Run-Length Encoding in Haskell

import Data.List
 
thing :: String
thing = "aaaabccaadeeee"
 
-- My attempt got me close enough to consider it solved.
encode :: (Eq a) => [a] -> [(Int, [a])]
encode xs = 
    let groupList = groupBy (\x y -> x == y) xs
        lengths = map length groupList
        letterList = map nub groupList
    in zip lengths letterList
 
-- from the haskell.org solutions:
encode2 :: (Eq a) => [a] -> [(Int, a)]
encode2 = map (\x -> (length x, head x)) . group