(define (lis less? lst)
  (define pile-tops (make-vector (length lst)))
  (define (bsearch-piles x len)
    (let aux ((lo 0)
	      (hi (- len 1)))
      (if (> lo hi)
	  lo
	  (let ((mid (quotient (+ lo hi) 2)))
	    (if (less? (car (vector-ref pile-tops mid)) x)
		(aux (+ mid 1) hi)
		(aux lo (- mid 1)))))))
  (let aux ((len 0)
	    (lst lst))
    (if (null? lst)
	(reverse (vector-ref pile-tops (- len 1)))
	(let* ((x (car lst))
	       (i (bsearch-piles x len)))
	  (vector-set! pile-tops i (cons x (if (= i 0)
					       '()
					       (vector-ref pile-tops (- i 1)))))
	  (aux (if (= i len) (+ len 1) len) (cdr lst))))))

(display (lis < '(3 2 6 4 5 1))) (newline)
(display (lis < '(0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15))) (newline)