Consider the variant of Gale$-$Shapley algorithm on groups A $=\{$a$1,...,$ an$\}$ and B $=\{$b$1,...,$ bn$\}$ where groups A and B alternate making offers: at odd times some unmatched ai in A makes an offer to the bj in B that is highest on its list that has not yet rejected ai$,$ and at even times some unmatched bj in B makes an offer to the highest ranked ai in A that has not yet rejected it$.$ The algorithm terminates when everyone is matched or there are no new offers which can be made.

$($a$)5$ points: What is the running time of this algorithm? Explain why your answer is correct