import Prelude hiding (last, take, unzip)

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

-- Splits a list of pairs into their elements:
unzip :: [(a,b)] -> ([a],[b])
unzip []          = ([],[])
unzip ((x,y):xys) = (x : xs, y : ys)
 where (xs,ys) = unzip xys


-- Sum up all integers and concatenate all lists:
sumConc :: [Either Int String] -> (Int,String)
sumConc []     = (0,"")
sumConc (x:xs) = case sumConc xs of
                   (sum,cs) -> case x of Left n  -> (n+sum, cs)
                                         Right s -> (sum, s++cs)

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

-- Returns the prefix with n elements of a list:
take :: Int -> [a] -> [a]
take n xs | n <= 0    = []
          | otherwise = case xs of []   -> []
                                   y:ys -> y : take (n - 1) ys