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.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] cnt = new int[13];
		cnt[0]++;
		for(int i=0;i<N;i++){
			cnt[D[i]]++;
		}
		
		for(int i=0;i<13;i++){
			if(i == 0 || i == 12){
				if(cnt[i] >= 2){
					Console.WriteLine(0);
					return;
				}
			}
			if(cnt[i] >= 3){
				Console.WriteLine(0);
				return;
			}
		}
		
		int max = 0;
		
		for(int t=0;t<1<<12;t++){
			bool[] choice = new bool[24];
			
			if(cnt[0] == 1) choice[0] = true;
			
			for(int j=1;j<12;j++){
				if(cnt[j] == 2){
					choice[j] = true;
					choice[24 - j] = true;
				}
				if(cnt[j] == 1){
					if(((t >> j) & 1) == 1){
						choice[j] = true;
					} else {
						choice[24 - j] = true;
					}
				}
			}
			
			if(cnt[12] == 1) choice[12] = true;
			
			
			int last = 0;
			int min = 24;
			for(int j=1;j<=24;j++){
				if(!choice[j % 24]) continue;
				int dist = j - last;
				min = Math.Min(min, dist);
				last = j;
			}
			
			max = Math.Max(max, min);
			
		}
		
		Console.WriteLine(max);
	}
	int N;
	int[] D;
	public Sol(){
		N = ri();
		D = ria();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}