Consider the algorithm that computes first xi $0$ for each i$,$ using the fast exponentiation algorithm from lectures $($without taking mod$).$ Then, it computes a$1$x$0,$ a$2$x$20,$ a$3$x$30,...,$anxn$0($independently$)$ and, fi$-$ nally, it adds all of these numbers to a$0$ to obtain p$($x$0).$ How many sums and how many multiplica$-$ tions are involved in this algorithm? Please provide short explanations. $($You can give your answer in O$-$notation.$)$