You play a game where you and an adversarial opponent take turns writing down positive integers on a chalkboard; the only condition is that, if m and n are written consecutively on the board, \gcd(m, n) must be squarefree. If your objective is to make sure as many integers as possible that are strictly less than 404 end up on the board (and your opponent is trying to minimize this quantity), how many more such integers can you guarantee will eventually be written on the board if you get to move first as opposed to when your opponent gets to move first?