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)

use std::cmp;
use std::collections::BTreeSet;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let mut count = vec![0; 12 + 1];
    count[0] = 1;
    for _ in 0..n {
        let x: usize = sc.read();
        count[x] += 1;
        if x == 0 {
            println!("0");
            return;
        }
    }

    let mut fixed = vec![12];
    let mut floating = vec![];
    for i in 1..13 {
        if count[i] >= 3 {
            println!("0");
            return;
        }
        if count[i] == 2 {
            if i == 12 {
                println!("0");
                return;
            }
            fixed.push(12 - i);
            fixed.push(i + 12);
        }
        if count[i] == 1 {
            if i == 12 {
                fixed.push(0);
            } else {
                floating.push(i);
            }
        }
    }

    let n = floating.len();

    let mut ans = 0;
    for mask in 0..(1 << n) {
        let mut v = fixed.clone();
        for i in 0..n {
            if mask & (1 << i) != 0 {
                v.push(12 + floating[i]);
            } else {
                v.push(12 - floating[i]);
            }
        }
        v.sort();
        let v0 = v[0];
        v.push(v0);

        let mut s = 24;
        for i in 0..(v.len() - 1) {
            let d = (v[i + 1] + 24 - v[i]) % 24;
            let d = cmp::min(d, 24 - d);
            s = cmp::min(s, d);
        }
        ans = cmp::max(ans, s);
    }

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

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}