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Let $C_0,C_1,C_2,...$ be the sequences of circles in the Cartesian plane defined as follows
(i) $C_0$ is the circle $x^2+y^2 = 1$
(ii) For n=0,1,2,... the circle $C_{n+1}$ lies in the upper half-plane and is tangent to $C_n$ as well as to both branches of the hyperbola $x^2-y^2=1$
Let $r_n$ be the radius of $C_n$. Show that $r_n$ is an integer and give a formula for $r_n$