Open and Close Lockers

After the drill, the 2018 military cadets entered the building as follows: the 1st cadet opens all the 2018 lockers. The 2nd cadet closed all the lockers that are multiples of 2. The 3rd cadet "changes" all lockers with multiples of 3 by closing the lockers that are open and opening lockers that are closed. The 4th cadet changes all lockers with multiples of 4, and so on, until the 2018th cadet changed all lockers with multiples of 2018. Assuming that they entered the building in this fashion until the end, let m be the number of closed lockers and n be the number of open lockers. Find the integral part of $\frac{mn}{m-n}$ .