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)

//#pragma warning disable
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System;
using System.Numerics;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
class Z { static void Main() => new K(); }
class K
{
	int F() => int.Parse(ReadLine());
	long FL() => long.Parse(ReadLine());
	int[] G() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(int.Parse).ToArray();
	long[] GL() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(long.Parse).ToArray();
	public const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Console.WriteLine(Solve());
		Out.Flush();
	}
	int Solve()
	{
		var N = F();
		var D = G();
		var cnt = new int[13];
		foreach (var d in D) cnt[d]++;
		var t = 0;
		if (cnt[0] > 0 || cnt[12] > 1) return 0;
		for (var i = 1; i < 12; i++)
		{
			if (cnt[i] > 2) return 0;
			if (cnt[i] > 0) t++;
		}
		var max = 0;
		for (var i = 0; i < (1 << t); i++)
		{
			var s = new bool[24];
			s[0] = true;
			s[12] = cnt[12] > 0;
			var j = 0;
			for (var k = 1; k < 12; k++)
			{
				if (cnt[k] == 0) continue;
				if (cnt[k] == 2) s[k] = s[24 - k] = true;
				else if ((i & (1 << (j++))) != 0) s[k] = true;
				else s[24 - k] = true;
			}
			var l = 23;
			while (!s[l]) l--;
			var min = 24 - l;
			j = 0;
			while (true)
			{
				var k = j + 1;
				while (k < 24 && !s[k]) k++;
				min = Min(min, k - j);
				if ((j = k) >= l) break;
			}
			max = Max(max, min);
		}
		return max;
	}
}