Taking Notes

Turing and Shannon, the two champions of last year's Honor Code, are playing a game with the prize money they won. They start with $N$ piles of 1000 rupee notes. The piles initially have $a_1,a_2,\cdots,a_N$ notes respectively. At each move, a player can choose a pile, remove as many notes as he wishes or remove no notes from the pile, and he has to split the remaining pile into two new piles