Remove the Peaks

For an array $A$, an element $A_i$ $(1 \lt i \lt |A|)$ is said to be a *peak* if $A_i \gt A_{i-1}$ and $A_i \gt A_{i+1}$. Note that the first and last elements are never peaks. You are given a permutation $P$ of length $N$, and an empty set $S$. In one operation, you can do the following: - Remove an element $P_i$ such that $P_i$ is a *peak*, and insert it into the set $S$. Note that subsequen