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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        //Solve();
        WriteLine(Solve());
    }
    static bool[] b;
    static int[] key;
    static int res;
    static int Solve()
    {
        var num = Input.num;
        var ds = Input.ar;
        var dic = new Dictionary<int, int>();
        for (var i = 0; i < num; i++)
            if (dic.ContainsKey(ds[i]))
                dic[ds[i]]++;
            else dic[ds[i]] = 1;
        if (dic.Any(v => v.Value > 2 || v.Key == 0)) return 0;
        b = new bool[24];b[0] = true;
        foreach (var d in dic)
        {
            if (d.Key == 12)
            {
                if (d.Value == 1) b[12] = true;
                else return 0;
            }
            else if (d.Value > 1)
                b[d.Key] = b[24 - d.Key] = true;
        }
        key = dic.Where(v => v.Value == 1 && v.Key != 12).Select(v => v.Key).ToArray();
        if (key.Length != 0)
        {
            dfs(0, true);
            dfs(0, false);
        }
        else
        {
            var i = 1;
            var min = int.MaxValue;
            while (i < 24)
            {
                var len = 1;
                while (i < 24 && !b[i])
                {
                    len++;
                    i++;
                }
                min = Min(len, min);
                i++;
            }
            res = Max(res, min);

        }
        return res;
    }
    static void dfs(int depth,bool s)
    {
        b[key[depth]] = s;
        b[key[depth] + 12] = !s;
        if (depth == key.Length - 1)
        {
            var i = 1;
            var min = int.MaxValue;
            while (i < 24)
            {
                var len = 1;
                while (i < 24 && !b[i])
                {
                    len++;
                    i++;
                }
                min = Min(len, min);
                i++;
            }
            res = Max(res, min);
            return;
        }
        dfs(depth + 1, true);
        dfs(depth + 1, false);
        b[key[depth]] = b[key[depth] + 12] = false;
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        return default(T);
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}