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.)