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 System.Text;

namespace ProgrammingContest
{
    class MainClass : IDisposable
    {
        Scanner sc;
        Writer wr;
        string backPath = "..";
        char dirSep = System.IO.Path.DirectorySeparatorChar;
        string inFilePath = null;
        string outFilePath = null;
        public MainClass()
        {
            this.inFilePath = this.backPath
                            + this.dirSep
                            + this.backPath
                            + this.dirSep
                            + "in.txt";
            this.outFilePath = this.backPath
                             + this.dirSep
                             + this.backPath
                             + this.dirSep
                             + "out.txt";
        }
        static void Main(string[] args)
        {
            using (var mainClass = new MainClass())
            {
                //mainClass.MakeTestCase();
                mainClass.Solve();
            }
        }

        public void Dispose()
        {
            if (this.sc != null)
            {
                this.sc.Dispose();
                this.sc = null;
            }
            if (this.wr != null)
            {
                this.wr.Dispose();
                this.wr = null;
            }
        }

        void MakeTestCase()
        {
            Random rand = new Random();
            this.wr = new Writer(inFilePath);


        }

        void Solve()
        {
            this.wr = new Writer(this.isReactive || true);
            //this.wr = new Writer(this.outFilePath);
#if DEBUG
            if (!this.isReactive)
                this.sc = new Scanner(this.inFilePath);
            else
                this.sc = new Scanner();
#else
            this.sc = new Scanner();
#endif

            int N = sc.NextInt;
            int[] D = new int[N].Select(e => sc.NextInt).ToArray();
            int[] cnt = new int[13];
            D.ToList().ForEach(d => cnt[d]++);
            cnt[0]++;
            if (cnt.Any(c => c >= 3))
            {
                wr.WriteLine(0);
                return;
            }
            cnt[0]--;
            int ans = 0;
            var oneList = new List<int>();
            var partList = new List<int>();
            for (int i = 0; i < cnt.Length; i++)
            {
                if (cnt[i] == 1)
                {
                    oneList.Add(i);
                }
                else if (cnt[i] == 2)
                {
                    partList.Add(i);
                    partList.Add(24 - i);
                }
            }
            for (int s = 0; s < (1 << oneList.Count); s++)
            {
                var bufList = new List<int>(partList);
                for (int i = 0; i < oneList.Count; i++)
                {
                    if ((s & (1 << i)) != 0)
                    {
                        bufList.Add(oneList[i]);
                    }
                    else
                    {
                        bufList.Add(24 - oneList[i]);
                    }
                }
                bufList.Add(0);
                bufList.Sort();
                int pre = 111;
                for (int i = 0; i < bufList.Count; i++)
                {
                    for (int j = i + 1; j < bufList.Count; j++)
                    {
                        pre = Math.Min(pre, Math.Min(bufList[j] - bufList[i], 24 - (bufList[j] - bufList[i])));
                    }
                }
                ans = Math.Max(ans, pre);
            }
            wr.WriteLine(ans);
        }

        bool isReactive = false; // TODO: reactive check !!

    }

    class Writer : IDisposable
    {
        private System.IO.TextWriter writer;
        private StringBuilder sb;
        private bool isReactive;
        public Writer(string path) : this(new System.IO.StreamWriter(path))
        {
        }
        public Writer(bool isReactive) : this(null, isReactive)
        {
        }
        public Writer(System.IO.TextWriter writer = null, bool isReactive = false)
        {
            this.writer = (writer ?? Console.Out);
            this.isReactive = isReactive;
            if (!this.isReactive)
                this.sb = new StringBuilder();
        }
        public void Dispose()
        {
            if (!this.isReactive)
                this.writer.Write(sb.ToString());
            if (!this.writer.Equals(Console.Out))
                this.writer.Dispose();
        }
        public void Write(object val)
        {
            if (this.isReactive)
            {
                this.writer.Write(val.ToString());
                this.writer.Flush();
            }
            else
                this.sb.Append(val.ToString());
        }
        public void Write(string format, params object[] vals)
        {
            if (this.isReactive)
            {
                this.writer.Write(format, vals);
                this.writer.Flush();
            }
            else
                this.sb.AppendFormat(format, vals);
        }
        public void WriteLine(object val = null)
        {
            this.Write((val ?? string.Empty).ToString() + System.Environment.NewLine);
        }
        public void WriteLine(string format, params object[] vals)
        {
            this.Write(format + System.Environment.NewLine, vals);
        }
    }

    class Scanner : IDisposable
    {
        private Queue<string> buffer;
        private char[] sep;
        private System.IO.TextReader reader;
        public Scanner(string path) : this(new System.IO.StreamReader(path))
        {
        }
        public Scanner(System.IO.TextReader reader = null)
        {
            this.buffer = new Queue<string>();
            this.sep = new char[] { ' ' };
            this.reader = (reader ?? Console.In);
        }
        private void CheckBuffer()
        {
            if (this.buffer.Count == 0)
            {
                string str = string.Empty;
                while (string.IsNullOrEmpty(str))
                    str = this.reader.ReadLine();

                str.Split(this.sep).ToList()
                   .ForEach(el => this.buffer.Enqueue(el));
            }
        }

        public void Dispose()
        {
            if (!this.reader.Equals(Console.In))
                this.reader.Dispose();
        }

        public string Next
        {
            get
            {
                this.CheckBuffer();
                return this.buffer.Dequeue();
            }
        }

        public int NextInt
        {
            get
            {
                return int.Parse(this.Next);
            }
        }
        public double NextDouble
        {
            get
            {
                return double.Parse(this.Next);
            }
        }

        public long NextLong
        {
            get
            {
                return long.Parse(this.Next);
            }
        }

        public bool IsEnd
        {
            get
            {
                this.CheckBuffer();
                return this.buffer.Count == 0;
            }
        }
    }
}