local mfl, mce = math.floor, math.ceil
local bls, brs = bit.lshift, bit.rshift
local m = io.read("*n")
local n = bls(1, m)
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end
local sz = 1
local dp1, dp2 = {}, {}
for i = 1, n do
  dp1[i] = 1
end
local f = true
local function getrate(x, y) return a[x] * a[x] / (a[x] * a[x] + a[y] * a[y]) end
while sz < n do
  local blocks = mfl(n / (sz * 2))
  local src = f and dp1 or dp2
  local dst = f and dp2 or dp1
  f = not f
  for i = 1, n do
    dst[i] = 0
  end
  for ib = 1, blocks do
    local offset = (ib - 1) * sz * 2
    for left = offset + 1, offset + sz do
      for right = offset + sz + 1, offset + sz * 2 do
        dst[left] = dst[left] + getrate(left, right) * src[left] * src[right]
        dst[right] = dst[right] + getrate(right, left) * src[left] * src[right]
      end
    end
  end
  sz = sz * 2
end
local tbl = f and dp1 or dp2
print(tbl[1])