Introduction to algorithms class. Please show your work. And please DO NOT copy any solutions to this problem that may already exist on Chegg Study.

Suppose you have a processor that can operate 24 hours a day, every day. People can submit jobs to the processor by giving a start and finish time during a day. The processor can only run one job at a time. If a job is accepted, it must run continuously between the start and finish times. For example, if the start time is 10 pm and the finish time is 3 am, then the job must run from 10 pm to 3 am every day. Give a polynomial time algorithm that on input such a list of such jobs outputs a set of compatible jobs of maximal size. Prove that your algorithm works