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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class C
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		int[] D = new int[N + 1];  // D[N] = 0
		for(int i = 0; i < N; i++)
			D[i] = GetInt();

		int[] cnt = new int[13];
		for(int i = 0; i <= N; i++)
			cnt[D[i]]++;

		var free = new List<int>();
		bool[] exist = new bool[24];
		exist[0] = true;
		for(int i = 0; i < N; i++)
		{
			if(cnt[D[i]] >= 3)
			{
				Console.WriteLine(0);
				return;
			}
			else if(cnt[D[i]] == 2)
			{
				if(D[i] == 0 || D[i] == 12)
				{
					Console.WriteLine(0);
					return;
				}
				else
				{
					exist[D[i]] = true;
					exist[24 - D[i]] = true;
				}
			}
			else if(cnt[D[i]] == 1)
				free.Add(i);
		}

		int ans = 0;
		int L = free.Count;
		for(int s = 0; s < (1 << L); s++)
		{
			bool[] tmpExist = new bool[24];
			Array.Copy(exist, tmpExist, 24);

			for(int i = 0; i < L; i++)
			{				
				if(contain(s, i))
					tmpExist[D[free[i]]] = true;
				else
					tmpExist[24 - D[free[i]]] = true;				
			}

			int min = int.MaxValue;
			for(int i = 0; i < 24; i++)
			{
				for(int j = i + 1; j < 24; j++)
				{
					if(tmpExist[i] && tmpExist[j])
						min = Math.Min(min, Math.Min(j - i, 24 - (j - i)));
				}
			}
			ans = Math.Max(ans, min);
		}

		Console.WriteLine(ans);
	}

	private bool contain(int s, int x) => ((s >> x) & 1) == 1;
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}