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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.*;

public class Main{
	static boolean temp[]=new boolean[24];
	static int time[]=new int[13];
	static int ans=0;
	public static void main(String[] args) throws IOException {
		StreamTokenizer in=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
		in.nextToken();
		int n=(int)in.nval;
		time[0]=1;
		boolean judge=true;
		for(int i=0;i<n;i++){
			in.nextToken();
			int t=(int)in.nval;
			time[t]++;
			if((t==12||t==0)&&time[t]>1)judge=false;
			else if(time[t]>2)judge=false;
		}
		if(judge){
			Arrays.fill(temp, false);
			temp[0]=true;
			dfs(1);
			out.println(ans);
		}else out.println(0);
		out.flush();
	}
	static void dfs(int now){
		if(now==13){
			int ans1=Integer.MAX_VALUE;
			int pos=0;
			for(int i=1;i<24;i++){
				if(temp[i]){
					ans1=Math.min(ans1, i-pos);
					pos=i;
				}
			}
			ans1=Math.min(ans1, 24-pos);
			ans=Math.max(ans, ans1);
		}else if(time[now]==1){
			temp[now]=true;
			dfs(now+1);
			temp[now]=false;
			temp[24-now]=true;
			dfs(now+1);
			temp[24-now]=false;
		}else if(time[now]==2){
			temp[now]=true;
			temp[24-now]=true;
			dfs(now+1);
		}else dfs(now+1);
	}
}