A composition of polynomials

Suppose ff and gg are polynomials with integer coefficients such that f(0)=0,f(0)=0, ff has degree at least two, and f(g(x))=f(x)+(x6+3x56x3+6x2).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)f(10).

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