# Problem 2 : Basic Operations

Algebra Level 4

A positive real number is given. In each move, we can either add $3$ to it, subtract $3$ to it, multiply it by $3$ and divide it by $3$. The sum of all numbers such that after exactly $3$ moves, the original number comes back is $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Find $a + b$.

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