# A composition of polynomials

Suppose $$f$$ and $$g$$ are polynomials with integer coefficients such that $$f(0)=0,$$ $$f$$ has degree at least two, and $f(g(x))=f(x)+(x^6+3x^5-6x^3+6x^2).$ Find the last three digits of the sum of absolute values of all distinct possible values of $$f(10)$$.

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