Recursive Function

Let \( f : \mathbb{N} \rightarrow \mathbb{N} \) be a function defined as follows:

\[ f(n) = \begin{cases} 1 & n=1 ,\\ f(k) & n = 2k, \\ f(k) + 1 & n = 2k+ 1. \\ \end{cases} \] Let \(A \) be the maximum value of \(f(n) \) on \( 1 \leq n \leq 2013 \). Calculate the number of values of \(n\) with \( 1 \leq n \leq 2013 \) such that \( f(n) = A \).

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