$($a$)$ Using dynamic programming algorithm, determine an optimal parenthesiza$-$

tion of a matrix$-$chain product whose dimensions are $207,710,106,65,$

$512,$ and $1215.$ How many scalar multiplications does an optimal solution

require? Show all steps.

$($b$)$ What is the exact value of $r$ returned by the following function, Mystery?

Derive your answer as a function of $n.$ if possible solve it using pen and paper and upload it