#include <bits/stdc++.h>

using namespace std;

double solve(vector<vector<pair<double, double> > > cur) {
  if (cur.size() == 1) {
    return cur[0][0].second;
  }

  vector<vector<pair<double, double> > > nxt;
  for (int i = 0; i < cur.size(); i += 2) {
    vector<pair<double, double> > &x = cur[i];
    vector<pair<double, double> > &y = cur[i+1];
    vector<pair<double, double> > z;
    
    for (int j = 0; j < x.size(); j++) {
      double acc = 0.0;
      for (int k = 0; k < y.size(); k++) {
        double win = x[j].first * x[j].first / (x[j].first * x[j].first + y[k].first * y[k].first);
        acc += x[j].second * y[k].second * win;
      }
      z.push_back({x[j].first,  acc});
    }

    for (int j = 0; j < y.size(); j++) {
      double acc = 0.0;
      for (int k = 0; k < x.size(); k++) {
        double win = y[j].first * y[j].first / (y[j].first * y[j].first + x[k].first * x[k].first);
        acc += y[j].second * x[k].second * win;
      }
      z.push_back({y[j].first, acc});
    }
    nxt.push_back(z);
  }

  return solve(nxt);
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  
  int m;
  cin >> m;
  int n = 1<<m;

  vector<double> s(n);
  for (int i = 0; i < n; i++)
    cin >> s[i];

  vector<vector<pair<double, double> > > v;
  for (int i = 0; i < n; i++)
    v.push_back({{s[i], 1.0}});

  cout << fixed << setprecision(12) << solve(v) << endl;
  
  return 0;
}