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A function $f(x)$ is such that $f(1) = 2$, $f(2)=1$, and $f(x)=\dfrac{1}{f(x-1)+f(x+1)}$ for $x \ge 2$. Find

$\large (f(2014)f(2015))^{(f(2012)f(2013))^{...^{...^{(f(2)f(3))^{f(1)}}}}}$

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