Find the number of positive integer $x$ that has $ {a}_{1},{a}_{2},\cdot \cdot \cdot {a}_{20} $ which follows the following ($x \ge 1000$) 1) $ {a}_{1}=2, {a}_{2}=1, {a}_{3}=x $ 2) for positive integer $n$, ($ 4 \le n \le 20 $), $ {a}_{n}={a}_{n-3}+\frac{(-2)^n}{{a}_{n-1}{a}_{n-2}} $