Given a vector $\overrightarrow{u} = \frac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$, the value of integral $\int (\nabla \times \overrightarrow{u}) \bullet \hat{n} \: dS$ evaluated on the curved surface of the hemishepre $S$ is
1. $- \frac{\pi}{2}$
2. $\frac{\pi}{3}$
3. $\frac{\pi}{2}$
4. $\pi$