Let $\mathbb{Z}_{\ge 0}$ denote the set of nonnegative integers.

Define a function $f:\mathbb{Z}_{\ge 0} \to \mathbb{Z}$ with $f\left(0\right)=1$ and 
\[ f\left(n\right)=512^{\left\lfloor n/10 \right\rfloor}f\left(\left\lfloor n/10 \right\rfloor\right) \]
for all $n \ge 1$. Determine the number of nonnegative integers $n$ such that the hexadecimal (base $16$) representation of $f\left(n\right)$ contains no more than $2500$ digits.

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