Topswops is a card game created by John Conway in the 1970's.



Assume you have a particular permutation of a set of   n   cards numbered   1..n   on both of their faces, for example the arrangement of four cards given by   [2, 4, 1, 3]   where the leftmost card is on top.

A round is composed of reversing the first   m   cards where   m   is the value of the topmost card.

Rounds are repeated until the topmost card is the number   1   and the number of swaps is recorded.



For our example the swaps produce:

    
    [2, 4, 1, 3]    # Initial shuffle
    [4, 2, 1, 3]
    [3, 1, 2, 4]
    [2, 1, 3, 4]
    [1, 2, 3, 4]

For a total of four swaps from the initial ordering to produce the terminating case where   1   is on top.



For a particular number    n    of cards,    topswops(n)    is the maximum swaps needed for any starting permutation of the   n   cards.



Task

The task is to generate and show here a table of    n    vs    topswops(n)    for    n    in the range   1..10   inclusive.



Note

Topswops   is also known as   Fannkuch   from the German word   Pfannkuchen   meaning   pancake.



Related tasks

   Number reversal game
   Sorting algorithms/Pancake sort


(de fannkuch (N)
   (let (Lst (range 1 N)  L Lst  Max)
      (recur (L)  # Permute
         (if (cdr L)
            (do (length L)
               (recurse (cdr L))
               (rot L) )
            (zero N)  # For each permutation
            (for (P (copy Lst)  (> (car P) 1)  (flip P (car P)))
               (inc 'N) )
            (setq Max (max N Max)) ) )
      Max ) )
 
(for I 10
   (println I (fannkuch I)) )