In Racket, create a recursive tree$-$insert which takes a tree and a number and returns the tree with the number instead. Within the code, you will see the expected return but that is not what I am getting. What needs to be adjusted so I can get the sub$-$trees the extra parenthesis needed?

How can I fix my code to get the return expected? Below is my code so far but I am unsure how to get the correct nesting.

Current code:

#lang racket

;; Define the function to incrementally insert and build the tree with quoted output

$($define $($tree$-$insert$-$custom value tree show$-$left? show$-$right?$)$

$($cond

;; If the tree is empty, return a new list with the value

$[($empty$?$ tree$)($list value$)]$

;; If the value is less than the current node, insert into the left subtree

$[(<$ value $($first tree$))$

$($let$*(($new$-$left $($tree$-$insert$-$custom value $($if $(>=($length tree$)2)($second tree$)\text{'}())$ #t show$-$right?$))$

$($right$-$subtree $($if $($and show$-$right? $(>=($length tree$)3))($third tree$)\text{'}())))$

$($list $($first tree$)$

new$-$left

right$-$subtree$))]$ ;; Include left and right subtrees directly

;; If the value is greater than the current node, insert into the right subtree

$[(>$ value $($first tree$))$

$($let$*(($left$-$subtree $($if $($and show$-$left? $(>=($length tree$)2))($second tree$)\text{'}()))$

$($new$-$right $($tree$-$insert$-$custom value $($if $(>=($length tree$)3)($third tree$)\text{'}())$ show$-$left? #t$)))$

$($list $($first tree$)$

left$-$subtree

new$-$right$))]$ ;; Include left and right subtrees directly

;; If the value is equal to the current node's value, return the tree unchanged

$[$else tree$]))$

;; Function to build a single cumulative tree from a list of elements

$($define $($build$-$tree$-$with$-$quote elements$)$

$($define $($helper lst tree$)$

$($if $($empty$?$ lst$)$

tree

$($helper $($rest lst$)($tree$-$insert$-$custom $($first lst$)$ tree #t #t$))))$

$`($quote $,($helper elements $\text{'}())))$ ;; Start with an empty tree and add each element, using quasiquote to include quote

$($define A $($build$-$tree$-$with$-$quote $\text{'}(8)))$ ;; Insert $8->\text{'}(8)$

$($define B $($build$-$tree$-$with$-$quote $\text{'}(812)))$ ;; Insert $12->\text{'}(8((12)))$

$($define C $($build$-$tree$-$with$-$quote $\text{'}(83)))$ ;; Insert $3->\text{'}(8((3))())$

$($define D $($build$-$tree$-$with$-$quote $\text{'}(8312)))$ ;; Insert $12->\text{'}(8((3)(12)))$

$($define E $($build$-$tree$-$with$-$quote $\text{'}(83124)))$ ;; Insert $4->\text{'}(8((3((4)))(12)))$

;; Display results with the quote included automatically

$($display A$)$ ;; Expected output: $\text{'}(8)$

$($newline$)$

$($display B$)$ ;; Expected output: $\text{'}(8((12)))$

$($newline$)$

$($display C$)$ ;; Expected output: $\text{'}(8((3))())$

$($newline$)$

$($display D$)$ ;; Expected output: $\text{'}(8((3)(12)))$

$($newline$)$

$($display E$)$ ;; Expected output: $\text{'}(8((3((4)))(12)))$

$($newline$)$

$=====================================$

Current output:

$\text{'}(8)$

$\text{'}(8()(12))$

$\text{'}(8(3)())$

$\text{'}(8(3)(12))$

$\text{'}(8(3()(4))(12))$