# Inspired by incomplete Muirhead

Algebra Level 5

$\large a^2 bc + b^2 cd$

Given that $$a,b,c$$ and $$d$$ are positive reals satisfying $$a+b+c+d=5$$. If the maximum value of the expression above can be expressed as $$\dfrac x{y^z}$$, where $$x,y$$ and $$z$$ are positive integers with $$y$$ prime, submit your answer as $$x+y+z$$.

If you get that no such maximum exists, enter $$490023$$ as your answer.

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