# Hey, kid, wanna buy a Math problem?

Algebra Level 3

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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