How do I find a matrix $S$ such that $S^\top A \, S$ is a diagonal matrix with entries $0,-1,1$?

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Given matrix $$A = \begin{pmatrix}1&2&2\\2&1&-2\\2&-2&1\end{pmatrix}$$ whose eigenvalues are $3,-3,-3$, how can I find a such a regular matrix $S$?