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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;
using static Extensions;
using static MathExtensions;

public static class Program
{
    public static void Solve()
    {
        var n = I;
        var d = Repeat(n, () => I).ToArray();

        if (n == 1) { Console.WriteLine(0); return; }

        var list = new List<Pair<int, int>>();

        for (var i = 0; i < n - 1; i++)
            for (var j = i + 1; j < n; j++)
            {
                var t1 = Abs(d[i] - d[j]);
                var t2 = Abs(d[i] - (24 - d[j]));
                if (t1 > t2) Swap(ref t1, ref t2);
                list.Add(Pair.Create(t1, t2));
            }

        var c1 = Comb(n, 2);
        Assert(list.Count == c1);

        var ans = 0;

        Func<int, int> TryInner = c2 =>
        {
            Assert(c2 > 0 || c1 - c2 > 0);
            var t1 = c2 > 0 ? list.Take(c2).Min(x => x.First) : int.MaxValue;
            var t2 = c1 - c2 > 0 ? list.AsEnumerable().Reverse().Take(c1 - c2).Min(x => x.Second) : int.MaxValue;
            return Min(t1, t2);
        };

        Action Try = () =>
        {
            var m1 = n;
            var m2 = 0;

            while (0 <= m1 && m1 <= n && 0 <= m2 && m2 <= n)
            {
                var c2 = Comb(m1, 2) + Comb(m2, 2);
                var t = TryInner(c2);
                ans = Max(ans, t);
                m1--; m2++;
            }
        };

        list.Sort((x, y) => y.CompareTo(x));
        Try();
        list = list.Select(p => Pair.Create(p.Second, p.First)).ToList();
        list.Sort((x, y) => y.CompareTo(x));
        Try();

        Assert(ans != int.MaxValue);
        Console.WriteLine(ans);
    }

    #region Scanners
    static Scanner _scanner;
    static char C => _scanner.NextChar();
    static string S => _scanner.NextString();
    static int I => _scanner.NextInt();
    static long L => _scanner.NextLong();
    static BigInteger B => _scanner.NextBigInteger();
    static double D => _scanner.NextDouble();
    static decimal M => _scanner.NextDecimal();
    #endregion

    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput());
        sw.NewLine = "\n";
#if DEBUG
        sw.AutoFlush = true;
        //Console.SetError(sw);
#else
        sw.AutoFlush = false;
#endif
        Console.SetOut(sw);
        _scanner = new Scanner(Console.OpenStandardInput());
        Solve();
        Console.Out.Flush();
    }
}

public struct Pair<T1, T2> : IComparable<Pair<T1, T2>>
    where T1 : IComparable<T1>
    where T2 : IComparable<T2>
{
    public T1 First;
    public T2 Second;

    public Pair(T1 first, T2 second)
    {
        First = first;
        Second = second;
    }

    public int CompareTo(Pair<T1, T2> other)
    {
        var t = First.CompareTo(other.First);
        if (t == 0) t = Second.CompareTo(other.Second);
        return t;
    }
}

public static class Pair
{
    public static Pair<T1, T2> Create<T1, T2>(T1 first, T2 second)
        where T1 : IComparable<T1>
        where T2 : IComparable<T2>
        => new Pair<T1, T2>(first, second);
}

public static partial class Extensions
{
    public static int Comb(int n, int r)
    {
        if (r > n) return 0;
        var acc = 1;
        for (var i = 1; i <= r; i++) acc = acc * (n - i + 1) / i;
        return acc;
    }
}

#region Library
public class Scanner
{
    private readonly Stream _stream;
    private const int _bufferSize = 1024;
    private readonly byte[] _buf = new byte[_bufferSize];
    private int _len, _ptr;

    public Scanner(Stream stream)
    {
        _stream = stream;
    }

    public byte ReadByte()
    {
        if (_ptr >= _len)
        {
            _len = _stream.Read(_buf, 0, _bufferSize);
            _ptr = 0;
        }
        return _buf[_ptr++];
    }

    public char ReadChar() => (char)ReadByte();

    public string ReadLine()
    {
        var r = new StringBuilder();
        if (_ptr == 0) r.Append(ReadChar());
        for (; _ptr < _len; _ptr++) r.Append((char)_buf[_ptr]);
        return r.ToString();
    }

    public char NextChar() => char.Parse(NextString());

    public string NextString()
    {
        var r = new StringBuilder();
        var b = ReadChar();
        while (b != ' ' && b != '\n')
        {
            r.Append(b);
            b = ReadChar();
        }
        return r.ToString();
    }

    public int NextInt() => (int)NextLong();

    public long NextLong()
    {
        var r = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n')
        {
            r = r * 10 + b - '0';
            b = ReadByte();
        }
        return n ? -r : r;
    }

    public BigInteger NextBigInteger()
    {
        var r = new BigInteger();
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n')
        {
            r = r * 10 + b - '0';
            b = ReadByte();
        }
        return n ? -r : r;
    }

    public double NextDouble()
    {
        var i = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != '.' && b != ' ' && b != '\n')
        {
            i = i * 10 + b - '0';
            b = ReadByte();
        }
        if (b != '.') return n ? -i : i;
        b = ReadByte();
        var f = 0L;
        var p = 0;
        while (b != ' ' && b != '\n')
        {
            f = f * 10 + b - '0';
            b = ReadByte();
            p++;
        }
        var r = i + (double)f / MathExtensions.Pow(10, p);
        return n ? -r : r;
    }

    public decimal NextDecimal() => decimal.Parse(NextString());

    public T Next<T>(Converter<string, T> parser) => parser(NextString());
}

[DebuggerStepThrough]
public static partial class Extensions
{
    public static void Assert(bool condition)
    {
        if (!condition) throw new Exception("Assertion failed");
    }

    public static string AsString(this IEnumerable<char> source) => new string(source.ToArray());

    public static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
    {
        foreach (var item in source) action(item);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, _> func)
    {
        foreach (var item in source) func(item);
    }

    public static void ForEach<T>(this IEnumerable<T> source, Action<T, int> action)
    {
        var i = 0;
        foreach (var item in source) action(item, i++);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, int, _> func)
    {
        var i = 0;
        foreach (var item in source) func(item, i++);
    }

    public static T Iterate<T>(int count, T seed, Func<T, T> func)
    {
        var r = seed;
        Repeat(count, () => { r = func(r); });
        return r;
    }

    public static void Repeat(int count, Action action)
    {
        for (var i = 0; i < count; i++) action();
    }

    public static void Repeat(int count, Action<int> action)
    {
        for (var i = 0; i < count; i++) action(i);
    }

    public static IEnumerable<T> Repeat<T>(Func<T> func)
    {
        for (var i = 0; ; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<T> func)
    {
        for (var i = 0; i < count; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(Func<int, T> func)
    {
        for (var i = 0; ; i++) yield return func(i);
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<int, T> func)
    {
        for (var i = 0; i < count; i++) yield return func(i);
    }

    public static void Swap<T>(ref T x, ref T y)
    {
        var tmp = x; x = y; y = tmp;
    }
}

[DebuggerStepThrough]
public static class MathExtensions
{
    public static int Gcd(int left, int right)
    {
        int r;
        while ((r = left % right) != 0) { left = right; right = r; }
        return right;
    }

    public static long Gcd(long left, long right)
    {
        long r;
        while ((r = left % right) != 0L) { left = right; right = r; }
        return right;
    }

    public static BigInteger Gcd(BigInteger left, BigInteger right)
        => BigInteger.GreatestCommonDivisor(left, right);

    public static int HighestOneBit(int x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        return x - (x >> 1);
    }

    public static long HighestOneBit(long x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        x |= x >> 32;
        return x - (x >> 1);
    }

    public static int Lcm(int left, int right) => left / Gcd(left, right) * right;

    public static long Lcm(long left, long right) => left / Gcd(left, right) * right;

    public static BigInteger Lcm(BigInteger left, BigInteger right)
        => left / Gcd(left, right) * right;

    public static int Pow(int value, int exponent)
    {
        var r = 1;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Pow(long value, int exponent)
    {
        var r = 1L;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Fact(int value)
    {
        var r = 1L;
        for (var i = 2; i <= value; i++) r *= i;
        return r;
    }
}
#endregion