Count Distinct Arrays

You are given a permutation $P$ of length $N$. For each prefix length $1 \leq i \leq N$: - Consider the prefix subarray $A = [P_1, P_2, \ldots, P_i]$. - Perform the following operation on $A$ any (possibly zero) number of times: - Select three **distinct** indices $j, k,$ and $l$ such that: - $1 \leq j < k < l \leq |A|$ - $A_j > A_k < A_l$ - Delete $A_k$ from $A$, and concatenat