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Maximizing a cyclic polynomial.

Suppose a,a, b,b, and cc are non-negative real numbers with a+b+c=1.a+b+c=1. The largest possible value of the expression ab2+bc2+ca2ab^2+bc^2+ca^2 can be written as nm,\frac{n}{m}, where nn and mm are coprime positive integers. What is the value of n+mn+m?

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