#include <bits/stdc++.h>
using namespace std;
int main(){
  cout << fixed << setprecision(20);
  int M;
  cin >> M;
  vector<int> S(1 << M);
  for (int i = 0; i < (1 << M); i++){
    cin >> S[i];
  }
  for (int i = 0; i < (1 << M); i++){
    S[i] = S[i] * S[i];
  }
  vector<vector<double>> dp(M + 1, vector<double>(1 << M, 0));
  dp[0] = vector<double>(1 << M, 1);
  for (int i = 0; i < M; i++){
    for (int j = 0; j < (1 << M); j += 1 << (i + 1)){
      for (int k = 0; k < (1 << i); k++){
        for (int l = 0; l < (1 << i); l++){
          int a = j + k;
          int b = j + (1 << i) + l;
          dp[i + 1][a] += dp[i][a] * dp[i][b] * S[a] / (S[a] + S[b]);
          dp[i + 1][b] += dp[i][a] * dp[i][b] * S[b] / (S[a] + S[b]);
        }
      }
    }
  }
  cout << dp[M][0] << endl;
}