$($b$)$ Consider a hybrid sorting algorithm that combines Quicksort with Insertion Sort for better efficiency. Once the size of a subarray in a recursive call of Quicksort is less than or equal to $16,$ the algorithm will switch to Insertion Sort. What is the number of key comparisons performed by this hybrid algorithm in the worst case when running on an input array of size $n?$ Briefly justify your answer. You could assume $n=2^k,$ for some integer $k>4.$

$(6$ marks$)$