(define (hanoi discs)
  (define (helper d direction currentState moveCount smallPosition solution)
    (display currentState) (newline)
    (cond
      [(>= moveCount (sub1 (expt 2 d))) (reverse solution)]
      [(= (modulo moveCount 2) 0)
       (helper d direction
               (list-update
                (list-update currentState smallPosition cdr)
                (modulo (+ smallPosition direction) 3)
                (λ (x) (cons d x)))
               (add1 moveCount)
               (modulo (+ smallPosition direction) 3)
               (cons (list smallPosition (modulo (+ smallPosition direction) 3)) solution))]
      [(> (car (list-ref currentState (car (remove smallPosition (list 0 1 2)))))
          (car (list-ref currentState (cadr (remove smallPosition (list 0 1 2))))))
       (helper d direction
               (list-update
                (list-update currentState (car (remove smallPosition (list 0 1 2))) cdr)
                (cadr (remove smallPosition (list 0 1 2)))
                (λ (x) (cons (car (list-ref currentState (car (remove smallPosition (list 0 1 2))))) x)))
               (add1 moveCount)
               smallPosition
               (cons (list (car (remove smallPosition (list 0 1 2))) (cadr (remove smallPosition (list 0 1 2)))) solution))]
      [else (helper d direction
                    (list-update
                     (list-update currentState (cadr (remove smallPosition (list 0 1 2))) cdr)
                     (car (remove smallPosition (list 0 1 2)))
                     (λ (x) (cons (car (list-ref currentState (cadr (remove smallPosition (list 0 1 2))))) x)))
                    (add1 moveCount)
                    smallPosition
                    (cons (list (cadr (remove smallPosition (list 0 1 2))) (car (remove smallPosition (list 0 1 2)))) solution))]))
  (if (= (modulo discs 2) 0)
      (helper discs 1 (list (reverse (build-list (add1 discs) values)) (list 0) (list 0)) 0 0 empty)
      (helper discs -1 (list (reverse (build-list (add1 discs) values)) (list 0) (list 0)) 0 0 empty)))