RU-ALLRUSSIAN 1967 Problem 7

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