7. (15%) There are N students in a class. How large N will let the probability of at least two students having the same birthday exceed 90%? Note: A year has 365 days.

【Hint: You may use the following characters:

(1) \(e^{-x}\geq 1 - x\) (2) \(e^{-1} = 0.3678;\ln (0.1) = -2.30259\)