Valentine Vex

Alice and Bob play a game on an array of $N$ integers. They alternate moves, with Alice making the first move. The rules are as follows: 1. On **their first move**, a player can pick **any** element in the array, add its value to their score, and then **remove** it from the array. 2. On a move that is **not their first move**, the player should pick an element with the **opposite [parity](https:/