Template Haskell: How to extract the number of arguments of a function?

I have a function which given a Name of a function it augments it, yielding another function applied to some other stuff (details not very relevant):

mkSimple :: Name -> Int -> Q [Dec]
mkSimple adapteeName argsNum = do
  adapterName <- newName ("sfml" ++ (capitalize . nameBase $ adapteeName))
  adapteeFn <- varE adapteeName
  let args = mkArgs argsNum
  let wrapper = mkApply adapteeFn (map VarE args)
  -- generates something like SFML $ liftIO $ ((f a) b) c)
  fnBody <- [| SFML $ liftIO $ $(return wrapper) |]
  return [FunD adapterName [Clause (map VarP args) (NormalB fnBody) []]]

  where
    mkArgs :: Int -> [Name]
    mkArgs n = map (mkName . (:[])) . take n $ ['a' .. 'z']


-- Given f and its args (e.g. x y z) builds ((f x) y) z)
mkApply :: Exp -> [Exp] -> Exp
mkApply fn [] = fn
mkApply fn (x:xs) = foldr (\ e acc -> AppE acc e) (AppE fn x) xs

This works, but it's tedious to pass externally the number of args the adaptee function has. There exists some TH function to extract the number of args? I suspect it can be achieved with reify but I don't know how.

Thanks!