You are playing a game called "Hovse." Initially, you have the number $0$ on a blackboard. At any moment, if the number $x$ is written on the board, you can perform one of the following operations:

- Replace $x$ with $3x + 1$
- Replace $x$ with $9x + 1$
- Replace $x$ with $27x + 3$
- Replace $x$ with $\left \lfloor \frac{x}{3} \right \rfloor$

You are not allowed to write a number greater than $2017$ on the board. How many positive numbers can you make with the game of "Hovse?"

Let's think step by step and output the final answer within \boxed{}.
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