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Algebra Level 4

Given real numbers \(x,y,z\) such that \(x+y+z=0\), find the sum of the maximum and minimum values of \(\dfrac{xy+yz+xz}{x^2+y^2+z^2}\).

If the sum of the maximum and minimum values of the above expression is \(\alpha\), submit your answer as the remainder when \(\huge \alpha^{2014^{2013^{\cdots^{1}}}}\) is divided by 3628800.

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