Electric Flux & Gauss's Law question from JEE Main 2025 (8 Apr, Shift 2)

An infinitely long wire has uniform linear charge density $\lambda = 2$ nC/m. The net flux through a Gaussian cube of side length $\sqrt{3}$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x$ Nm${}^{2}\text{C}^{-1}$, where $x$ is:

[Neglect any edge effects and use $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI units]