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Let x,y,x, y,x,y, and zzz be real numbers satisfying xy+z+yz+x+zx+y=1.\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}=1.y+zx+z+xy+x+yz=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}.y+zx2+z+xy2+x+yz2.
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