Splitting Rose Trees

type 'a rtree = Node of 'a * 'a rtree list

Implement the function

val split : ('a * 'b) rtree -> 'a rtree * 'b rtree

so that split t constructs two trees of the same structure as t, one with the left element of the tuple in each node of t, and one with the right element of the tuple in each node.

Examples

let t = Node ((1, "a"), [Node ((2, "b"), []); Node ((3, "c"), [])])
let _ = assert (split t =
    ( Node (1, [Node (2, []); Node (3, [])])
    , Node ("a", [Node ("b", []); Node ("c", [])])
    ))
let _ = assert (split (Node ((1, "a"), [])) = (Node (1, []), Node ("a", [])))