Kolpona has the set of numbers $\{1, 2, 3, \dots, 1024\}$. She will repeatedly pick three integers $a, b, c$ from this set such that $a, b, c$ are pairwise co-prime to each other and remove them from the set. If Kolpona performs all the operations optimally, what will be the minimum number of integers left in the set after she is done?