Let $S$ be a subset of $1,2,3,\dots ,1500$ such that the following two conditions hold:

• If $x$ and $y$ are distinct elements of $S$, then $|x-y|>3$.
• If $x$ and $y$ are distinct odd elements of $S$, then $|x-y|>7$.

What is the maximum possible number of elements in $S$?