Chef & Cook Game

There is a non-negative integer array $A$ of length $N$. Chef and Cook will play a game on the array with Chef starting first. In one turn the player will perform the following operation: - Choose two indices $i,j$ such that $1 \leq i \lt j \leq N$ and $A_i > 0$. - Set $A_i \gets A_i - 1$ and $A_j \gets A_j + 1$, i.e, subtract $1$ from $A_i$ and add $1$ to $A_j$. The player who is unable to per