Strange Equality Condition

Algebra Level 4

Let x,y,x, y, and zz be real numbers satisfying xy+z+yz+x+zx+y=1.\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}=1.

Find the maximum value of x2y+z+y2z+x+z2x+y.\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}.

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