1000 Doors

In a room there is $1000$ doors and each door is numbered $1$ to $1000$ . Initially all the doors are closed. In a group of 1000 people each one of them is also numbered $1$ to $1000$ . Person with numbered 1 goes inside the room and opened all the doors, person with numbered 2 then goes next and closed all the doors which are multiple of two. In general, $r^{th}$ person changes the state of those doors having multiple of r. All the $1000$ person does the same. After this practice how many doors will be remain opened $?$

NOTE : A person doesn't touch other doors which are not multiple of his number