elementary set theory - Prove that $^{mathbb{N}}mathcal P left({mathbb{N}}right) sim mathcal P left({mathbb{N}}right)$

The set of all functions from $A$ to $B$ is denoted $^{A}B$. Prove that $^{\mathbb{N}}\mathcal P \left({\mathbb{N}}\right) \sim \mathcal P \left({\mathbb{N}}\right)$.

Previous question proved that for any set $A$, $^{A}\{yes,no\}\sim \mathcal P \left({A}\right)$. The symbol $\sim$ means equinumerous to. $\mathbb{N}$ does not include $0$ here. $\mathcal P$ is power set operation. I know we have to create a bijection between $^{\mathbb{N}}\mathcal P \left({\mathbb{N}}\right) \sim \mathcal P \left({\mathbb{N}}\right)$. I believe I might be close to a solution, but am looking for some suggestions first.