Sequence Creation

Chef has two sequences of integers $(A_1, A_2, \ldots, A_N)$ and $(B_1, B_2, \ldots, B_N)$. A sequence of integers is *beautiful* if it contains only distinct integers. For each valid $i$: - Chef wants to create a beautiful sequence $S_i$. Let's denote the length of this sequence by $L_i$ and the sequence by $S_{i,1}, S_{i,2}, \ldots, S_{i,L_i}$. - The sequence $S_i$ is *good* if for each valid $