Problem:
Score : 300 points

Problem Statement

You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 \leq i \leq N) is v_i.

When you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.

After you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.

Constraints

2 \leq N \leq 50

1 \leq v_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
v_1 v_2 \ldots v_N

Output

Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
3 4

Sample Output 1

3.5

If you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.

Printing 3.50001, 3.49999, and so on will also be accepted.

Sample Input 2

3
500 300 200

Sample Output 2

375

You start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:

Use the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.

Use the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.

Use the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.

Thus, the maximum possible value of the last ingredient remaining is 375.

Printing 375.0 and so on will also be accepted.

Sample Input 3

5
138 138 138 138 138

Sample Output 3

138

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

#if true
//#if false
#define UTAKA_DEBUG
#endif

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

namespace UtakaApp
{
    public partial class Program
    {
        public const string ContestName = "abc138";
        public const string ProblemName = "C";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var console = new MyConsole();
            new Program().Solve(System.Console.In, console);
            console.Flush();
#endif
            var sw = new StreamWriter(System.Console.OpenStandardOutput()) {AutoFlush = false};
        }

        public void Solve(TextReader textReader, IConsole console)
        {
            var cin = new ConsoleInput(textReader, ' ');

            int N = cin.ReadInt;
            int[] V = cin.ReadIntArray(N);

            Array.Sort(V);

            double maxSum = 0;

            do
            {
                double[] dv = new double[N];
                for (int i = 0; i < N; i++)
                {
                    dv[i] = (double)V[i];
                }
                
                for (int i = 0; i < N - 1; i++)
                {
                    dv[i + 1] = (dv[i] + dv[i + 1]) / 2;
                }

                maxSum = Math.Max(maxSum, dv[N - 1]);
                
            } while (NextPermutation(V, 0, N));

            console.WriteLine(maxSum.ToString());
        }

        public static bool NextPermutation<T>(T[] array, int start, int length)
            where T : IComparable
        {
            int end = start + length - 1;

            // 範囲が狭すぎる
            if (end <= start) return false;

            int last = end;
            while (true)
            {
                int pos = last--;

                if (array[last].CompareTo(array[pos]) < 0)
                {
                    int i;
                    for (i = end + 1; array[last].CompareTo(array[--i]) >= 0;)
                    {
                    }

                    T tmp = array[last];
                    array[last] = array[i];
                    array[i] = tmp;
                    Array.Reverse(array, pos, end - pos + 1);
                    return true;
                }

                if (last == start) // 最後の順列
                {
                    Array.Reverse(array, start, end - start);
                    return false;
                }
            }

            // ここに来ることはない
            throw new Exception("NextPermutation: Fatal error");
        }
    }

    public partial class Program
    {
        public const int ModLarge = 1000000007;
    }

    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);

        public string[] ReadStrArray(long N)
        {
            var ret = new string[N];
            for (long i = 0; i < N; ++i) ret[i] = Read;
            return ret;
        }

        public int[] ReadIntArray(long N)
        {
            var ret = new int[N];
            for (long i = 0; i < N; ++i) ret[i] = ReadInt;
            return ret;
        }

        public long[] ReadLongArray(long N)
        {
            var ret = new long[N];
            for (long i = 0; i < N; ++i) ret[i] = ReadLong;
            return ret;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(string str);
        void WriteLine(string str);
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(System.Console.OpenStandardOutput()) {AutoFlush = false};
            System.Console.SetOut(sw);
        }

        public void Flush()
        {
            System.Console.Out.Flush();
        }

        public void Write(string str)
        {
            System.Console.Write(str);
        }

        public void WriteLine(string str)
        {
            System.Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string DirectoryPath => $"../../../../{Program.ContestName}/{Program.ProblemName}";

        private string GetInputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.in";
            return $"{DirectoryPath}/in_{testCaseNumber}.txt";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.out";
            return $"{DirectoryPath}/out_{testCaseNumber}.txt";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsole();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems()
        {
            var isSuccessAll = true;

            var testCaseNumber = 1;
            while (true)
            {
                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                System.Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    System.Console.WriteLine($"Success");
                }
                else
                {
                    isSuccessAll = false;
                    System.Console.WriteLine($"Failure *****");
                }

                testCaseNumber++;
            }

            if (isSuccessAll)
            {
                System.Console.WriteLine($"!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            System.Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            System.Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}