Fibonacci Reversed

Algebra Level 2

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

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

What is the value of f1(f1(f1(13)))f^{-1}(f^{-1}(f^{-1}(13)))?

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