import Prelude hiding (last, unzip, take)

-- Last element of a list.
last :: [a] -> a
last (x : xs@(_:_)) = last xs
last [x]            = x  -- [x] == x : []


unzip :: [(a,b)] -> ([a], [b])
unzip []            = ([], [])
unzip ((x,y) : xys) = case unzip xys of
                        (xs, ys) -> (x:xs, y:ys)

-- Adds all integer and concatenates all string in a mixed list:
sumConc :: [Either Int String] -> (Int,String)
sumConc []     = (0, "")
sumConc (x:xs) = case sumConc xs of
                   (n,s) -> case x of Left  m -> (m+n, s)
                                      Right t -> (n, t ++ s)

fac :: Integer -> Integer
fac n | n == 0    = 1
      | otherwise = n * fac (n - 1)

-- Take the first n elements of a list:
take :: Int -> [a] -> [a]
take n xs | n <= 0    = []
          | otherwise = case xs of []     -> []
                                   (x:xs) -> x : take (n - 1) xs