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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] peopleCount = new int [13];
		for (int i=0;i<n;i++) {
			peopleCount[sc.nextInt()]++;
		}

		System.out.println(solve(peopleCount));

	}

	static int solve(int[] peopleCount) {
		if (peopleCount[0]>0) {
			return 0;
		}
		for (int i=1;i<=11;i++) {
			if (peopleCount[i]>2) {
				return 0;
			}
		}
		if (peopleCount[12]>1) {
			return 0;
		}

		int ans = 0;

		for (int i=0;i<2048;i++) {
			boolean[] used = new boolean[24];
			used[12]=true;
			for (int j=1;j<=11;j++) {
				if (peopleCount[j]==2) {
					used[12+j]=true;
					used[12-j]=true;
				} else if (peopleCount[j]==1) {
					if ((i & (1<<(j-1))) > 0) {
						used[12+j]=true;
					} else {
						used[12-j]=true;
					}
				}
			}
			if(peopleCount[12]==1) {
				used[0]=true;
			}
			int s = 24;
			int pos = -1;
			for(int j=0;j<48;j++) {
				if(used[j%24]) {
					if(pos >= 0) {
						s=Math.min(j-pos, s);
					}
					pos = j;
				}
			}

			ans = Math.max(s, ans);

		}
		return ans;
	}

}