import Prelude hiding (last,unzip,take)

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


-- Unzip a list of pairs into two lists.
unzip :: [(a,b)] -> ([a],[b])
unzip []         = ([],[])
unzip ((x,y):ps) = case unzip ps of
                     (xs,ys) -> (x:xs, y:ys) 

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

-- Returns 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