ILL 1992 Problem 14

Integers $a_1, a_2, . . . , a_n$ satisfy $|a_k| = 1$ and $$\sum_{k=1}^{n} a_ka_{k+1}a_{k+2}a_{k+3} = 2,$$ where $a_{n+j} = a_j$ . Prove that $n \neq 1992.$