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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TimeGap solver = new TimeGap();
        solver.solve(1, in, out);
        out.close();
    }

    static class TimeGap {
        int[] D;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            D = new int[N];
            for (int i = 0; i < N; i++) D[i] = in.nextInt();

            if (N == 1) {
                out.println(Math.min(D[0], 24 - D[0]));
                return;
            }

            if (N > 13) {
                out.println(0);
                return;
            }

            int ans = find(0, N, new int[N]);
            out.println(ans == Integer.MAX_VALUE ? D[0] : ans);
        }

        private int find(int idx, int n, int[] times) {
            if (idx == n) {
                return computeMin(times);
            }
            times[idx] = Math.min(D[idx], 24 - D[idx]);
            int ans = find(idx + 1, n, times);
            times[idx] = Math.max(D[idx], 24 - D[idx]);
            ans = Math.max(ans, find(idx + 1, n, times));
            return ans;
        }

        private int computeMin(int[] times) {
            int ans = Integer.MAX_VALUE;
            for (int i = 0; i < times.length; i++) {
                for (int j = 0; j < times.length; j++) {
                    if (i != j) {
                        ans = Math.min(ans, timeGap(times[i], times[j]));
                    }
                }
            }
            return ans;
        }

        private int timeGap(int t1, int t2) {
            int d = ((t2 - t1) + 48) % 24;
            return Math.min(d, 24 - d);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}