Let $A=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1\end{array}\right]$ satisfy

$\mathrm{A}^2+\alpha(\operatorname{adj}(\operatorname{adj}(\mathrm{A})))+\beta(\operatorname{adj}(\mathrm{A})(\operatorname{adj}(\operatorname{adj}(\mathrm{A}))))=\left[\begin{array}{ccc}2 & -2 & 2 \\ -2 & 0 & -1 \\ 0 & 0 & -1\end{array}\right]$ for some $\alpha, \beta \in \mathbb{R}$.

Then $(\alpha-\beta)^2$ is equal to $\_\_\_\_$