Figure $2$ shows a Java implementation of mergesort whose input is a linked list.

Answer the following questions.

Figure $2.$ An implementation of mergesort of which an input is a linked list.

$(1)$ The following codes sort the list A$,$ and print all the elements of A from its head to

tail. $($Note that A$.$ getHead$()$ and A$.$getTail$()$ return the head and tail nodes of

A$,$ respectively.$)$ However, when you print the sorted list using the following codes,

you can find out the function mergeSort $()$ does not work correctly.

Why does mergeSort $()$ work incorrectly? How can you fix mergeSort $()$ to make

the function work correctly? $[10$ points$]$

$(2)$ Let $n$ be the length of an input linked list. How many times is mergeSort$()$

called to sort the list? The initial call of the function should be included. $[10$ points$]$