Consider the following recursive algorithm for computing the sum of the first $n$ cubes: $S(n)=1^{{?}^{{?}^{?}}}3+2^{{?}^{{?}^{?}}}3+$dots$+n^{{?}^{{?}^{?}}}3.$

Algorithm S$(n)$

$//$Input: A positive integer $n$

$//$Output: The sum of the first $n$ cubes

if $n=1$ return $1$

else return $S(n-1)+n**n**n$

a$.$ What is the input size?

b$.$ What is its basic operation? choose your answer...

c$.$ How many times is the basic operation executed? choose your answer...

d$.$ What is the efficiency class of this algorithm? choose your answer...