data Tree a = Empty | Branch a (Tree a) (Tree a)
  deriving (Show, Eq)

isMirror :: Tree a -> Tree a -> Bool
isMirror Empty Empty = True
isMirror (Branch _ l1 r1) (Branch _ l2 r2) = isMirror l1 r2 && isMirror r1 l2
isMirror _ _ = False

symmetric :: (Eq a) => Tree a -> Bool
symmetric Empty = True
symmetric (Branch _ l r) = isMirror l r

cbalTree :: Int -> [Tree Char]
cbalTree 0 = [Empty]
cbalTree n =
  if even (n - 1)
    then [Branch 'x' l r | l <- tree_even, r <- tree_even]
    else [Branch 'x' l r | l <- tree_odd1, r <- tree_odd2] ++ [Branch 'x' l r | l <- tree_odd2, r <- tree_odd1]
  where
    tree_even = cbalTree $ (n - 1) `div` 2
    tree_odd1 = cbalTree $ (n - 1) `div` 2
    tree_odd2 = cbalTree $ (n - 1) `div` 2 + 1

symCbalTrees :: Int -> [Tree Char]
symCbalTrees = filter symmetric . cbalTree