package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getInts(N int) []int {
	ret := make([]int, N)
	for i := 0; i < N; i++ {
		ret[i] = getInt()
	}
	return ret
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

// min, max, asub, absなど基本関数
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func asub(a, b int) int {
	if a > b {
		return a - b
	}
	return b - a
}

func abs(a int) int {
	if a >= 0 {
		return a
	}
	return -a
}

func lowerBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] >= x
	})
	return idx
}

func upperBound(a []int, x int) int {
	idx := sort.Search(len(a), func(i int) bool {
		return a[i] > x
	})
	return idx
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 1000000)
	M := getInt()
	n := 1 << M
	s := make([]float64, n)
	for i := 0; i < n; i++ {
		s[i] = float64(getInt())
	}
	dp := make([][]float64, M+1)
	for i := 0; i <= M; i++ {
		dp[i] = make([]float64, n)
	}
	for i := 0; i < n; i++ {
		dp[0][i] = 1.0
	}

	m := 1
	for i := 1; i <= M; i++ {
		for k := 0; k < n; k++ {
			x := k / m
			idx := 2 * (x / 2)
			if x%2 == 0 {
				idx++
			}
			idx *= m
			// fmt.Print(k, ":")
			for j := 0; j < m; j++ {
				e := idx + j
				// fmt.Print(e, s[k], s[e], ", ")
				p := s[k] * s[k] / (s[k]*s[k] + s[e]*s[e])
				// out(p)
				dp[i][k] += p * dp[i-1][e] * dp[i-1][k]
			}
			// out()
		}
		// out(dp[i])
		m *= 2
	}
	out(dp[M][0])
}