KZ-MO 1999 Problem 6

In a sequence of natural numbers $a_1$ , $a_2$ , $\dots$ , $a_ {1999}$ , $a_n-a_ {n-1} -a_ {n-2}$ is divisible by $100 (3 \leq n \leq 1999)$ . It is known that $a_1 = 19$ and $a_2 = 99$ . Find the remainder of $a_1 ^ 2 + a_2 ^ 2 + \dots + a_ {1999} ^ 2$ by $8$ .