A collection of $n$ squares on the plane is called tri-connected if the following criteria are satisfied:
(i) All the squares are congruent.
(ii) If two squares have a point $P$ in common, then $P$ is a vertex of each of the squares.
(iii) Each square touches exactly three other squares.
How many positive integers $n$ are there with $2018\leq n \leq 3018$, such that there exists
a collection of $n$ squares that is tri-connected?
APMO 2018 Problem 3
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