Drawing of a Relation

Given a 5x5 grid divided into 1x1 squares. Two squares are considered related if they are in the same row or column, and the distance between their centers is 2 or 3.
For example, in the drawing, all the squares related to the red square are marked in gray. Sammy receives a blank grid and wants to mark as many squares as possible such that no two of them are related. What is the maximum number of squares he can mark?

Difficulty level (1 very easy - 10 very hard): 2

Topics:
Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Minimum and Maximum Problems / Optimization Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
Sources:
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