Assume the [Carmichael's Totient Function Conjecture](https://en.wikipedia.org/wiki/Carmichael%27s_totient_function_conjecture).

How fast does this chain grow?

$$n_0=\phi(3^2)\rightarrow n_1=\phi((\phi^{-1}(n_0))^2)\rightarrow n_2=\phi((\phi^{-1}(n_1))^2)\rightarrow\dots$$

where $\phi^{-1}(\phi(x))$ is the smallest second integer $y\neq x$ such that $\phi(x)=\phi(y)$.