// includes
#include <bits/stdc++.h>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}

double s[1026];
double dp[1026][11];

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int m;
  cin >> m;
  rep(i, (1 << m)){
    cin >> s[i];
  }
  rep(i, (1 << m))dp[i][0] = 1.;
  for(int j = 1; j <= m; j++){
    for(int i = 0; i < (1 << m); i++){
      int l = (i / (1 << j)) * (1 << j);
      int r = l + (1 << j);
      if(i < (l + r) / 2){
        for(int k = (l + r) / 2; k < r; k++){
          dp[i][j] += s[i] * s[i] / (s[i] * s[i] + s[k] * s[k]) * dp[k][j-1] * dp[i][j-1];
        }
      }else{
        for(int k = l; k < (l + r) / 2; k++){
          dp[i][j] += s[i] * s[i] / (s[i] * s[i] + s[k] * s[k]) * dp[k][j-1] * dp[i][j-1];
        }
      }
    }
  }
  cout << setprecision(20);
  cout << dp[0][m] << endl;
	return 0;
}