using System;

class Program
{
    public static void Main(string[] args)
    {
        var m = int.Parse(Console.ReadLine());
        int count = (int)Math.Round(Math.Pow(2, m));
        double[] strength = new double[count];
        for (int i = 0; i < strength.Length; i++)
        {
            var s = int.Parse(Console.ReadLine());
            strength[i] = s * s;            
        }
        double[,] percentages = new double[m+1,count];
        {
            for (int k = 0; k < count; k++)
            {
                percentages[0, k] = 1;
            }
        }
        for (int i = 1; i <= m; i++)
        {
            for (int k = 0; k < count; k++)
            {
                int block = (int)Math.Round(Math.Pow(2, i));
                int start = block* (k/block);
                int end = start + block;
                if (k < (start + end)/2)
                {
                    start += block/2;
                }
                else
                {
                    end -= block/2;
                }
                double pSum = 0;
                for (int j = start; j < end; j++)
                {
                    if (j == k)
                    {
                        continue;
                    }
                    pSum += percentages[i - 1, j] * strength[k]/(strength[k] + strength[j]);
                }
                percentages[i, k] = percentages[i - 1, k]*pSum;
            }
            //for (int t = 0; t < count; t++)
            //{
            //    Console.Write(percentages[i, t] + ",");
            //}
            //Console.WriteLine();
        }
        Console.WriteLine(percentages[m,0]);

    }
}