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

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 \(a+b-c\).

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