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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