# Avoid lattice midpoints

Geometry Level 2

You select a set of $$N$$ specific points in the 2D plane with integer coordinates such that, for every pair of the $$N$$ points, the midpoint of the segment connecting them does not have integer coordinates.

What is the greatest possible value of $$N?$$

Below is an invalid selection of 3 points (in red), since the midpoint of $$BC$$ has integer coordinates.

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