Nine, (15 points) satisfying the following two conditions:
(1) For all natural numbers $x, x^{2}-2001 x+n$ $\geqslant 0$
(2) There exists a natural number $x_{0}$, such that $x_{0}^{2}-2002 x_{0}+n$ $<0$ the number of positive integers $n$ equals $\qquad$
$Nine, 1001$