ILL 1985 Problem 40

Each of the numbers $x_1, x_2, \dots, x_n$ equals $1$ or $-1$ and $$\sum_{i=1}^n x_i x_{i+1} x_{i+2} x_{i+3} =0.$$ where $x_{n+i}=x_i$ for all $i$ . Prove that $4\mid n$ .