Largely wrong

A sequence of integers \(A_i\) is defined by \(A_1 = 1, A_2 = 2\) and \(A_n = A_{n-1} -A_1A_2\cdots A_{n-2}\) for \(n \geq 3.\) What is \(\left\vert A_{1000} \right\vert \)?

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