Your stumble upon a long hallway in the Library of Babel which has 1000 doors, numbered 1 through 1000. Originally, all of the doors are closed. On the first day, you open every door. On the second day, you close every door whose number is even. On the third day, for every door whose number is a multiple of three, you close it if it was open and open it if it was closed. This continues: on the n-th day, you only visit doors whose number are multiples of n, and close them if they are open, or open them if they are closed. After 1000 days, which doors are open?