Evaluate the line integral $\oint_C \mathbf{F} \cdot d\mathbf{r}$ for $\mathbf{F} = \langle -y^3, x^3, z^3 \rangle$ where $C$ is the intersection curve of the cylinder $x^2 + y^2 = 1$ and the saddle surface $z = xy$, oriented counterclockwise when viewed from above.