CMIMC 2021 Team Problem 6

Let P(x), Q(x), and R(x) be three monic quadratic polynomials with only real roots, satisfying

\begin{aligned} & P(Q(x))=(x-1)(x-3)(x-5)(x-7) \\ & Q(R(x))=(x-2)(x-4)(x-6)(x-8) \end{aligned}

for all real numbers x. What is P(0)+Q(0)+R(0)?