Sereja and Game

Sereja and Dima play the game. The rules are as follows: Initially, there are n cards on the table, each card has a positive integer written on it. At the beginning Sereja writes down the number 0 on the sheet of paper. Then players pick cards from the table alternately. When a player picks a card, he writes down the greatest common divisor of a number that is written on a card and a number that