A polygon $A_1A_2A_3\dots A_n$ is called $NeXgon$ if there exist indices $i$, $j$, and $k$ such that $\measuredangle A_iA_jA_k = 144^\circ$ . Compute the number of integers $3 \le n \le 2024$ for which a regular $n$-gon is a $NeXgon$ .