Let
\[f(x)= \begin{cases}
1-\sqrt{x} & \text{ if } x\geq 0 \\
\sqrt{1-x} & \text{ if } x<0.
\end{cases} \]
If \((f^{-1}\circ f^{-1})(a)=100,\) where \(a\) is a constant, what is the value of \(a^2?\)

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