Given a positive integer $n$, let $S(n)$ denote the digit sum of $n$. Consider the sequence of numbers given by

$\begin{cases} n_1 = S(n) \\ n_k = S(n_{k-1} ) & k \geq 2 \\ \end{cases}$

For how many positive integers $n \le 2013$ does the sequence $\{ n_k \}$ contain the number $9$?

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