Problem:
Score : 500 points

Problem Statement

In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.

Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.
The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours.
Here, we are using 24-hour notation.
That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.

Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.

Find the maximum possible value of s.

Constraints

1 \leq N \leq 50

0 \leq D_i \leq 12

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the maximum possible value of s.

Sample Input 1

3
7 12 8

Sample Output 1

4

For example, consider the situation where it is 7, 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.

Sample Input 2

2
11 11

Sample Output 2

2

Sample Input 3

1
0

Sample Output 3

0

Note that Takahashi himself is also a participant.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case)]

use std::io::{stdin, Read};
use std::str::FromStr;
fn read_option<T: FromStr>() -> Option<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()
}
fn read<T: FromStr>() -> T {
    let opt = read_option();
    opt.expect("failed to parse token")
}

fn main() {
    let N: usize = read();
    use std::collections::HashMap;
    let mut map: HashMap<usize, usize> = HashMap::new();
    map.insert(0, 1);
    for _ in 0..N {
        let entry = map.entry(read()).or_insert(0);
        *entry += 1;
        if *entry >= 3 {
            println!("0");
            return;
        }
    }
    let mut vec: Vec<(usize, usize)> = vec![];
    for v in map {
        vec.push(v);
    }
    let mins = dfs(0, &vec, vec![]);
    println!("{}", mins.iter().max().unwrap());
}

fn dfs(depth: usize, vec: &[(usize, usize)], times: Vec<usize>) -> Vec<usize> {
    if depth == vec.len() {
        let mut now_times = times;
        now_times.sort();
        now_times.push(24);
        let min = now_times
            .windows(2)
            .fold(1000, |acc, v| std::cmp::min(acc, (v[1] - v[0]) % 24));
        return vec![min];
    }
    let v = vec[depth].0;
    let count = vec[depth].1;
    if count == 2 {
        let mut now_times = times;
        now_times.push(v);
        now_times.push(24 - v);
        dfs(depth + 1, vec, now_times)
    } else {
        let mut now_times_mut = times.clone();
        now_times_mut.push(v);
        let mins1 = dfs(depth + 1, vec, now_times_mut);
        let mut now_times_mut = times;
        now_times_mut.push(24 - v);
        let mins2 = dfs(depth + 1, vec, now_times_mut);
        [mins1, mins2].concat()
    }
}