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$\begin{cases} f(1) = 2 \\ f(2) = 3 \\ f(3) = 5 \\ f(4) = 8 \\ f(5) = 13 \end{cases}$

Let $f$ be the function with one-to-one relation similar to the Fibonacci sequence as shown above.

What is the value of $f^{-1}(f^{-1}(f^{-1}(13)))$?

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