Minimum Set

You are given an integer $N$. Let us call a set of pairs of integers $S = \{(A_1, B_1), (A_2, B_2), (A_3, B_3), \ldots, (A_K, B_K)\}$ good if it satisfies the following conditions: - $1 \le A_i < B_i \le N$ - For every permutation $P$ of the integers $[1, N]$, it is possible to sort $P$ with the usage of the following operation as many times as you want: - Choose $(x, y) \in S$, and then