numbers

There are 50 doors in a tower and there are 50 tourists; the first one opens all 50 doors of the tower; next the second one closes the doors 2,4,6,8,10 and so on to door 50; the third one changes the state(opens the door closed, closes the door opened) on door 3,6,9,12,15 and so on; the fourth one changes the state of doors 4,8,12,16 and so on. This goes on until every tourist had their turn. how many doors were touched exactly twice??

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