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::io::Write;
use std::ops::{Add, Mul, Sub};

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

fn main() {
    let _n: usize = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        s.parse().unwrap()
    };

    let d: Vec<isize> = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        s.split_whitespace().map(|x| x.parse().unwrap()).collect()
    };

    let mut counts = vec![0; 13];
    counts[0] += 1;
    for x in d {
        counts[x as usize] += 1;
    }

    let mut a = vec![];
    let mut b = vec![];
    for i in 0..13 {
        if counts[i] == 1 {
            a.push(i as isize);
        } else if counts[i] == 2 {
            b.push(i as isize);
        } else if counts[i] >= 3 {
            // answer
            println!("0");
            return;
        }
    }

    let mut v = vec![];
    for x in b {
        v.push(x);
        v.push(24 - x);
    }

    let mut max = 0;
    let l = a.len();
    for bits in 0..(1 << l) {
        let mut v = v.clone();
        for (i, x) in a.iter().enumerate() {
            if is_plus(bits, i) {
                v.push(*x);
            } else {
                v.push(24 - *x);
            }
        }

        let tmp = calc_min(&v);
        if max < tmp {
            // debugln!("{}, {:?}", tmp, v);
            max = tmp;
        }
    }

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

fn calc_min(v: &Vec<isize>) -> isize {
    let mut min = std::isize::MAX;
    for i in 0..v.len() {
        for j in (i + 1)..v.len() {
            let tmp = calc_diff(v[i], v[j]);
            if tmp < min {
                min = tmp;
            }
        }
    }

    min
}

fn calc_diff(a: isize, b: isize) -> isize {
    std::cmp::min((a - b).abs(), (24 - (a - b).abs()))
}

fn is_plus(bits: isize, index: usize) -> bool {
    (bits & (1 << index)) > 0
}