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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;


    void solve()
    {
        int N = cin.nextint;
        var D = cin.scanint;
        int M = D.Min();
        Array.Sort(D);
        for (int i = 0; i < M; i++)
        {
            //WriteLine($"{i}: {string.Join(" ", D)}");
            

            for (int j = 0; j < N; j++)
            {

                if (j == N - 1)
                {
                    int d = D[N - 1] - D[0];
                    //WriteLine(d);
                    if (Math.Min(d, 24 - d) <= i)
                    {
                        //WriteLine(" " + i);
                        var b = true;
                        for (int k = 0; k < N; k++)
                        {
                            if (k == N - 1) continue;
                            int t = Math.Abs(-D[N - 1] - D[k]);
                            if (Math.Min(t, 24 - t) <= i)
                            {
                                b = false;
                                break;
                            }
                        }
                        if (b)
                        {
                            D[N - 1] = -D[N - 1];
                        }
                        else
                        {
                            b = true;
                            for (int k = 0; k < N; k++)
                            {
                                if (k == 0) continue;
                                int t = Math.Abs(-D[0] - D[k]);
                                if (Math.Min(t, 24 - t) <= i)
                                {
                                    b = false;
                                    break;
                                }
                            }
                            if (b)
                            {
                                D[0] = -D[0];
                            }
                            else
                            {
                                WriteLine(i);
                                return;
                            }
                        }
                        Array.Sort(D);
                    }

                }
                else
                {
                    int d = D[j + 1] - D[j];
                    //WriteLine(d);
                    if (Math.Min(d, 24 - d) <= i)
                    {
                        //WriteLine(" " + i);
                        var b = true;
                        for (int k = 0; k < N; k++)
                        {
                            if (k == j + 1) continue;
                            int t = Math.Abs(-D[j + 1] - D[k]);
                            if (Math.Min(t, 24 - t) <= i)
                            {
                                b = false;
                                break;
                            }
                        }
                        if (b)
                        {
                            D[j + 1] = -D[j + 1];
                        }
                        else
                        {
                            b = true;
                            for (int k = 0; k < N; k++)
                            {
                                if (k == j) continue;
                                int t = Math.Abs(-D[j] - D[k]);
                                if (Math.Min(t, 24 - t) <= i)
                                {
                                    b = false;
                                    break;
                                }
                            }
                            if (b)
                            {
                                D[j] = -D[j];
                            }
                            else
                            {
                                WriteLine(i);
                                return;
                            }
                        }
                        Array.Sort(D);
                        j--;
                    }
                }
               

            }
        }
        WriteLine(M);
    }

}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}