Suppose you're in a hallway lined with **100 closed lockers.**

You begin by opening every locker. Then, you close every second locker (#2, #4, \(\ldots\)). After that, you "toggle" every third locker (open it if it's closed, close it if it's open).

You proceed to "toggle" every \(n\)th locker for \(n=4,5,\ldots,100.\) At the end of this process, how many lockers are open?

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