Coreputer

Coreputer, the brand new computing machine has $N$ cores numbered from $0$ to $N - 1$. Recent maintenance revealed that some of the cores are malfunctioning. It is unknown which specific cores are malfunctioning, but there is at least one malfunctioning core.

To find the malfunctioning cores, Coreputer can run diagnostic scans. In each scan, the user tags a (possibly empty) group of distinct cores $T[0],\dots ,T[l - 1]$ for some $0 ≤ l ≤ N$. The rest of the cores are untagged. Coreputer then benchmarks the tagged cores and the untagged ones. Finally, it reports which of the two groups contains a greater number of malfunctioning cores, or that the two groups contain an equal number of malfunctioning cores. Note that an empty group contains 0 malfunctioning cores.

Your task is to find the malfunctioning cores by running diagnostic scans on Coreputer.

• $2 ≤ N ≤ 16$