: Let A be the fastest algorithm that takes as input two n$-$bit integers x and y$,$ and returns the product xy$.$ Let T$($n$)$ be the running time $($in terms of bit$-$operations$)$ of this algorithm.Let A be the fastest algorithm that takes as input one n$-$bit integer x$,$ and returns the square x$2.$ Let T$($n$)$ be the running time $($in terms of bit$-$operations$)$ of this algorithm. Explain, in at most two sentences, why T $($n$)=$ O$($T $($n$)).$ Professor Taylor Swift claims that T$($n$)=$ o$($T$($n$)),$ i$.$e$.,$ T$($n$)$ is asymptotically smaller than T $($n$).$ Her reasoning is that the input to algorithm A is just one integer, whereas the input to algorithm A consists of two integers.Is Professor Swifts claim correct? As always, justify your answer.