package main

import "fmt"

func mypow(a int, n int) int {
  var res = 1
  for ; n>0; n>>=1 {
    if n&1 == 1 { res *= a }
    a *= a
  }
  return res
}

func mypowf64(a int, n int) float64 { return float64(mypow(a, n)) }

func main() {
  var m int; fmt.Scanf("%d", &m)
  sz := mypow(2, m)
  s := make([]int, sz)
  for i := range s {
    fmt.Scanf("%d", &s[i])
  }
  vs:= make([][]float64, sz)
  for i := range vs {
    vs[i] = make([]float64, sz)
    for j := range vs[i] {
      vs[i][j] = mypowf64(s[i], 2) / (mypowf64(s[i], 2) + mypowf64(s[j], 2))
    }
  }
  prob := make([][]float64, m+1)
  for i := range prob { prob[i] = make([]float64, sz) }
  for j := range prob[0] { prob[0][j] = 1. }
  for i:=1; i<len(prob); i++ {
    for j := range prob[i] {
      prob[i][j] = 0.
      start := j / mypow(2, i) * mypow(2, i)
      kosuu := mypow(2, i)
      for k :=start; k<start+kosuu; k++ {
        if(j/mypow(2,i-1) == k/mypow(2,i-1)) { continue }
        prob[i][j] += prob[i-1][j] * vs[j][k] * prob[i-1][k]
      }
    }
  }
  fmt.Printf("%f\n", prob[m][0])
}