The equation $ x^3 \minus{} 9x^2 \plus{} 8x \plus{} 2 \equal{} 0$ has three real roots $ p$, $ q$, $ r$.  Find $ \frac {1}{p^2} \plus{} \frac {1}{q^2} \plus{} \frac {1}{r^2}$.

Let's think step by step and output the final answer within \boxed{}.
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