Finite symmetric difference equivalence relation on A $\subseteq \mathbb{N}$

Question

Given the equivalence relation: $A \sim B $ $\iff$ $A \Delta B$ is finite, where $\Delta$ is the symmetric difference, we define: $S := \{ A \subseteq \mathbb{N} \mid A \sim \mathbb{N} \}$. I am asked to calculate $\left| S \right|$.

Any tips, or suggestions?

Thank you!