Let $S$ be the set of lattice points $(x,y)$ with $1 \leq x \leq 20$ and $1 \leq y \leq 30.$ Let $B \subseteq S$ be a subset of $S$ such that no set of $4$ vertices in $B$ form a (non-degenerate) parallelogram. What is the largest possible number of elements in $B?$

**Details and assumptions**

A figure is degenerate if it has 0 area.

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