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 static AtCoderProject.Utility;
using BigInteger = System.Numerics.BigInteger;
using BitArray = System.Collections.BitArray;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using TextReader = System.IO.TextReader;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var diffs = new int[13];
            diffs[0] = 1;
            foreach (var d in consoleReader.Split.Int)
                diffs[d]++;

            if (diffs.Any(i => i > 2)) return 0;
            if (diffs[0] > 1) return 0;
            if (diffs[12] > 1) return 0;

            var fix = new List<int>();
            var notFix = new List<int>();
            if (diffs[0] == 1) fix.Add(0);
            if (diffs[12] == 1) fix.Add(12);
            for (int i = 1; i < 12; i++)
            {
                if (diffs[i] > 1)
                {
                    fix.Add(i);
                    fix.Add(24 - i);
                }
                else if (diffs[i] == 1)
                {
                    notFix.Add(i);
                }
            }

            if (notFix.Count == 0)
                return F(new SortedSet<int>(fix));

            var max = 0;
            for (int i = 0; i < (1 << notFix.Count); i++)
            {
                max = Math.Max(G(fix, notFix, i), max);
            }

            return max;
        }
        static int G(List<int> fix, List<int> notFix, int mask)
        {
            var set = new SortedSet<int>(fix);
            for (int i = 0; i < notFix.Count; i++)
            {
                if (((mask >> i) & 1) == 0)
                    set.Add(notFix[i]);
                else
                    set.Add(24 - notFix[i]);
            }
            return F(set);
        }

        static int F(SortedSet<int> set)
        {
            var first = set.First();
            var prev = first;
            var min = 24;
            int diff;
            foreach (var item in set.Skip(1))
            {
                diff = item - prev;
                if (diff > 12) diff = 24 - diff;
                min = Math.Min(diff, min);
                prev = item;
            }
            diff = 24 + first - prev;
            if (diff > 12) diff = 24 - diff;
            return Math.Min(diff, min);
        }


        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }

    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String { get; }
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    public static class Utility
    {
        public static IComparer<T> ReverseComparer<T>() where T : IComparable<T>
            => Comparer<T>.Create((x, y) => y.CompareTo(x));
    }
    #endregion

}