Locker Check

There is a school with 1000 students and 1000 lockers numbered 1 to 1000. The first student goes through and opens all the lockers. The second student goes through and closes the even lockers. The third student switches the lockers divisible by 3 (3, 6, 9, 12...). The fourth student switches the lockers divisible by 4 (4, 8, 12, 16...). This continues for all 1000 students. How many lockers are left open in the end?