import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int M = sc.nextInt();
    int[] s = new int[(int)Math.pow(2, M) + 1];
    for(int i = 1; i < s.length; i++) {
      s[i] = sc.nextInt();
    }
    int num = s.length;
    // dp[j][i]は選手iがj回戦に勝つ確率
    double[][] dp = new double[M + 1][num];
    for(int i = 1; i < num; i++) {
      int aite = i + 1;
      if(i % 2 == 0) aite = i - 1;
      dp[1][i] = (double)(s[i] * s[i]) / (double)(s[i] * s[i] + s[aite] * s[aite]);
    }
    for(int j = 2; j <= M; j++) {
      for(int i = 1; i < num; i++) {
        int k = (i + (int)Math.pow(2, j - 1) - 1) / (int)Math.pow(2, j - 1);
        int aite = k + 1;
        if(k % 2 == 0) aite = k - 1;
        double p = 0;
        for(int l = (int)Math.pow(2, j - 1) * (aite - 1) + 1; l <= (int)Math.pow(2, j - 1) * aite; i++) {
          p += (dp[j - 1][l] * ((double)(s[i] * s[i]) / (double)(s[i] * s[i] + s[l] * s[l])));
        }
        dp[j][i] = dp[j - 1][i] * p;
      }
    }
    System.out.println(dp[M][1]);
  }
}