MathNet 1967 — Part 01 Question 8

What is the maximum possible length of a sequence of natural numbers $x_{1}, x_{2}, x_{3}, \ldots$ such that $x_{i} \leq 1998$ for $i \geq 1$, and $x_{i} = |x_{i - 1} - x_{i - 2}|$ for $i \geq 3$.