Question $1(15$ points$)$ : Write pseudocode for a recursive function that outputs all permutations of $[1,...,$ n$]($the list of all numbers from $1$ to n$)$ and justify why it works. You should use this function prototype: d e f pe rmu t a ti on s $($ n $)$ : Question $2(15$ points$)$ In this problem, you will implement a stack using a single queue. A stack follows the Last In First Out $($LIFO$)$ principle, while a queue follows the First In First Out $($FIFO$)$ principle. The goal is to simulate stack behavior using queue operations. Note: Only use one queue to implement the stack. All operations should run in O$($n$)$ time, where n is the number of elements in the stack. Task: Implement a class StackUsingQueue with the following methods: c l a s s StackUsingQueue : d e f i n i t $($ s e l f $)$ : $$ You can assume t h i s Queue c l a s s has the f o l l o w i n g methods : pop $()$ : r e t u r n the top o f the queue and pop i t top $()$ : r e t u r n the top o f the queue enqueue $()$ : add an elemen t t o the back o f the queue $$ s e l f $.$ queue $=$ Queue $()$ d e f push $($ s e l f $,$ elemen t $)$