For a positive integer $n$, let $f(n)$ be the integer formed by reversing the digits of $n$ (and removing any leading zeroes). For example, $f(14172) = 27141$. Define a sequence of numbers $\{a_n\}_{n \ge 0}$ by $a_0 = 1$ and for all $i \ge 0$, $a_{i+1} = 11a_i$ or $a_{i+1} = f(a_i)$. How many possible values are there for $a_8$?

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