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::{max,min};
fn main() {
    let _n = rv::<usize>()[0];
    let mut c = [0;13];
    c[0]=1;
    for d in rv::<usize>() {
        c[d]+=1;
    }
    let mut x = vec![];
    let mut y = vec![];
    for i in 0..13i8 {
        let c=c[i as usize];
        if i==0 || i==12 {
            if c>1 {
                println!("{}",0);
                return;
            }
            if c==1 {
                x.push(i);
            }
        }
        else {
            if c>2 {
                println!("{}",0);
                return;
            }
            if c==2 {
                x.push(i);
                x.push(24-i);
            }
            else if c==1 {
                y.push(i);
            }
        }
    }
    let n=x.len();
    let m=y.len();
    let mut t=0;
    for b in 0..1<<m {
        x.truncate(n);
        for i in 0..m {
            x.push(if b>>i&1==0 {y[i]} else {24-y[i]});
        }
        let mut s=12;
        for i in 0..n+m { for j in 0..n+m { if i!=j {
            let d=(x[i]-x[j]).abs();
            s = min(s,min(d,24-d));
        }}}
        t = max(t,s);
    }
    println!("{}",t);
}
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T> where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}