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

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b$.$ What is its basic operation?

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

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

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