Consider the following algorithm:

ALGORITHM X$($n$)$

$//$Input: positive integer n

i$$n$-1$

j$1$

for k $0$ to n$-2$ do

j$$ j$*$n

i$$ i$*$k

return i $,$ j

a$)$ What is the basic operation?

b$)$ Show and simplify a summation for the number of times the basic operation is executed.

c$)$ What is the input size?

d$)$ What is the $\backslash$Theta time$-$efficiency class of the algorithm? Prove your result.

e$)$ Indicate whether the efficiency class is constant, logarithmic, linear, quadratic, exponential, etc. in the input size.