import "JavaBuiltin" as Java

main = foldl Java.iadd (0 :: Integer) (concat (concat (Single (1 :: Integer)) 
      (Single (2 :: Integer))) (Single (3 :: Integer))) 

data Digit a = Digit1 a
             | Digit2 a a
             | Digit3 a a a
             | Digit4 a a a a
data Node a = Node2 a a | Node3 a a a
data FingerTree a = Empty | Single a | Deep (Digit a) (FingerTree (Node a)) (Digit a)

insertL :: a -> FingerTree a -> FingerTree a
insertL a Empty      = Single a
insertL a (Single b) = Deep (Digit1 a) Empty (Digit1 b)
insertL a (Deep (Digit1 b) m r) = Deep (Digit2 a b) m r
insertL a (Deep (Digit2 b c) m r) = Deep (Digit3 a b c) m r
insertL a (Deep (Digit3 b c d) m r) = Deep (Digit4 a b c d) m r
insertL a (Deep (Digit4 b c d e) m r) = Deep (Digit2 a b) (insertL (Node3 c d e) m) r

insertR :: FingerTree a -> a -> FingerTree a
insertR Empty a      = Single a
insertR (Single a) b = Deep (Digit1 a) Empty (Digit1 b)
insertR (Deep l m (Digit1 a)) b = Deep l m (Digit2 a b)
insertR (Deep l m (Digit2 a b)) c = Deep l m (Digit3 a b c)
insertR (Deep l m (Digit3 a b c)) d = Deep l m (Digit4 a b c d)
insertR (Deep l m (Digit4 a b c d)) e = Deep l (insertR m (Node3 a b c)) (Digit2 d e)

foldl :: (a -> b -> a) -> a -> FingerTree b -> a
foldl f init Empty = init
foldl f init (Single x) = f init x
foldl f init (Deep l m r) = foldlD (foldl foldlN (foldlD init l) m) r
  where
    foldlD init (Digit1 a) = f init a
    foldlD init (Digit2 a b) = f (f init a) b
    foldlD init (Digit3 a b c) = f (f (f init a) b) c
    foldlD init (Digit4 a b c d) = f (f (f (f init a) b) c) d
    
    foldlN init (Node2 a b) = f (f init a) b
    foldlN init (Node3 a b c) = f (f (f init a) b) c

data View a = Nil | Cons a (FingerTree a)

viewL :: FingerTree a -> View a
viewL Empty = Nil
viewL (Single a) = Cons a Empty
viewL (Deep (Digit1 a) m r) = Cons a tail
  where
    tail = match viewL m with
        Nil -> digitToFingerTree r
        Cons h t -> Deep (nodeToDigit h) t r
viewL (Deep (Digit2 a b) m r) = Cons a (Deep (Digit1 a) m r)
viewL (Deep (Digit3 a b c) m r) = Cons a (Deep (Digit2 a b) m r)
viewL (Deep (Digit4 a b c d) m r) = Cons a (Deep (Digit3 a b c) m r)

concat :: FingerTree a -> FingerTree a -> FingerTree a
concat Empty a = a
concat a Empty = a
concat (Single a) b = insertL a b
concat a (Single b) = insertR a b
concat (Deep l1 m1 r1) (Deep l2 m2 r2) = Deep l1 mm r2
  where
    mm = concatAux m1 (digitsToNodes r1 l2) m2
    
// --- Implementation details -------------------------------------------------

digitToFingerTree :: Digit a -> FingerTree a
digitToFingerTree (Digit1 a)       = Single a
digitToFingerTree (Digit2 a b)     = Deep (Digit1 a)   Empty (Digit1 b)
digitToFingerTree (Digit3 a b c)   = Deep (Digit2 a b) Empty (Digit1 c)
digitToFingerTree (Digit4 a b c d) = Deep (Digit2 a b) Empty (Digit2 c d)

nodeToDigit :: Node a -> Digit a
nodeToDigit (Node2 a b)   = Digit2 a b
nodeToDigit (Node3 a b c) = Digit3 a b c
    
concatAux :: FingerTree a -> Digit a -> FingerTree a -> FingerTree a
concatAux Empty ds a = insertLD ds a
concatAux a ds Empty = insertRD a ds
concatAux (Single a) ds b = insertL a (insertLD ds b)
concatAux a ds (Single b) = insertR (insertRD a ds) b
concatAux (Deep l1 m1 r1) ds (Deep l2 m2 r2) = Deep l1 mm r2
  where
    mm = concatAux m1 (digitsToNodes3 r1 ds r2) m2

insertLD :: Digit a -> FingerTree a -> FingerTree a
insertLD (Digit1 a) t = insertL a t
insertLD (Digit2 a b) t = insertL a (insertL b t)
insertLD (Digit3 a b c) t = insertL a (insertL b (insertL c t))
insertLD (Digit4 a b c d) t = insertL a (insertL b (insertL c (insertL d t)))

insertRD :: FingerTree a -> Digit a -> FingerTree a
insertRD t (Digit1 a) = insertR t a
insertRD t (Digit2 a b) = insertR (insertR t a) b
insertRD t (Digit3 a b c) = insertR (insertR (insertR t a) b) c
insertRD t (Digit4 a b c d) = insertR (insertR (insertR (insertR t a) b) c) d
    
digitsToNodes :: Digit a -> Digit a -> Digit (Node a)
digitsToNodes (Digit1 a) x = dd1 a x
digitsToNodes (Digit2 a b) x = dd2 a b x 
digitsToNodes (Digit3 a b c) x = dd3 a b c x
digitsToNodes (Digit4 a b c d) x = dd4 a b c d x 

digitsToNodes3 :: Digit a -> Digit a -> Digit a -> Digit (Node a)
digitsToNodes3 (Digit1 a) x y = ddd1 a x y
digitsToNodes3 (Digit2 a b) x y = ddd2 a b x y
digitsToNodes3 (Digit3 a b c) x y = ddd3 a b c x y
digitsToNodes3 (Digit4 a b c d) x y = ddd4 a b c d x y   
    
d2 a b = Digit1 (Node2 a b)
d3 a b c = Digit1 (Node3 a b c)
d4 a b c d = Digit2 (Node2 a b) (Node2 c d)
d5 a b c d e = Digit2 (Node3 a b c) (Node2 d e)
d6 a b c d e f = Digit2 (Node3 a b c) (Node3 d e f)
d7 a b c d e f g = Digit3 (Node3 a b c) (Node2 d e) (Node2 f g)
d8 a b c d e f g h = Digit3 (Node3 a b c) (Node3 d e f) (Node2 g h)
d9 a b c d e f g h i = Digit3 (Node3 a b c) (Node3 d e f) (Node3 g h i)
d10 a b c d e f g h i j = Digit4 (Node3 a b c) (Node3 d e f) (Node2 g h) (Node2 i j)
d11 a b c d e f g h i j k = Digit4 (Node3 a b c) (Node3 d e f) (Node3 g h i) (Node2 j k)
d12 a b c d e f g h i j k l = Digit4 (Node3 a b c) (Node3 d e f) (Node3 g h i) (Node3 j k l)

dd1 a (Digit1 b) = d2 a b
dd1 a (Digit2 b c) = d3 a b c
dd1 a (Digit3 b c d) = d4 a b c d
dd1 a (Digit4 b c d e) = d5 a b c d e
dd2 a b (Digit1 c) = d3 a b c
dd2 a b (Digit2 c d) = d4 a b c d
dd2 a b (Digit3 c d e) = d5 a b c d e
dd2 a b (Digit4 c d e f) = d6 a b c d e f
dd3 a b c (Digit1 d) = d4 a b c d
dd3 a b c (Digit2 d e) = d5 a b c d e
dd3 a b c (Digit3 d e f) = d6 a b c d e f
dd3 a b c (Digit4 d e f g) = d7 a b c d e f g
dd4 a b c d (Digit1 e) = d5 a b c d e
dd4 a b c d (Digit2 e f) = d6 a b c d e f
dd4 a b c d (Digit3 e f g) = d7 a b c d e f g
dd4 a b c d (Digit4 e f g h) = d8 a b c d e f g h
dd5 a b c d e (Digit1 f) = d6 a b c d e f
dd5 a b c d e (Digit2 f g) = d7 a b c d e f g
dd5 a b c d e (Digit3 f g h) = d8 a b c d e f g h
dd5 a b c d e (Digit4 f g h i) = d9 a b c d e f g h i
dd6 a b c d e f (Digit1 g) = d7 a b c d e f g
dd6 a b c d e f (Digit2 g h) = d8 a b c d e f g h
dd6 a b c d e f (Digit3 g h i) = d9 a b c d e f g h i
dd6 a b c d e f (Digit4 g h i j) = d10 a b c d e f g h i j
dd7 a b c d e f g (Digit1 h) = d8 a b c d e f g h
dd7 a b c d e f g (Digit2 h i) = d9 a b c d e f g h i
dd7 a b c d e f g (Digit3 h i j) = d10 a b c d e f g h i j
dd7 a b c d e f g (Digit4 h i j k) = d11 a b c d e f g h i j k
dd8 a b c d e f g h (Digit1 i) = d9 a b c d e f g h i
dd8 a b c d e f g h (Digit2 i j) = d10 a b c d e f g h i j
dd8 a b c d e f g h (Digit3 i j k) = d11 a b c d e f g h i j k
dd8 a b c d e f g h (Digit4 i j k l) = d12 a b c d e f g h i j k l

ddd1 a (Digit1 b) y = dd2 a b y
ddd1 a (Digit2 b c) y = dd3 a b c y
ddd1 a (Digit3 b c d) y = dd4 a b c d y
ddd1 a (Digit4 b c d e) y = dd5 a b c d e y
ddd2 a b (Digit1 c) y = dd3 a b c y
ddd2 a b (Digit2 c d) y = dd4 a b c d y
ddd2 a b (Digit3 c d e) y = dd5 a b c d e y
ddd2 a b (Digit4 c d e f) y = dd6 a b c d e f y
ddd3 a b c (Digit1 d) y = dd4 a b c d y
ddd3 a b c (Digit2 d e) y = dd5 a b c d e y
ddd3 a b c (Digit3 d e f) y = dd6 a b c d e f y
ddd3 a b c (Digit4 d e f g) y = dd7 a b c d e f g y
ddd4 a b c d (Digit1 e) y = dd5 a b c d e y
ddd4 a b c d (Digit2 e f) y = dd6 a b c d e f y
ddd4 a b c d (Digit3 e f g) y = dd7 a b c d e f g y
ddd4 a b c d (Digit4 e f g h) y = dd8 a b c d e f g h y

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