Let $$[t]$$ denote the largest integer less than or equal to $$t$$. If $$\int_0^3 \left([x^2] + \left[\frac{x^2}{2}\right]\right) dx = a + b\sqrt{2} - \sqrt{3} - \sqrt{5} + c\sqrt{6} - \sqrt{7}$$, where $$a, b, c \in \mathbb{Z}$$, then $$a + b + c$$ is equal to ___________