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$\large S = \sqrt{x^2+\dfrac{1}{y^2}}+\sqrt{y^2+\dfrac{1}{z^2}}+\sqrt{z^2+\dfrac{1}{x^2}}$

Given that $x,y$ and $z$ are non-zero reals. Let the minimum value of $S$ be $S_{\min}$. Find $(S_{\min})^2$.

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