There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:
- Toggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.
- On the i-th trip down the alley, start with door i and visit every i-th door.
Given n doors, return the list of open doors.
Let's say n = 3.
- On your first trip, you start from the first door and toggle every door. Now all three doors are open.
- On your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.
- On your third trip, you start from the third door and toggle every third door. Now only door 1 is open.
Input n = 3
Output y is 1