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.Linq;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        Console.ReadLine();
        int[] i = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        //被りの振り分け
        Array.Sort(i);
        List<int> j = new List<int>();
        List<int> k = new List<int>();
        j.Add(0);
        k.Add(0);
        for (int a = 0; a < i.Length; a++)
        {
            if (a % 2 == 0)
            {
                j.Add(i[a]);
            }
            else
            {
                k.Add(i[a]);
            }
        }
        int minvalue = 24 - (j.Last() + k.Last());
        for (int a = 0; a < j.Count - 1; a++)
        {
            minvalue = Math.Min(minvalue,Math.Abs(j[a] - j[a + 1]));
        }
        for (int a = 0; a < k.Count - 1; a++)
        {
            minvalue = Math.Min(minvalue, Math.Abs(k[a] - k[a + 1]));
        }
        Console.WriteLine(minvalue);
    }
}