Let $f$ be defined by\[f(x) = \left\{ \begin{array}{cl} 2-x & \text{ if } x \leq 1, \\ 2x-x^2 & \text{ if } x>1. \end{array} \right.\]Calculate $f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$.
f^{-1}(-3)+f^{-1}(0)+f^{-1}(3) = -8.
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