Min-Max Game

Given a permutation$^\dagger$ $P$ of the integers $1$ to $N$, Alice and Bob will play a game on it as follows. - On Alice's turn, she will choose a contiguous subarray of $P$ of length **strictly greater** than $1$, and delete the **maximum** element from it. - On Bob's turn, he will choose a contiguous subarray of $P$ of length **strictly greater** than $1$, and delete the **minimum** element fro