A function \(f: \Bbb{N^+} \rightarrow \Bbb{N^+}\), defined on the set of…

A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$, defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties:

$f(n)=f(n/2)$ if $n$ is even

$f(n) = f(n+5)$ if $n$ is odd

Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is __________.