(de perfectShuffle (Lst)
   (mapcan '((B A) (list A B))
      (cdr (nth Lst (/ (length Lst) 2)))
      Lst ) )

(for N (8 24 52 100 1020 1024 10000)
   (let (Lst (range 1 N)  L Lst  Cnt 1)
      (until (= Lst (setq L (perfectShuffle L)))
         (inc 'Cnt) )
      (tab (5 6) N Cnt) ) )