Damn! It's not just MY birthday!

It is well known from the "birthday paradox problem" that the chances at least two people among 23 have the same birthday is larger than 0.5.


However, it is still not nice if someone else's birthday is the day after yours or the day before yours!

Find the minimum number of people \(n\) such that the chances that at least two have birthdays that are at most one day apart is larger than 0.5.

Note: Forget about leap years.


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