Yet Another Array Game

Alice and Bob play a game on a array $A$ of size $N$. Alice moves first and their turns alternate. Alice also has with her another array $B$, initially empty. On Alice's turn, she chooses any element that remains in $A$, deletes it from $A$, and **appends** it to $B$. On Bob's turn, he chooses any element that remains in $A$ and deletes it. This proceeds till $A$ is empty. Alice *must* ens