probability - On average, how many friends would I need to have to have at least one friend's birthday every day?

I know that because of the birthday problem, even after 365 friends, you're going to have a lot of doubles and that there's also an infinitesimal chance that even with infinite friends that there's one day left out. But I was curious how many friends you'd need on average to have every day represented (this is ignoring leap day and assuming birthdays are equally distributed). Or to generalize it further, given n unique boxes and you're placing balls in them with an equal 1/n chance for the ball to go into any box, how many balls would you have to place on average before every box had at least one ball?