You found an awesome deal online and ordered a kit that contains $1024$ pairs of nuts and bolts. Each nut and bolt pair are a unique size, so each nut fits exactly one bolt $($and conversely, each bolt fits exactly one nut$).$ Unfortunately, they$$re all mixed up and loose. You want to organize your kit and put each nut on its corresponding bolt. Because they$$re all mixed up$,$ you fear that it will take an incredibly long time.

Fortunately, you can compare any nut to any bolt and instantly know if

the bolt is too small for the nut, or

they match, or

the nut is too small for the bolt.

Come up with an algorithm that uses a $$divide and conquer$$ approach to pair up all your nuts and bolts.

HINT: Think about how you could modify the Quick Sort algorithm.