Gauss's Law - Closed Half Cylinder

A particle with charge $q = +10$ is at position $(x,y,z) = \Big(\frac{1}{2},\frac{1}{3},\frac{2}{3} \Big)$ . A closed surface consists of four sub-surfaces put together.

The first sub-surface is a half-disk in the plane $z = 0$ :

$x^2 + y^2 \leq 1 \\ x \geq 0 \\ z = 0$

The second sub-surface is a half-disk in the plane $z = 1$ :

$x^2 + y^2 \leq 1 \\ x \geq 0 \\ z = 1$

The third sub-surface is a half cylinder:

$x^2 + y^2 = 1 \\ x \geq 0 \\ 0 \leq z \leq 1$

The fourth sub-surface is a rectangle:

$x = 0 \\ -1 \leq y \leq 1\\ 0 \leq z \leq 1$

Let the electric fluxes through the four sub-surfaces be $\phi_1,\phi_2,\phi_3,\phi_4$ . Determine the following ratio:

$\frac{\phi_1 \, \phi_2 \, \phi_3 \, \phi_4}{ \phi_1 + \phi_2 + \phi_3 + \phi_4}$

Details and Assumptions:
1) Electric permittivity $\epsilon_0 = 1$
2) Use outward-facing normal vectors