A new school is being opened. The school has exactly 1000 lockers and 1000 students. On the first day of school, the students meet outside the building and agree on the following plan: The first student will enter the school and open all of the lockers. The second student will enter and close every locker with an even number. The third student will then "reverse" every third locker; that is, if the locker is closed, he will open it; if its open,he will close it. The fourth student will then "reverse" every fourth locker; and so on until all 1000 students in turn have entered the building and "reversed" the proper lockers. Which lockers will finally remain open?