HMMT November 2016 U17

Let $p(x)=x^{2}-x+1$ . Let $\alpha$ be a root of $p(p(p(p(x)))$ . Find the value of

$(p(\alpha)-1) p(\alpha) p(p(\alpha)) p(p(p(\alpha))$

Dataset text NuminaMath olympiads. Quoted with source.

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