There are 1000 lockers in a high school with 1000 students. The problem begins with the first student opening all 1000 lockers; next the second student closes lockers 2,4,6,8,10 and so on to locker 1000; the third student changes the state (opens lockers which are closed, closes lockers which are open) on lockers 3,6,9,12,15 and so on; the fourth student changes the state of lockers 4,8,12,16 and soon. This goes on until every student has had a turn. A. How many lockers will be open at the end?