My friend Leo wants to have a emergency plan for his final exams on University of Southern Algorithm Ville. He has N subjects to prepare for, and for each subject, his score is determined only by the time he spend on learning. It’s not surprising that Leo found out he actually spent zero time on preparing before. At least he knows when he can start learning all of these subjects. For each subject i there is a start time si when he can get all materials ready to start learning. And there is also a ending time ei for each subject, when his learning materials expire and he can’t learn anymore. We know that si and ei are integers, and Leo can only dedicate to a single subject within each time phase. In Universtiy of Southern Algorithm Ville (USA), a student’s total grade is the minimum grade among all subjects. Leo wants you to help him find out the best outcome. Given N subjects and their time intervals (si , ei), design an algorithm to find out the maximum time possible for the least prepared subject. Prove the correctness of your algorithm. (Hint: It’s not enough to use the network flow algorithm alone to determine the answer.)