Split or Decrease

Chef and Chefina are playing a game. **Chef plays first**. There are $N$ piles where the $i^{th}$ pile contains $A_i$ stones. In his/her turn, a player can do **one** of the following: - Take any non-empty pile and remove $1$ stone from it. - Take any pile containing atleast $2$ stones and split it into two piles containing $X$ and $Y$ stones such that $X+Y$ equals the initial number of stones