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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        n: usize,
        mut d: [i64; n],
    }
    d.push(0);
    d.sort();

    for mindiff in (0..=d[1]).rev() {
        let clocks = vec![0; n+1];
        if dfs(clocks, 1, mindiff, &d) {
            println!("{}", mindiff);
            return;
        }
    }
}

fn dfs(mut clocks: Vec<i64>, pos: usize, mindiff: i64, d: &[i64]) -> bool {
    if pos == d.len() {
        return true;
    }

    let mut res = false;
    for &clock in &[d[pos], 24 - d[pos]] {
        if clocks.iter().take(pos).all(|c| diff(*c, clock) >= mindiff) {
            clocks[pos] = clock;
            res = res || dfs(clocks.clone(), pos+1, mindiff, d);
        }
    }
    res
}

fn diff(a: i64, b: i64) -> i64 {
    min((a-b).abs(), 24-(a-b).abs())
}