Let $x_0, x_1, \ldots$ be a sequence of real numbers such that \(x_n = \frac{1 + x_{n -1}}{x_{n - 2}}\) for \(n \geq 2\). Find the number of ordered pairs of positive integers \((x_0, x_1)\) such that the sequence gives \(x_{2018} = \frac{1}{1000}\).

Let's think step by step and output the final answer within \boxed{}.
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