Game on Array

Alice and Bob play a game with $N$ piles of stones where the $i^{th}$ pile has $A_i$ stones initially. They take alternate turns starting with Alice. On Alice's turn, she will: - Choose indices $i$ and $j \ (1 \le i, j \le N)$ where $i$ and $j$ have the **same** [parity](https://en.wikipedia.org/wiki/Parity_(mathematics)). - Remove $1$ stone each from piles $i$ and $j$. - Note that both pil