Your task is to schedule the final exams for Math $115,$ Math $116,$ Math $185,$ Math $195,$ CS $101,$ CS $102,$ CS $273,$ and CS $473,$ using the fewest number of different time slots, if there are no students taking both

Math $115$ and CS $473,$

Math $116$ and CS $473,$

Math $195$ and CS $101,$

Math $195$ and CS $102,$

Math $115$ and Math $116,$

Math $115$ and Math $185,$ and

Math $185$ and Math $195,$

but every other pair of courses have some students in common.

What is the minimum number of time slots?