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)

//AtCoder Regular Contest 011
//B. ルイス・キャロルの記憶術
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int inputMax = int.Parse(Console.ReadLine());
            string[] inputs = Console.ReadLine().Split(' ');
            int[] d = new int[inputMax];
            for (int i = 0; i < inputMax; i++)
            {
                d[i] = int.Parse(inputs[i]);
            }
            Array.Sort(d);
            int[] placeTimes = new int[inputMax + 1];
            placeTimes[0] = 0;
            int placeTimeMax = 1;
            int clockWiseMin = int.MaxValue, counterClockWiseMin = int.MaxValue;
            for (int i = 0; i < inputMax; i++)
            {
                clockWiseMin = int.MaxValue;
                int[] placeTimesTest = new int[placeTimeMax + 1];
                Array.Copy(placeTimes, placeTimesTest, placeTimeMax);
                placeTimesTest[placeTimeMax] = d[i];
                Array.Sort(placeTimesTest);
                for (int j = 0; j < placeTimeMax; j++)
                {
                    clockWiseMin = Math.Min(clockWiseMin, Math.Abs(placeTimesTest[j + 1] - placeTimesTest[j]));
                }
                clockWiseMin = Math.Min(clockWiseMin, Math.Abs(24 - placeTimesTest[placeTimeMax]));

                counterClockWiseMin = int.MaxValue;
                placeTimesTest = new int[placeTimeMax + 1];
                Array.Copy(placeTimes, placeTimesTest, placeTimeMax);
                placeTimesTest[placeTimeMax] = 24-d[i];
                Array.Sort(placeTimesTest);
                for (int j = 0; j < placeTimeMax; j++)
                {
                    counterClockWiseMin = Math.Min(counterClockWiseMin, Math.Abs(placeTimesTest[j + 1] - placeTimesTest[j]));
                }
                counterClockWiseMin = Math.Min(counterClockWiseMin, Math.Abs(24 - placeTimesTest[placeTimeMax]));

                //counterClockWiseMin = int.MaxValue;
                //placeTimes[placeTimeMax] = 24 - d[i];
                //for (int j = 0; j < placeTimeMax; j++)
                //{
                //    counterClockWiseMin = Math.Min(counterClockWiseMin, Math.Abs(placeTimes[j + 1] - placeTimes[j]));
                //}
                //counterClockWiseMin = Math.Min(counterClockWiseMin, Math.Abs(24 - placeTimes[placeTimeMax]));

                if (clockWiseMin > counterClockWiseMin)
                {
                    placeTimes[placeTimeMax] = d[i];
                }
                else
                {
                    placeTimes[placeTimeMax] = 24-d[i];
                }
                Array.Sort(placeTimes,0, placeTimeMax+1);
                placeTimeMax++;
                if (Math.Max(clockWiseMin, counterClockWiseMin) == 0)
                {
                    Console.WriteLine(0);
                    return;
                }
            }
            Console.WriteLine(Math.Max(clockWiseMin, counterClockWiseMin));
        }
    }
}