import Base(ana,cata)

data Tree a = Leaf a | Bin (Tree a) (Tree a) deriving Show

balance :: [a] -> Tree a
balance = ana ba

ba :: [a] -> FunctorOf Tree a [a]
ba xs = case xs of
          []     -> error "Can't represent the empty list"
	  [x]    -> Left x
	  xs	 -> Right (splitAt (length xs `div` 2) xs)

t1 :: Tree Char
t1 = balance "Patrik"

main :: IO ()
main = print (t1,depth t1)

depth :: Tree a -> Int
depth = cata de

de :: FunctorOf Tree a Int -> Int
de = either (const 0) (\(m,n)-> 1 + max m n)