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: Wrong Answer)



import java.util.*;

public class Main {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int [] d = new int[n + 1];
        PriorityQueue<Integer> time = new PriorityQueue<>();
        time.add(0);
        d[0] = 0;
        for (int i = 1; i <= n; ++i) {
            int current = scanner.nextInt();
            current = Math.min(current, 24 - current);
            time.add(current);
            d[i] = current;
        }
        int max = 0;
        while (time.size() == n + 1) {
            int current = time.poll();
            int originalCurrent = current;
            int currentMin = 24;
       //     System.out.println("current: " + current);
            PriorityQueue<Integer> copy = new PriorityQueue<>(time);
            while (!time.isEmpty()) {
                int nextTime = time.poll();
           //     System.out.println("next: " + nextTime);
                if (nextTime - current == 24) {
                    currentMin = Math.min(currentMin, 0);
                } else {
                    currentMin = Math.min(currentMin, nextTime - current);
                }
                current = nextTime;
            }
       //     System.out.println("currentMin: " + currentMin);
            max = Math.max(max, currentMin);
    //        System.out.println("max: " + max);
            if (24 - originalCurrent > originalCurrent) {
                copy.add(24 - originalCurrent);
            //    System.out.println("push: " + (24 - originalCurrent));

            }
        //    System.out.println("==============");
            time = new PriorityQueue<>(copy);
        }
        if (max == 24) {
            System.out.println(0);
            return;
        }
        System.out.println(max);

    }
}