Parity Fun

Chef has $N$ numbers written on his board. He wants only one number to remain on the board and so he devises a special tactic to do so. He randomly picks up $2$ numbers written on the board say $A$ and $B$ respectively. He erases both of them from the board and writes a new number on the board which equals - - $A - B$ if parity of $A$ $=$ parity of $B$ - $A + B$ if parity of $A$ $\neq$ parity