M = gets.to_i
N = 2 ** M
S = N.times.map { gets.to_i }

dp = Array.new(N, 1.0)
play_cnt = N / 2

M.times do
  temp = Array.new(N, 0.0)
  len = N / play_cnt

  play_cnt.times do |i|
    l = i * len
    m = i * len + len / 2
    r = (i + 1) * len - 1

    l.upto(m - 1) do |a|
      m.upto(r) do |b|
        next if a == b

        win_rate = Rational(S[a] ** 2, S[a] ** 2 + S[b] ** 2)
        temp[a] += win_rate * dp[b] * dp[a]

        win_rate = Rational(S[b] ** 2, S[a] ** 2 + S[b] ** 2)
        temp[b] += win_rate * dp[a] * dp[b]
        # temp[b] += 1.0 - win_rate
      end
    end
  end

  dp = temp
  play_cnt /= 2
end

puts dp[0].to_f