Area of the region $\left\{(x, y): x^{2}+(y-2)^{2} \leq 4, x^{2} \geq 2 y\right\}$ is

Question

$2 \pi+\frac{16}{3}$

$\pi-\frac{8}{3}$

$\pi+\frac{8}{3}$

$2 \pi-\frac{16}{3}$

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