Let $C$ be the positively oriented boundary of the domain bounded by the curves $y=2 x^{2}$ and $y^{2}=4 x$. Then the value of the line integral
$$\oint_{C}\left(2 y^{2}+2 x y+4 y\right) d x+\left(x^{2}+4 x y+8 x\right) d y $$ is equal to
- $\frac{8}{3}$
- $\frac{2}{3}$
- $\frac{4}{3}$
- $\frac{1}{3}$
