Permutation Filling

The score of a permutation $P$ of integers $[1, N]$ is defined as follows: $$\sum_{L = 1}^{N} \sum_{R = L}^{N} \text{MEX}(P[L, R])$$ where $P[L, R]$ denotes the subarray $[P_L, P_{L + 1}, P_{L + 2}, \ldots, P_R]$ and $\text{MEX}(A)$ represents the minimal non-negative integer not present in $A$. --- You are given a partially filled permutation $Q$, i.e. $Q$ is formed by replacing some (possibl