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Algebra Level 5

\[f(x,y,z,v,w)=xz+2yz+3zv+7zw\]

Let \(M\) be the maximal value of \(f\) if \(x^2+y^2+z^2+v^2+w^2=2016\) and all variables are positive. If \(M=f(x_0,y_0,z_0,v_0,w_0)\), find \(w_0\).

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