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: Wrong Answer)

use std::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let mut d: Vec<i32> = (0..n)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();
    d.push(0);
    d.sort();

    let mut unko = Vec::new();
    let mut unti = vec![0; 13];
    for i in 0..n + 1 {
        unti[d[i] as usize] += 1;
        if i % 2 == 0 {
            unko.push(d[i]);
        } else {
            unko.push((24 - d[i]) % 24);
        }
    }

    if unti[0] > 1 || unti[12] > 1 {
        println!("{}", 0);
        return;
    }
    for i in 1..12 {
        if unti[i] > 2 {
            println!("{}", 0);
            return;
        }
    }

    let mut ans = 1 << 30;
    for i in 0..n + 1 {
        for j in 0..n + 1 {
            if i != j {
                ans = min(ans, (unko[i] - unko[j]).abs());
            }
        }
    }
    println!("{}", ans);
}