The not-so-hard-working flights

In the country of Brilliantia, there are \(n > 60\) airports built recently such that the distances between any two airports are all different from one another.

A plane will always fly from an airport to the nearest airport. Let an origin of an airport \(\text{A}\) be another airport that flies planes to \(\text{A}\).

What is the maximum number of origins an airport can have?

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