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.*;

class Main {
    static int f(int[]e){
        int m=24;
        for(int i=0;i<24;++i)
            for(int j=0;j<24;++j)
                if(i!=j&&e[i]>0&&e[j]>0)
                    m=Math.min(m,Math.min((i-j+24)%24,(j-i+24)%24));
        return m;
    }
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n=scan.nextInt();
        int[]d=new int[13];
        d[0]=1;
        for(int i=0;i<n;++i){
            d[scan.nextInt()]++;
        }
        for(int i=0;i<=12;++i)
            if(((i==0||i==12)&&d[i]>=2)||(i!=0&&i!=12&&d[i]>=3)){
                System.out.println(0);
                return;
            }
        int[]e=new int[24];
        int s=0;
        for(int i=0;i<=12;++i){
            if(d[i]==0)continue;
            if(((i==0||i==12)&&d[i]==1)||(i!=0&&i!=12&&d[i]==2)){
                e[i]=e[(24-i)%24]=1;
                continue;
            }
            s|=1<<i;
        }
        int m=0;
        for(int t=0;t<=s;++t){
            if((t|s)!=s)continue;
            for(int i=1;i<=11;++i)
                if((t&1<<i)!=0)e[i]=1;
                else if((s&1<<i)!=0)e[24-i]=1;
            m=Math.max(m,f(e));
            for(int i=1;i<=11;++i)
                if((s&1<<i)!=0)e[i]=e[24-i]=0;
        }
        System.out.println(m);
    }
}