For a set S \subseteq \mathbb{N}, define f(S)=\{\lceil\sqrt{s} \mid s \in S\}. Find the number of sets T such that |f(T)|=2 and f(f(T))=\{2\}.
For a set S \subseteq \mathbb{N}, define f(S)=\{\lceil\sqrt{s} \mid s \in S\}. Find the number of sets T such that |f(T)|=2 and f(f(T))=\{2\}.