How many lockers are open?

In a strange little town there is a school with 1000 students. Each student has a locker. The first student enters the locker room and opens all the lockers. The second closes all the even numbered lockers 2, 4, 6,...etc. The third student reverses the locker position (open locked doors and close opened doors) of locksers 3, 6, 9...etc. Similarly fourth student reverses the locker position of 4, 8, 12..etc. All the 1000 students follow the same procedure. The question is, after the 1000th student how many doors are still open?