Recursive Digit Sum

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

{n1=S(n)nk=S(nk1)k2 \begin{cases} n_1 = S(n) \\ n_k = S(n_{k-1} ) & k \geq 2 \\ \end{cases}

For how many positive integers n2013n \le 2013 does the sequence {nk} \{ n_k \} contain the number 99?

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