2006 AMC 12B Question 25

A sequence $a_1,$ $a_2,$ $\ldots$ of non-negative integers is defined by the rule $a_{n+2} = |a_{n+1} - a_n|$ for $n \ge 1.$ If $a_1 = 999,$ $a_2 \lt 999,$ and $a_{2006} = 1,$ how many different values of $a_2$ are possible?