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)


fn getline() -> String {
    let mut res = String::new();
    std::io::stdin().read_line(&mut res).ok();
    res
}

#[allow(unused_macros)]
macro_rules! readl {
    ($t: ty) => {
        {
            let s = getline();
            s.trim().parse::<$t>().unwrap()
        }
    };
    ($( $t: ty),+ ) => {
        {
            let s = getline();
            let mut iter = s.trim().split(' ');
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
}

#[allow(unused_macros)]
macro_rules! readlvec {
    ($t: ty) => {
        {
            let s = getline();
            let iter = s.trim().split(' ');
            iter.map(|x| x.parse().unwrap()).collect::<Vec<$t>>()
        }
    }
}

#[allow(unused_macros)]
macro_rules! debug {
    ($x: expr) => {
        println!("{}: {:?}", stringify!($x), $x)
    }
}

fn printiter<'a, T>(v: &'a T)
where
    &'a T: std::iter::IntoIterator,
    <&'a T as std::iter::IntoIterator>::Item: std::fmt::Display,
{
    for (i, e) in v.into_iter().enumerate() {
        if i != 0 {
            print!(" ");
        }
        print!("{}", e);
    }
    println!("");
}

#[allow(unused_imports)]
use std::cmp::{min, max};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, BTreeMap, HashMap, HashSet};
#[allow(unused_imports)]
use std::collections::btree_map::Entry::{Occupied, Vacant};
fn main() {
    use std::io::Write;
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    #[allow(unused_macros)]
    macro_rules! print { ($($arg:tt)*) => (write!(out, $($arg)*).unwrap()); }
    #[allow(unused_macros)]
    macro_rules! println { () => (writeln!(out).unwrap()); ($($arg:tt)*) => (writeln!(out, $($arg)*).unwrap()); }
    
    let n = readl!(usize);
    let mut d = readlvec!(i32);
    d.push(0);

    let mut cnt = BTreeMap::new();
    for &e in &d {
        let hoge = cnt.entry(e).or_insert(0);
        *hoge += 1;
    }

    let mut s = 1;
    let mut de = Vec::new();
    for (&k, &c) in &cnt {
        if c == 1 {
            s |= 1<<k;
        } else if c == 2 {
            de.push(k);
            de.push(24-k);
        } else {
            println!("0");
            return;
        }
    }

    
    let mut ans = 0;
    for mask in 0..(1<<13) {
        let mut vec = Vec::<i32>::new();
        for i in 0..13 {
            if (s>>i)&1 == 1 {
                if ((mask >> i)&1) == 1 {
                    vec.push(i);
                } else {
                    vec.push((24-i)%24);
                }
            }
        }
        vec.append(&mut de.clone());
        let mut mi = 24;
        for i in 0..vec.len() {
            for j in 0..i {
                mi = min(mi, min(24-(vec[i]-vec[j]).abs(), (vec[i]-vec[j]).abs()));
            }
        }
        // debug!(mi);
        ans = max(mi, ans);
    }
    println!("{}", ans);
}