ZA-SAMO 2020 Problem 3

If $x$ , $y$ , $z$ are real numbers satisfying \begin{align*} (x + 1)(y + 1)(z + 1) & = 3 (x + 2)(y + 2)(z + 2) & = -2 (x + 3)(y + 3)(z + 3) & = -1, \end{align*} find the value of $$(x + 20)(y + 20)(z + 20).$$