Professor Holmes has come up with a new sorting algorithm. He calls it Trinary Sort and $$claims$$ that it is asymptotically faster than Merge Sort, despite the fact both the algorithms operate using similar logic. But, unlike Merge Sort, Trinary Sort splits the input array into $($roughly$)3$ equal parts at each step of the recursion as long as the array is splittable $($i$.$e$.,$ has at least $3$ elements$).$ Trinary Sort$$s merge subroutine, similar in principle to the one used by Merge Sort, takes $3$ sorted subarrays and merges them to produce a single sorted array. Given all of this, answer the following questions. $($a$)[4$ points$]$ In Merge Sort, the merge subroutine makes n$1$ comparisons to merge $2$ arrays of size n$/2,$ which takes $\backslash$Theta $($n$)$ time. How many comparisons will the merge subroutine of Page $5$ of $6$ Trinary Sort make to merge $3$ arrays of size n$/3?$ What would be the $\backslash$Theta $()$ bound on the running time for this subroutine?