Consider a circle $C_1: x^2+y^2-4 x-2 y=\alpha-5$. Let its mirror image in the line $y=2 x+1$ be another circle $C_2: 5 x^2+5 y^2-10 f x-10 g y+36=0$. Let $r$ be the radius of $C_2$. Then $\alpha+r$ is equal to
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