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

Let's think step by step and output the final answer within \boxed{}.
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