In the following p- V diagram the equation of state along the curved path is given by $$(V-2)^{2}=4ap$$ where a is a constant. The total work done in the closed path is

A

$$-\frac{1}{a}$$

B

$$-\frac{1}{3a}$$

C

$$\frac{1}{2a}$$

D

$$+\frac{1}{3a}$$