\[\large a^2 bc + b^2 cd \]

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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