Pls help hard polynomials question

Let \(r_1, r_2, \dots r_7\) be the roots of \(f(x) = x^7 + 5x^5 - 4x^4 + 5x^3 - 9x^2 + x + a,\) where \(a\) is some real constant.

Let \(g(x) = x^3 + 3x - 3.\) Then the product \(g(r_1) g(r_2) \dotsm g(r_7)\) can be expressed as a polynomial in \(a.\) Find this polynomial.

Any help or ideas appreciated!!!

(Reposting because the prior answer was wrong.)