E - Mex and Max

You are given a set $S$, consisting of $n$ **distinct** non-negative integers. In one move, you can perform exactly one of the following two operations: - Insert $\text{mex}(S)$ into $S$. - Delete $\max(S)$ from $S$. This can only be done if $S$ is not empty. Here, $\text{mex}(S)$ denotes the minimum excluded value of $S$, which is the smallest non-negative integer not present in $S$. For ex