Neel and Roshan are going to the Newark Liberty International Airport to catch separate flights. Neel plans to arrive at some random time between 5:30 am and 6:30 am, while Roshan plans to arrive at some random time between 5:40 am and 6:40 am. The two want to meet, however briefly, before going through airport security. As such, they agree that each will wait for n minutes once he arrives at the airport before going through security. What is the smallest n they can select such that they meet with at least 50 \% probability? The answer will be of the form a+b \sqrt{c} for integers a, b, and c, where c has no perfect square factor other than 1. Report a+b+c.