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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int[] D = new int[N];
        for (int i = 0; i < N; i++) {
            int t = scan.nextInt();
            D[i] = Math.min(t, 24-t);
        }
        Arrays.sort(D);
        int[][][] dp = new int[N+1][24+1][24+1];
        for (int i = 0; i <= N; i++) {
            for (int j = 0; j <= 24; j++) {
                Arrays.fill(dp[i][j], Integer.MAX_VALUE);
            }
        }
        dp[0][0][24] = 24;
        for (int i = 1; i <= N; i++) {
            for (int right = 0; right < 24; right ++) {
                for (int left = 24; right <= left; left--) {
                    if (dp[i-1][right][left] == Integer.MAX_VALUE) {
                        continue;
                    }
                    dp[i][D[i-1]][left] = Math.min(dp[i-1][D[i-1]][left], Math.min(Math.abs(left-D[i-1]),Math.abs(D[i-1]-right)));
                    dp[i][right][24-D[i-1]] = Math.min(dp[i-1][right][24-D[i-1]], Math.min(Math.abs(left-(24-D[i-1])), Math.abs(24-D[i-1]-right)));
                }
            }
        }
        int ans = 0;
        for (int right = 0; right < 24; right++) {
            for (int left = 24; right <= left; left--) {
                if (dp[N][right][left] == Integer.MAX_VALUE) {
                    continue;
                }
                ans = Math.max(ans, dp[N][right][left]);
            }
        }
        System.out.println(ans);
    }
}