Better call Saul!

_"Don't Drink and Drive, but when you do, Better Call Saul."_ Once Jesse and Walter were fighting over extra cash, and Saul decided to settle it with a game of stone piles whose winner gets the extra money. The game is described as follows : There are $N$ piles of stones with $A$$1$$,$ $A$$2$$,$ $...$ $A$$N$ stones in each pile. Jesse and Walter move alternately, and **in one move, they remove