package no93;

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int m = sc.nextInt();
		int n = 1 << m;
		double[] s = new double[n];
		for(int i=0;i<n;i++) {
			int x = sc.nextInt();
			s[i] = x * x;
		}
		double[][] p = new double[m+1][n];
		for(int i=0;i<n;i++) {
			p[0][i] = 1D;
		}
		for(int i=0;i<m;i++) {
			for(int j=0;j<(1<<m-1-i);j++) {
				int l1 = (1<<i+1) * j;
				int r1 = l1 + (1 << i);
				int l2 = r1;
				int r2 = l2 + (1 << i);
				for(int k1=l1;k1<l2;k1++) {
					for(int k2=l2;k2<r2;k2++) {
						double p1 = (double) s[k1] / (s[k1] + s[k2]);
						p[i+1][k1] += p[i][k1] * p[i][k2] * p1;
						p[i+1][k2] += p[i][k1] * p[i][k2] * (1 - p1);
					}
				}

			}
		}
		System.out.println(p[m][0]);
	}

}