is_comp {
                        break;
                    }
                }

                // while !(q.is_empty()) {
                // let ;
                is_visit[hh * w + ww] = true;
                // dist[hh - 1][ww - 1] = d;
                // eprintln!("{:?}", ((hh, ww), d));
                new_ans = max(new_ans, d);

                for i in 0..4 {
                    let new_h = hh as i64 + del_h[i];
                    let new_w = ww as i64 + del_w[i];

                    if new_h < 0 || new_w < 0 || new_h >= h as i64 || new_w >= w as i64 {
                        continue;
                    }

                    let new_h = new_h as usize;
                    let new_w = new_w as usize;

                    // eprintln!("{}, {}, {}", new_h, new_w, maze[new_h][new_w]);
                    // if maze[new_h][new_w] == '#' || dist[new_h - 1][new_w - 1] < 1000 {
                    if s[new_h][new_w] == '#' || is_visit[new_h * w + new_w] {
                        continue;
                    }

                    q.push_back((new_h, new_w, d + 1));
                }

                // eprintln!(
                //     "{}, {}",
                //     q.is_empty(),
                //     is_visit.iter().all(|row| row.iter().all(|a| *a))
                // );
            }

            ans = max(ans, new_ans);
        }
    }

    println!("{}", ans);
}

// let mut values = VALUES.lock().unwrap();
// values.extend_from_slice(&[1, 2, 3, 4]);
// assert_eq!(&*values, &[1, 2, 3, 4]);