The 2N Relation

Let \( f\) be a function from the positive integers to the positive integers satisfying

\[ f(1) = 2, f(2) = 1, f(3n) = 3f(n)\] \[f(3n+1) = 3f(n) + 2, f(3n+2) = 3f(n) + 1.\]

How many positive integers \( N \leq 1000\) satisfy \( f(N) = 2N\)?

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