import std.algorithm, std.array, std.container, std.range, std.bitmanip;
import std.numeric, std.math, std.bigint, std.random, core.bitop;
import std.string, std.conv, std.stdio, std.typecons;

void main()
{
  auto m = readln.chomp.to!size_t;
  auto n = 1 << m;
  auto si = iota(n).map!(_ => readln.chomp.to!int).array;

  auto opposites(size_t i, size_t j) {
    auto k = i;
    btc(&k, j - 1);
    if (j == 1) {
      return iota(k, k + 1);
    } else {
      size_t l = (1 << (j - 1)) - 1;
      return iota(k & ~l, (k | l) + 1);
    }
  }

  auto pij = new real[][](m + 1, n);
  pij[0][] = 1;

  foreach (i; 1..m + 1) {
    foreach (j; 0..n) {
      real p = 0;
      foreach (k; opposites(j, i)) {
        auto s1 = si[j], s2 = si[k];
        p += pij[i - 1][k] * s1 ^^ 2 / (s1 ^^ 2 + s2 ^^ 2);
      }
      pij[i][j] = p * pij[i - 1][j];
    }
  }

  writeln(pij[m][0]);
}