University Career Fair - Company-specific OAs / Twitter OA

You are an event organizer at a university, and n companies would like to do a presentation about their company at your university on Career Day. However, each company have a tight schedule as to when they can come and present and how long they will present. For the ith company, starting from 0, they can present starting from minute starts[i] and they can present for durations[i] minutes. To give every student a chance to listen to every presentation, the University can allow only one company to present at a time. You would like to host as many presentations as possible, so given each company's schedule, find the maximum number of presentations that the university can hold.

This is a companion discussion topic for the original entry at