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: Accepted)

using System;
using System.Collections.Generic;//list用
using System.Text.RegularExpressions;//正規表現用
using System.Text;//StringBuilder用
using System.Collections;//ハッシュテーブル用
using System.Linq;
//デリゲータの使い方をマスターしたい

class Program
{
    Hashtable ht = new Hashtable();
    static List<double> s = new List<double>();
    static double result;
    static int K;
    StringBuilder strresult= new StringBuilder("");//Append(str ○○)関数で文字を追加していく



    static void Main()
    {
        //Modular mo = new Modular();//素数で割った余りを出せで使う★使い方：Modular型で宣言すると、その時点でのその素数で割った余りを保持する変数になる（powべき乗、Fac累乗、nCr組み合わせも関数として存在）()内は初期値
        //Node no = new Node<>();//UnionFind★Find関数で根っこの値を返す（根っこの値が一緒なら同グループ）、Unite関数で二つの木をくっつける
        //Permutation pe = new Permutation<>();//配列＆リストを並べ替えた場合の全ケースを出力★All関数でリスト形式で返す。
        //Treap tr = new Treap<>();//平衡二分木★Insert()関数で挿入、FindIndex()関数で該当する大きさの物が入るべき配列番号を返す。
        // delegate int CFunc();//下関数に使うデリゲータ。コイツと同じ引数と戻り値で関数作って、下の評価式の部分に関数名※（）いらないを入れる。
        //PriorityQueue pr = new PriorityQueue<>(評価式);//優先度付キュー★Enqueue()で格納、Dequeue()で取りだし。引数は評価式（大と小のどちらが優先か）。
        Read1();
        Read2(K);
      for(int i=0;i<K;i++){
        s.Sort();
        if(s[1]!=1001){
        s[0]=(double)(s[0]+s[1])/2;
        s[1]=1001;
        }
        }

      result=s[0];
      
      
        Console.WriteLine(result.ToString());
    }


    static void Read1()
    {
        string tmp = Console.ReadLine();
        K = int.Parse(tmp);
    }

    static void Read2(int kosuu)
    {
        string[] tmp = Console.ReadLine().Split(' ');
        for (int i = 0; i < kosuu; i++) { s.Add(double.Parse(tmp[i])); }
    }
}