The area (in sq. units) of the region $$S = \{z \in \mathbb{C} : |z - 1| \leq 2; (z + \bar{z}) + i(z - \bar{z}) \leq 2, \text{Im}(z) \geq 0\}$$ is

A

$$\frac{7\pi}{3}$$

B

$$\frac{7\pi}{4}$$

C

$$\frac{17\pi}{8}$$

D

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