Исходное бинарное дерево превратить в бинарное дерево поиска, при этом сохранив его структуру

data Tree a = Z | N (Tree a) a (Tree a) deriving Show
 
l2t = fst . go where
    go []     = (Z, [])
    go (0:xs) = (Z, xs)
    go (x:xs) = (N l x r, xr) where (l,xl) = go xs; (r,xr) = go xl
 
t2l Z         = [0]
t2l (N l a r) = a : t2l l ++ t2l r
 
lftCnt Z         = Z
lftCnt (N l a r) = N (lftCnt l) (leaves l) (lftCnt r) where
    leaves Z         = 0
    leaves (N l a r) = 1 + leaves l + leaves r
 
bld _ Z         = Z
bld v (N l a r) = N (bld vl l) (head vr) (bld (tail vr) r) where (vl, vr) = splitAt a v
 
res l = t2l . bld (sort . filter (/=0) $ l) . lftCnt . l2t $ l
 
main = print $ res [1,4,6,10,0,0,0,7,0,8,0,0,2,5,0,0,3,9,0,0,0]

data Tree a = Z | N (Tree a) a (Tree a) deriving Show
 
l2t = (\(t,_,_) -> t) . go where
    go (0:xs) = (Z, xs, 0)
    go (x:xs) = (N l nl r, xr, nl+nr+1) where (l,xl,nl) = go xs; (r,xr,nr) = go xl
 
t2l Z         = [0]
t2l (N l a r) = a : t2l l ++ t2l r
 
bld _ Z         = Z
bld v (N l a r) = N (bld vl l) h (bld vr r) where (vl, h:vr) = splitAt a v
 
res l = t2l . bld (sort . filter (/=0) $ l) . l2t $ l
 
main = print $ res [1,4,6,10,0,0,0,7,0,8,0,0,2,5,0,0,3,9,0,0,0]