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++14 (GCC 5.4.1) (judge verdict: Accepted)

//Generated at 2019-08-18 20:13:00 UTC+8
//Created by Alphagocc
#if __cplusplus < 201103L
#define ___TR1(x) <tr1/x>
#else
#define ___TR1(x) <x>
#endif
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <climits>
#include <clocale>
#include <cmath>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include ___TR1(cstdbool)
#include ___TR1(cstdint)
#include ___TR1(ctgmath)
#include ___TR1(cfenv)
#include ___TR1(cinttypes)
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cstdalign>
#else
#include <tr1/complex>
#endif
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include ___TR1(array)
#include ___TR1(random)
#include ___TR1(tuple)
#include ___TR1(unordered_map)
#include ___TR1(unordered_set)
#if __cplusplus >= 201103L
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <type_traits>
#include <typeindex>
#endif
#ifdef USE_PBDS
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#endif
#define FORCE_INLINE __inline__ __attribute__((always_inline)) 
// struct IO
struct IO
{
    bool goodReadBit;
    IO()
    {
        goodReadBit = 1;
        space       = ' ';
    }
    template <typename T>
    FORCE_INLINE void __RI(T &x)
    {
        int ch = getchar(), neg = 1;
        x = 0;
        for (; !(isdigit(ch) || ch == '-' || ch == EOF); ch = getchar())
            ;
        if (ch == EOF)
        {
            goodReadBit = 0;

            return;
        }
        if (ch == '-') neg = -1, ch = getchar();
        for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - 48;
        x *= neg;
    }
    FORCE_INLINE void R(int &x) { __RI(x); }
    FORCE_INLINE void R(int64_t &x) { __RI(x); }
    template <typename T1, typename T2>
    FORCE_INLINE void R(std::pair<T1, T2> &x)
    {
        R(x.first);
        R(x.second);
    }
    template <typename T>
    FORCE_INLINE void R(std::vector<T> &x)
    {
        for (typename std::vector<T>::iterator it = x.begin(); it != x.end(); ++it) { R(*it); }
    }
    template <typename T>
    FORCE_INLINE void R(T &x)
    {
        std::cin >> x;
        if (!std::ios::goodbit) goodReadBit = 0;
    }
    template <typename T, typename... Args>
    FORCE_INLINE void RA(T *a, int n)
    {
        for (int i = 0; i < n; ++i) R(a[i]);
    }
#if __cplusplus >= 201103L
    template <typename T, typename... Args>
    FORCE_INLINE void R(T &x, Args &... args)
    {
        R(x), R(args...);
    }
    template <typename T, typename... Args>
    FORCE_INLINE void RA(T *a, int n, Args... args)
    {
        for (int i = 0; i < n; ++i) RA(a[i], args...);
    }
#endif
    bool goodRead() { return goodReadBit; }
    char space;
    template <typename T>
    FORCE_INLINE void __WI(T x)
    {
        if (x == 0) putchar('0');
        if (x < 0) putchar('-'), x = -x;
        char ch[128];
        int  pos = 0;
        while (x) ch[pos++] = x % 10 + 48, x /= 10;
        while (pos) putchar(ch[--pos]);
    }
    FORCE_INLINE void W() {}
    FORCE_INLINE void W(const int &x) { __WI(x); }
    FORCE_INLINE void W(const int64_t &x) { __WI(x); }
    FORCE_INLINE void W(const unsigned int &x) { __WI(x); }
    FORCE_INLINE void W(const uint64_t &x) { __WI(x); }
    FORCE_INLINE void W(const double &x) { printf("%lf", static_cast<double>(x)); }
    FORCE_INLINE void W(const char &x) { putchar(x); }
    FORCE_INLINE void W(const std::string &x) { printf("%s", x.c_str()); }
    template <typename T1, typename T2>
    FORCE_INLINE void W(const std::pair<T1, T2> &x)
    {
        W(x.first);
        W(space);
        W(x.second);
    }
    template <typename T>
    FORCE_INLINE void W(const std::vector<T> &x)
    {
        for (typename std::vector<T>::const_iterator it = x.begin(); it != x.end(); it++)
        {
            W(*it);
            W(space);
        }
        W('\n');
    }
    template <typename T>
    FORCE_INLINE void W(const T &x)
    {
        std::cout << x;
    }
    FORCE_INLINE void WL() { W('\n'); }
    template <typename T>
    FORCE_INLINE void WL(const T &x)
    {
        W(x), W('\n');
    }
    FORCE_INLINE void WS() { W(space); }
    template <typename T>
    FORCE_INLINE void WS(const T &x)
    {
        W(x), W(space);
    }
    template <typename T>
    FORCE_INLINE void WA(T *a, int n)
    {
        for (int i = 0; i < n; i++) WS(a[i]);
        WL();
    }
#if __cplusplus >= 201103L
    template <typename T, typename... Args>
    FORCE_INLINE void W(const T &x, const Args &... args)
    {
        W(x), W(space), W(args...);
    }
    template <typename... Args>
    FORCE_INLINE void WL(const Args &... args)
    {
        W(args...), W('\n');
    }
    template <typename T, typename... Args>
    FORCE_INLINE void WA(T *a, int n, Args... args)
    {
        for (int i = 0; i < n; i++) WA(a[i], args...);
    }
#endif
    template <typename T>
    FORCE_INLINE IO &operator>>(T &x)
    {
        R(x);
        return (*this);
    }
    template <typename T>
    FORCE_INLINE IO &operator<<(const T &x)
    {
        W(x);
        return (*this);
    }
} io; // struct IO
namespace Alphagocc
{
#if __cplusplus >= 201103L
decltype(std::chrono::high_resolution_clock::now()) tStart;
};
void      TimeBegin() { Alphagocc::tStart = std::chrono::high_resolution_clock::now(); }
long long TimeEnd()
{
    return (std::chrono::high_resolution_clock::now() - Alphagocc::tStart).count();
#endif
} // namespace Alphagocc
#if __cplusplus >= 201103L
std::random_device randomDevice;
std::mt19937       randomGenerator(randomDevice());
#else
std::tr1::random_device randomDevice;
std::tr1::mt19937       randomGenerator(randomDevice());
#endif
using namespace std;
#if __cplusplus < 201103L
using namespace tr1;
#endif
#define REP(i, x, y) for (int i = x; i < y; i++)
const int8_t  INFC = 0x3f;
const int16_t INFS = 0x3f3f;
const int32_t INF  = 0x3f3f3f3f;
const int64_t INFL = 0x3f3f3f3f3f3f3f3fLL;


int main()
{
    int n;
    io >> n;
    vector<double> a(n);
    io >> a;
    sort(a.begin(),a.end());
    for (int i=0;i<n-1;i++)
    {
        a[i+1]=(a[i+1]+a[i])/2;
    }
    io.WL(a.back());
    return 0;
}