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$\large [ (x_1 - x_2)^2 + ( 12 - \sqrt{1 - (x_1)^2} - \sqrt{4x_2} )^2 ]^\frac{1}{2}$

The minimum value of the expression above for all permissible values of $x_1$ and $x_2$ is equal to $a\sqrt{b} -c$ , where $a,b$ and $c$ are positive integers. Find $a+b-c$ .