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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.regex.Pattern;
import java.util.stream.Collectors;

public class Main {
    public void solve(final BufferedReader stdin, final PrintWriter stdout) throws NumberFormatException, IOException {
        int n = Integer.parseInt(stdin.readLine());
        Map<Integer, Long> d = Pattern.compile(" ")
                                      .splitAsStream(stdin.readLine())
                                      .map(Integer::valueOf)
                                      .collect(Collectors.groupingBy(Function.identity(), Collectors.counting()));
        d.put(0, d.getOrDefault(0, 0L) + 1);

        List<List<Integer>> times = new ArrayList<>();
        times.add(new ArrayList<>());
        for (Entry<Integer, Long> e : d.entrySet()) {
            if (e.getValue() > 2) {
                stdout.println(0);
                return ;
            }

            if (e.getValue() == 1) {
                List<List<Integer>> temp = new ArrayList<>();
                for (List<Integer> time : times) {
                    List<Integer> time1 = new ArrayList<>(time);
                    List<Integer> time2 = new ArrayList<>(time);
                    time1.add(e.getKey());
                    time2.add(e.getKey() * -1);
                    temp.add(time1);
                    temp.add(time2);
                }
                times = temp;
            } else {
                // e.getValue() == 2
                for (List<Integer> time : times) {
                    time.add(e.getKey());
                    time.add(e.getKey() * -1);
                }
            }
        }

        int max = -1;
        for (List<Integer> time : times) {
            int min = Integer.MAX_VALUE;
            for (int i = 0; i < time.size(); i++) {
                for (int j = i + 1; j < time.size(); j++) {
                    int x = Math.abs(time.get(i) - time.get(j));
                    int y = Math.min(x, 24 - x);
                    min = Math.min(min, y);
                }
            }
            max = Math.max(max, min);
        }

        stdout.println(max);
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }
}