;This is the toh program that uses n pegs to transfer disks from given src to dest

(defun toh_n_pegs (src dest aux taken_aux n n_aux n_pegs)

    ; if number of disks is 1, move the disk from src to dest peg
    (cond ((= n 1) 
	   (print_func src dest)
            
          )
	  ;if the number of aux pegs available is 1, call the 3 pegs toh program
          ((= n_aux 1)
	       (cond ((listp aux)
	      	        (toh src dest (car aux) n)
		     )
		     (t (toh src dest aux n) 
		     )
	       )
	   )
	   (t 
		;if the number of pegs is more than 1, recurse again until number of disks is 1 or number of aux pegs available is 1
		(setq loop_cnt n_aux)
		(cond ((< n n_aux) (setq loop_cnt n) (setq n_aux n) 
			  (setq aux (del_aux aux))
                      )
		)
		 	  
		     (dotimes (cnt (- n_aux 1) 0)

	                 (cond ((listp aux) 
		                   (setq temp_aux (create_aux_list src (car aux) taken_aux n_pegs))
                                )
		                (t (setq temp_aux (create_aux_list src aux taken_aux n_pegs))
                                )
                         )

	                 (if (not (listp aux))
		             (setq aux (cons aux ()))
                         )
			 
			 (cond ((= cnt 0)

				   (toh_n_pegs src (car aux) temp_aux taken_aux (+ (truncate (/ n n_aux)) (mod n n_aux)) (length temp_aux) n_pegs)
			       )
			       (t   (toh_n_pegs src (car aux) temp_aux taken_aux (truncate (/ n n_aux)) (length temp_aux) n_pegs)
			       ) 
			 )
			 (setq taken_aux (cons (car aux) taken_aux))
			 
			
			 (setq aux (cdr aux))

		      )

		      (setq temp_aux (create_aux_list src dest taken_aux n_pegs))
                               

	              (if (not (listp aux))
		          (setq aux (cons aux ()))
                      )

                      (toh_n_pegs src dest temp_aux taken_aux (truncate (/ n n_aux)) (length temp_aux) n_pegs)
			

	              (setq aux taken_aux)
                      (setq new_aux nil)
		      (setq new_aux (create_aux_list (car aux) dest taken_aux n_pegs))
                      		
     		      (dotimes (cnt (- n_aux 2) 0)
	                   (toh_n_pegs (car aux) dest new_aux taken_aux (truncate (/ n n_aux)) (length new_aux) n_pegs)
                           (setq taken_aux (update_taken_list (car aux) dest taken_aux))
			   (setq new_aux (cons (car aux) new_aux))
		           (setq aux (cdr aux))
		      )
		      (toh_n_pegs (car aux) dest new_aux taken_aux (+ (truncate (/ n n_aux)) (mod n n_aux)) (length new_aux) n_pegs)
		      (setq taken_aux (update_taken_list (car aux) dest taken_aux))
		      (setq new_aux (cons (car aux) new_aux))
		      (setq aux (cdr aux))
             )

        )		
    
		
)