Prefix Suffix Distinct

For an array $A$ of $N$ integers, define * An array $P$ of length $N$, where $P_i$ is the number of distinct elements in the subarray $A[1:i]$ of $A$. * An array $S$ of length $N$, where $S_i$ is the number of distinct elements in the subarray $A[i:N]$ of $A$. You are given arrays $P$ and $S$. Determine whether there exists an array $A$ corresponding to the given $P$ and $S$ arrays. ### Inp