Door make's you forget things

Number Theory Level pending

In a row there are 100 rooms whose door number is 1,2,3....,100 . Initially all doors are closed a person takes 'n' round of the row numbered as 1st , 2nd.... 'n' round . In each round he interchanged the positions of the door no. whose number is multiple of the round no. . Find out after 99th round how many doors will be opened.

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