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)

#[test]
fn test_solve() {
    assert_eq!(solve("3\n7 12 8\n"), "4\n");
    assert_eq!(solve("2\n11 11\n"), "2\n");
    assert_eq!(solve("1\n0\n"), "0\n");
    assert_eq!(solve("1\n12\n"), "12\n");
    assert_eq!(solve("3\n4 4 4\n"), "0\n");
    assert_eq!(solve("11\n 2 2 4 4 6 6 8 8 10 10 12\n"), "2\n");
    assert_eq!(solve("2\n12 12"), "0\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n = sc.read();
    let d: Vec<usize> = (0..n).map(|_| sc.read()).collect();
    let mut cnt = vec![0; 13];
    for &d in &d {
        cnt[d] += 1;
    }
    let cnt = cnt;

    let mut ext = vec![false; 24];

    if cnt[0] > 0 || cnt[12] > 1 {
        return "0\n".to_string();
    }
    ext[0] = true;
    ext[12] = cnt[12] > 0;

    for i in 1..12 {
        if cnt[i] > 2 {
            return "0\n".to_string();
        }
        ext[i] = cnt[i] > 0;
        ext[24 - i] = cnt[i] > 1;
    }

    let mut ret = 0;
    for s in 0..1 << 11 {
        for k in 1..12 {
            if s&(1<<(k-1)) != 0 && ext[k] && !ext[24-k] {
                ext[k] = false;
                ext[24-k] = true;
            }
            if s&(1<<(k-1)) == 0 && !ext[k] && ext[24-k] {
                ext[k] = true;
                ext[24-k] = false;
            }
        }
        let mut r = 12;
        for dis in (1..12).rev() {
            for i in 0..24 {
                if ext[i] && ext[(i+dis)%24] {
                    r = dis;
                }
            }
        }
        ret = std::cmp::max(ret, r);
    }

    format!("{}\n", ret)
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}