Gauss's Law of Magnetism

Consider a sphere of radius $1$ centered on the origin. Quadrant $1$ of the sphere has positive $x$ and positive $z$ . Quadrant $2$ of the sphere has negative $x$ and positive $z$ . Quadrant $3$ of the sphere has negative $x$ and negative $z$ . Quadrant $4$ of the sphere has positive $x$ and negative $z$ .

There is an infinitely long wire directed into the page along the line $(x = 2, y = y, z = 0)$ , which carries $100$ units of electric current. Recall the formula for magnetic flux through a surface.

$\phi = \int \int_S \vec{B} \cdot \vec{dS}$

Let $(\phi_1, \phi_2, \phi_3, \phi_4)$ be the magnetic fluxes through the four respective quadrants. Determine the following sum:

$\phi_1 + \phi_2 + \phi_3 + \phi_4 + |\phi_1 | + |\phi_2| + |\phi_3| + |\phi_4|$

Details and Assumptions:
1) Magnetic permeability $\mu_0 = 1$
2) Be mindful of the signs of the fluxes (positive and negative)