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::prelude::*;
use std::io;

fn min2(x: i32, y: i32) -> i32 {
    if x <= y {
        x
    } else {
        y
    }
}

fn max2(x: i32, y: i32) -> i32 {
    if x >= y {
        x
    } else {
        y
    }
}

fn main() {
    let stdin = io::stdin();
    let mut stdin = io::BufReader::new(stdin.lock());

    let mut tmp = String::new();
    stdin.read_line(&mut tmp).unwrap();
    let _: i32 = tmp.trim().parse().unwrap();

    tmp.clear();
    stdin.read_line(&mut tmp).unwrap();
    let data: Vec<i32> = tmp.split_whitespace()
                            .map(|x| x.parse::<i32>().unwrap())
                            .collect();

    let mut dt = [0; 13];
    for v in data {
        dt[v as usize] += 1;
    }
    if dt[0] >= 1 || dt[12] >= 2 {
        println!("0");
        return;
    }
    for &x in &dt {
        if x >= 3 {
            println!("0");
            return;
        }
    }

    let mut ans = 0;
    for i in 0..(1 << 11) {
        let mut dd = [false; 24];
        dd[0] = true;
        for (x, &y) in dt.iter().enumerate() {
            if y == 1 && (x == 0 || x == 12) {
                dd[x] = true;
            } else if y == 2 {
                dd[x] = true;
                dd[24 - x] = true;
            } else if y == 1 {
                if (i >> (x - 1)) & 1 != 0 {
                    dd[x] = true;
                } else {
                    dd[24 - x] = true;
                }
            }
        }

        let mut start: i32 = -1;
        let mut last: i32 = -1;
        let mut min_gap: i32 = 24;
        for (x, &y) in dd.iter().enumerate() {
            if !y {
                continue;
            }
            if start == -1 {
                start = x as i32;
            } else {
                min_gap = min2(min_gap, x as i32 - last);
            }
            last = x as i32;
        }
        min_gap = min2(min_gap, (start + 24) - last);
        ans = max2(ans, min_gap);
    }

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