import Prelude as P
import Data.List
import Data.Vector.Unboxed as V hiding(sum,forM,forM_,map)
import Data.Array.Unboxed  as A
import Data.Array.MArray
import Data.Array.ST
import Control.Monad
import Control.Monad.ST

type P = Vector Double
type DP s = STUArray s (Int,Int) Double

setArr :: DP s -> P -> Int -> ST s ()
setArr dparr ps n = do
  let p i  = ps V.! (i-1)
      p_ i = 1-(p i)
  forM_ [1..n] $ \i -> writeArray dparr (0,i) $ (V.scanl (\x y -> x*(1-y)) 1 ps) V.! i
  forM_ [1..div (n-1) 2] $ \i -> do
    writeArray dparr (i,i)   $ (V.scanl (\x y -> x*y) 1 ps) V.! i

dp_i :: DP s -> P -> Int -> Int -> ST s ()
dp_i dparr ps k i = do
  let p i  = ps V.! (i-1)
      p_ i = 1-(p i)
  ek  <- readArray dparr (k,i-1)
  ek1 <- readArray dparr (k-1,i-1)
  writeArray dparr (k,i) $ ek*(p_ i) + ek1*(p i)

solve :: P -> Int -> ST s Double
solve ps n = do
  dparr <- newArray ((0,1),(div (n-1) 2,n)) 0
  setArr dparr ps n
  forM_ [1..div (n-1) 2] $ \k ->
   forM_ [k+1..n] $ \i -> dp_i dparr ps k i
  ans0 <- forM [0..div (n-1) 2] $ \k -> readArray dparr (k,n)
  return $ 1-(sum ans0)

main :: IO ()
main = do
  n <- read <$> getLine
  ps <- map read.words <$> getLine
  putStrLn $ show $ runST $ solve (V.fromList ps)  n
