# 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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