Let \[f(x) = \left\{
\begin{array}{cl}
x^2 &\text{ if }x \le 3, \\
2x - 1 &\text{ if }x > 3.
\end{array}
\right.\]
Find $f(f(f(1)))$. Let's think step by step and output the final answer within \boxed{}.
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