Electrostatics: JEE Main 2024 Physics question

An infinite plane sheet of charge having uniform surface charge density $+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$ is placed on $x$-$y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}: 1$. The value of $n$ is _________.