#include <bits/stdc++.h>
#define EPS 1e-9
#define INF 1070000000LL
#define MOD 1000000007LL
#define fir first
#define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++)
#define numa(x,a) for(auto x: a)
#define ite iterator
#define mp make_pair
#define mt make_tuple
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define pb push_back
#define pf push_front
#define sec second
#define sz(x) ((int)(x).size())
#define ALL( c ) (c).begin(), (c).end()
#define gcd(a,b) __gcd(a,b)
#define mem(x,n) memset(x,n,sizeof(x))
#define endl "\n"
using namespace std;
template <int POS, class TUPLE> void deploy(std::ostream &os, const TUPLE &tuple){}
template <int POS, class TUPLE, class H, class ...Ts> void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get<POS>(t); deploy<POS + 1, TUPLE, Ts...>(os, t); }
template <class T,class U> std::ostream& operator<<(std::ostream &os, std::pair<T,U> &p){ os << "(" << p.first <<", " << p.second <<")";return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "}" : ", "); return os; }
#define DEBUG1(var0) { std::cerr << (#var0) << "=" << (var0) << endl; }
#define DEBUG2(var0, var1) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG1(var1); }
#define DEBUG3(var0, var1, var2) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG2(var1,var2); }
#define DEBUG4(var0, var1, var2, var3) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG3(var1,var2,var3); }
using ll = long long;

int M;
double S[1080];
double win[15][1080];

vector <int> enemy_calc(int k,int player){
  int full_player = 1<<k;
  int enemy_size = 1 << (k-1);
  vector <int> ret;
  bool less = (player % full_player < enemy_size);
  if(less){
    player -= player % full_player;
    for (int i = 0; i < enemy_size;i++){
      ret.pb(player+enemy_size+i);
    }
  }else{
    player -= player % full_player;
    for (int i = 0; i < enemy_size;i++){
      ret.pb(player+i);
    }
  }
  return ret;
}

int main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> M;
  rep(i,(1<<M)){
    cin >> S[i];
    win[0][i] = 1;
  }

  for (int k = 1; k <= M; k++) {
    for (int player = 0; player < (1<< M); player++) {
      auto enemy = enemy_calc(k,player);
      //DEBUG3(k,player,enemy);
      numa(ene, enemy){
        win[k][player] += S[player] * S[player] / (S[ene] * S[ene] + S[player] * S[player]) * win[k-1][player] * win[k-1][ene];
      }
    }
  }
  cout << fixed << setprecision(10) << win[M][0] << endl;
  
  return 0;
}