import java.util.Arrays;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {
	
	public static long MOD = 1000000007;
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		final int M = sc.nextInt();
		final int size = 1 << M;
		
		double[] power = new double[size];
		for(int i = 0; i < size; i++){
			power[i] = sc.nextDouble();
		}
		
		final int DP_size = 2 * size - 1;
		double[][] DP = new double[DP_size][size];
		for(int i = 0; i < size; i++){
			final int index = i + (size - 1);
			
			DP[index][i] = 1.0;
		}
		
		for(int curr = size - 2; curr >= 0; curr--){ 
			
			for(int left = 0; left < size; left++){
				final int left_curr = curr * 2 + 1;
				if(DP[left_curr][left] == 0){ continue; }
				
				for(int right = left; right < size; right++){
					final int right_curr = curr * 2 + 2;
					if(DP[right_curr][right] == 0){ continue; }
					
					final double left_d = power[left] * power[left];
					final double right_d = power[right] * power[right];
					
					final double left_win_rate  = left_d  / (left_d + right_d);
					final double right_win_rate = right_d / (left_d + right_d);
					//System.out.println(curr + " " + left + " " + right + " : " + left_win_rate + " " + right_win_rate);
					
					DP[curr][left]  += DP[left_curr][left] * DP[right_curr][right] * left_win_rate;
					DP[curr][right] += DP[left_curr][left] * DP[right_curr][right] * right_win_rate;
				}
			}
			
			//System.out.println(Arrays.toString(DP[curr]));
		}
		
		System.out.printf("%.8f\n", DP[0][0]);
	}
}