An algorithm running on an array determines $8$ subarrays each of which is of length ${|}_{{?}_{?}}\frac{n}{2_{{?}_{?}}}|$ where $n$ is the number of elements in the original array. The algorithm needs $(n)$ time in order to determine these subarrays. Then it calls itself for each of these subarrays.

a$.(10$ pts$)$ Write the recurrence relation.

b$.(15$ pts$)$ Use a recursion tree to determine asymptotic bound for the recurrence in $($a$).$

c$.(20$ pts$)$ Use substitution method to verify your answer in $($b$)$ as an asymptotic bound estimation. Do not forget to evaluate the base case for the solution.