There are 100 doors in a row that are all initially closed.

You make 100 passes by the doors.

The first time through, visit every door and  toggle  the door  (if the door is closed,  open it;   if it is open,  close it).

The second time, only visit every 2nd door   (door #2, #4, #6, ...),   and toggle it.

The third time, visit every 3rd door   (door #3, #6, #9, ...), etc,   until you only visit the 100th door.



Task

Answer the question:   what state are the doors in after the last pass?   Which are open, which are closed?


Alternate:
As noted in this page's   discussion page,   the only doors that remain open are those whose numbers are perfect squares.

Opening only those doors is an   optimization   that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.




 
$$ MODE TUSCRIPT
DICT doors create
COMPILE
LOOP door=1,100
 LOOP pass=1,100
 SET go=MOD (door,pass)
 DICT doors lookup door,num,cnt,status
   IF (num==0) THEN
     SET status="open"
     DICT doors add  door,num,cnt,status
   ELSE
    IF (go==0) THEN
       IF (status=="closed") THEN
         SET status="open"
       ELSE
         SET status="closed"
       ENDIF
     DICT doors update door,num,cnt,status
     ENDIF
   ENDIF
 ENDLOOP
ENDLOOP
ENDCOMPILE
DICT doors unload door,num,cnt,status
 