GATE Computer Science (CS) 2016 Shift 1 Solved Paper

A function f: N⁺ → N⁺, defined on the set of positive integers 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 | ∃ j: f(j) = i} be the set of distinct values that f takes. The maximum possible size of R is _______.