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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;

namespace AtCoder
{
    class Program
    {
        static public int[] Sarray() { return ReadLine().Split().Select(int.Parse).ToArray(); }
        static public List<int> Slist() { return ReadLine().Split().Select(int.Parse).ToList(); }

        static int N;
        static List<int> D;
        static int[] mincol;
        static int[,] dp;
        static int maxmins;
        static void Main(string[] args)
        {
            N = Slist()[0];
            D = Slist();
            D.Insert(0, 0);
            mincol = new int[N + 1];
            dp = new int[N + 1, N + 1];
            maxmins = int.MaxValue;

            int mini = 0;
            for (var i = 0; i < N; ++i)
            {
                int minc = int.MaxValue;
                for (var j = i + 1; j < N + 1; ++j)
                {
                    var t = Math.Abs(D[i] - D[j]);
                    dp[i, j] = t <= 12 ? t : 24 - t;
                    if (dp[i, j] < maxmins)
                    {
                        maxmins = dp[i, j];
                        mini = i;
                    }
                    if (dp[i, j] < minc)
                    {
                        minc = dp[i, j];
                        mincol[i] = j;
                    }
                }
            }
            dfs(1, mini);
            dfs(1, mincol[mini]);
            WriteLine(maxmins);
        }
        static void dfs(int dpt, int ch)
        {
            //元のを記録しておく
            var dprecol = new int[dp.GetLength(0)];
            for (var i = 0; i < dp.GetLength(0); ++i)
                dprecol[i] = dp[i, ch];
            var dprerow = new int[dp.GetLength(1)];
            for (var i = 0; i < dp.GetLength(1); ++i)
                dprerow[i] = dp[ch, i];
            var mincolpre = new int[mincol.Length];
            Array.Copy(mincol, mincolpre, mincol.Length);

            D[ch] = 24 - D[ch];
            //24-Dに変更したのでその分を更新
            //行について
            int s = int.MaxValue;
            for (var i = ch + 1; i < N + 1; ++i)
            {
                var t = Math.Abs(D[ch] - D[i]);
                dp[ch, i] = t <= 12 ? t : 24 - t;
                if (dp[ch, i] < s)
                {
                    s = dp[ch, i];
                    mincol[ch] = i;
                }
            }
            //列について
            for (var i = 0; i < ch; ++i)
            {
                var t = Math.Abs(D[ch] - D[i]);
                dp[i, ch] = t <= 12 ? t : 24 - t;
                if (mincol[i] != ch)
                {
                    if (dp[i, ch] < dp[i, mincol[i]])
                        mincol[i] = ch;
                }
                else
                {
                    s = int.MaxValue;
                    for (var j = i + i; j < N + 1; ++j)
                        if (dp[i, j] < s)
                        {
                            s = dp[i, j];
                            mincol[i] = j;
                        }
                }
            }
            var min = int.MaxValue;
            int mini = 0, minj = 0;
            for (var i = 0; i < N; ++i)
                if (dp[i, mincol[i]] < min)
                {
                    mini = i;
                    minj = mincol[i];
                    min = dp[i, mincol[i]];
                }

            if (maxmins <= min)
            {
                maxmins = min;
                var cha = Math.Abs(D[mini] + D[minj] - 24);
                if (maxmins < cha)
                {
                    if (maxmins < 24 - D[mini])
                        dfs(dpt + 1, mini);
                    if (maxmins < 24 - D[minj])
                        dfs(dpt + 1, minj);
                }
            }
            //元に戻す
            D[ch] = 24 - D[ch];
            for (var i = 0; i < dp.GetLength(0); ++i)
                dp[i, ch] = dprecol[i];
            for (var i = 0; i < dp.GetLength(1); ++i)
                dp[ch, i] = dprerow[i];
            Array.Copy(mincolpre, mincol, mincolpre.Length);

        }
    }
}