Longest MEX Sequence

For an array $B$ of length $M$, we define $\text{score}(B)$ to be the largest integer $K$ such that $B$ can be **partitioned** into $K$ non-empty subsets that all have distinct MEX-es. Formally, this is the largest integer $K$ such that there exists a sequence of sets $S_1, S_2, \ldots, S_K$ satisfying the following conditions: - Each $S_i$ is non-empty, and contains only integers in the range