Racing Competition: You are given the task of grading $n$ cars in a racing competition based on who

they won against and who they lost against as each car goes head to head. You are given a graph with

$n$ nodes $($one for each car$)$ and there is a directed edge from $x$ to $Y$ if car $x$ won a race against car

$Y.$ For each car $C,$ you must assign a positive integer grading $g(C).$ The grading system must follow

these rules:

If car $x$ won a match against car $Y$ then $g(x)g(Y).$

Please design a reasonably efficient algorithm that assigns a rating to each team with the rules pre$-$

viously mentioned that maximizes the number of different grading values. This MUST include the

following: a reasonably efficient and correct high level algorithm description paired with a correctness

proof, correct time analysis, and make sure this is an efficient algorithm.