Exit Door

There are $N$ people sitting in a single row inside a movie theatre. Each person has a unique number from $1$ to $N$, representing their *priority* or *importance*. You are given a **permutation** $P_1, P_2, \ldots, P_N$ where $P_i$ is the number of the person sitting in the $i^{th}$ seat (from left to right). After the movie ends, people start leaving the hall **one by one** — in order of **