In ocaml, we've a the two given types and a function ncompress of type $\text{'}$a n$\_$tree $->(\text{'}$a $*$ int$)$ list$$ that converts an ntree into a list of tuples. The first element of the tuple is stored in the node and the second is the number of immediate children. This follows preorder traversal.

Write a function ndecompress of type$(\text{'}$a $*$ int$)$ list $->\text{'}$a n$\_$tree that takes the $(\text{'}$a $*$ int$)$ list converts it back to an ntree. If the input list is empty, raise an Invalid$\_$arg exception using failwith because it can't represent a completely empty tree.

Can use functions found in Stdlib and List, but not any submodules of Stdlib

type 'a flat $=$ Le $|$ No of $\text{'}$a

type 'a ntree $=$ Node of $\text{'}$a $*$ 'a ntree list

let t $=$ Node $("$A$",[$ Node $("$B$",[])$; Node $("$C$",[$Node $("$D$",[])$; Node $("$F$",[$Node $("$E$",[])])])$; Node $("$G$",[$Node $("$H$",[])])])$

let com $=$ ncompress t;;

com:$($string $*$ int$)$ list $=[("$A$",3)$; $("$B$",0)$; $("$C$",2)$; $("$D$",0)$; $("$F$",1)$; $("$E$",0)$; $("$G$",1)$; $("$H$",0)]$

let deco $=$ ndecompress com;;

deco $=$ t;;