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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
class Program
{

    static void Main(string[] args)
    {
        Solve();
    }
    static long ans;
    static long[] map = new long[13];
    static void Solve()
    {
        //var NM = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = long.Parse(Console.ReadLine());
        var D = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        ans = D.Min();
        for (int i = 0; i < N; i++)
        {
            map[D[i]]++;
        }
        ans = Math.Min(ans, Cul(0, new List<long>()));
        Console.WriteLine(ans);
    }

    static long Cul(int depth,List<long> nums)
    {
        if(depth == 13)
        {
            long tmp = long.MaxValue;
            for (int i = 0; i < nums.Count; i++)
            {
                for (int j = i+1; j < nums.Count; j++)
                {
                    var diff = Math.Abs(nums[i] - nums[j]);
                    diff = Math.Min(24 - diff, diff);
                    tmp = Math.Min(tmp, diff);
                }
            }
            return tmp;
        }
        else
        {
            var next1 = new List<long>(nums);
            var next2 = new List<long>(nums);
            if(map[depth] == 0)
            {
                return Cul(depth + 1, next1);
            }
            else if (map[depth] == 1)
            {
                next1.Add(depth);
                next2.Add(24 - depth);
                return Math.Max(Cul(depth + 1, next1), Cul(depth + 1, next2));
            }
            else if (map[depth] == 2){
                next1.Add(depth);
                next1.Add(24 - depth);
                return Cul(depth + 1, next1);
            }
            else
            {
                return 0;
            }
        }
    }

}