There are 0000 guests in a hotel with 0000 rooms numbered from 0 to 0000. A guest staying in one room at the hotel leaves the door of the room open, while a guest staying in two rooms changes the state of the door: if it is closed, it opens, if it is open, it closes. A guest staying in three rooms closes the door of the room if it is open, and opens it if it is closed. In this way, each guest goes around the hotel as many times as there are rooms and changes the status of the doors.

When all guests complete the tour, how many open doors will there be?