#include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <sstream>
#include <set>
#include <map>
#include <algorithm>
#include <cstdio>
#include <cstdlib>

#define rep(i,n) for(int i=0;i<(int)(n);++i)
//#define iter(a) __typeof(a.begin())
//#define FOR(it,a) for(iter(a)it=a.begin();it!=a.end();++it)
#define F first
#define S second
#define SZ(a) (int)((a).size())
#define sz(a) SZ(a)
#define pb(a) push_back(a)
#define mp(a,b) make_pair(a,b)
#define ALL(a) (a).begin(),(a).end()
using namespace std;

typedef long long ll;
typedef pair<int,int> PI;
typedef unsigned long long ull;

#define PR(...) do{cerr << "line : " << __LINE__ << endl; pr(#__VA_ARGS__, __VA_ARGS__);}while(0);
template<class T>
void pr(const string& name, T t){
  cerr << name << ": " << t << endl;
}

template<typename T, typename ... Types>
void pr(const string& names, T t, Types ... rest) {
  auto comma_pos = names.find(',');
  cerr << names.substr(0, comma_pos) << ": " << t << ", ";
  
  auto next_name_pos = names.find_first_not_of(" \t\n", comma_pos + 1);
  pr(string(names, next_name_pos), rest ...);
}

template<class T,class U> ostream& operator<< (ostream& o, const pair<T,U>& v){return o << "(" << v.F << ", " << v.S << ")";}
template<class T> ostream& operator<< (ostream& o, const vector<T>& v){o << "{";rep(i,SZ(v)) o << (i?", ":"") << v[i];return o << "}";}


#define endl '\n'


ll s[1<<12];

double dp[1<<12][12];
bool vis[1<<12][12];
int m;
double rec(int a,int p){
  if(p==0) return 1;
  if(vis[a][p])
    return dp[a][p];
  vis[a][p] = 1;
  double & ret = dp[a][p]  = 0;
  
  int b = (a>>p) << p;
  int e = b + (1<<p);
  int b1 = (a>>(p-1))<<(p-1);
  int e1 = b1 + (1<<(p-1));
  ret = rec(a,p-1);
  double t = 0;
  for(int i = b; i < e; ++i){
    if(b1 <= i && i < e1) continue;
    //if(i==a) continue;
    ll h = s[i]*s[i]+s[a]*s[a];
    t += rec(i,p-1)*s[a]*s[a]/h;
  }
  ret *= t;
  //cout << a << " " << p << " " << ret << " " << t << endl;
  return ret;
}

int main(int argc, char *argv[])
{
  cin >> m;
  rep(i,1<<m) cin >> s[i];

  printf("%.8f\n",rec(0,m));
  
  return 0;
}