using System;
using System.IO;
using System.Text;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using Enu = System.Linq.Enumerable;

class Program
{
    void Solve()
    {
        int M = reader.Int();
        int N = 1 << M;
        var S = Enu.Range(0, N).Select(i => reader.Double()).ToArray();
        var winProb = new double[N, N];
        for (int a = 0; a < N; a++)
            for (int b = 0; b < N; b++)
                winProb[a, b] = S[a] * S[a] / (S[a] * S[a] + S[b] * S[b]);
        var dp = Enu.Repeat(1.0, N).ToArray();

        for (int t = 0; t < M; t++)
        {
            var next = new double[N];
            for (int a = 0; a < N; a++)
            {
                int start = (a ^ (1 << t)) & ~((1 << t) - 1);
                for (int num = 0; num < (1 << t); num++)
                {
                    int b = start + num;
                    next[a] += dp[a] * dp[b] * winProb[a, b];
                }
            }
            dp = next;
        }

        Console.WriteLine(dp[0]);
    }






    static void Main() { new Program().Solve(); }
    Reader reader = new Reader(Console.In);
    class Reader
    {
        private readonly TextReader reader;
        private readonly char[] separator = { ' ' };
        private readonly StringSplitOptions removeOp = StringSplitOptions.RemoveEmptyEntries;
        private string[] A = new string[0];
        private int i;

        public Reader(TextReader r) { reader = r; }
        public bool HasNext() { return Enqueue(); }
        public string String() { return Dequeue(); }
        public int Int() { return int.Parse(Dequeue()); }
        public long Long() { return long.Parse(Dequeue()); }
        public double Double() { return double.Parse(Dequeue()); }
        public int[] IntLine() { var s = Line(); return s == "" ? new int[0] : Array.ConvertAll(Split(s), int.Parse); }
        public int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); }
        public int[][] IntGrid(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); }
        public string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Line()).ToArray(); }
        public string Line() { return reader.ReadLine().Trim(); }
        private string[] Split(string s) { return s.Split(separator, removeOp); }
        private bool Enqueue()
        {
            if (i < A.Length) return true;
            string line = reader.ReadLine();
            if (line == null) return false;
            if (line == "") return Enqueue();
            A = Split(line);
            i = 0;
            return true;
        }
        private string Dequeue() { Enqueue(); return A[i++]; }
    }
}