Let the domain of the function $ f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2) $ be (a, b). If $ \int_0^{a+b} [x^2] dx = p - q\sqrt{r} $, $ p, q, r \in \mathbb{N} $, gcd(p, q, r) = 1, where [.] is the greatest integer function, then p + q + r is equal to