Define a regular $$n$$-pointed star to be the union of $$n$$ line segments $$P_1P_2, P_2P_3,\ldots, P_nP_1$$ such that the points $$P_1, P_2,\ldots, P_n$$ are coplanar and no three of them are collinear, each of the $$n$$ line segments intersects at least one of the other line segments at a point other than an endpoint, all of the angles at $$P_1, P_2,\ldots, P_n$$ are congruent, all of the $$n$$ line segments $$P_2P_3,\ldots, P_nP_1$$ are congruent, and the path $$P_1P_2, P_2P_3,\ldots, P_nP_1$$ turns counterclockwise at an angle of less than 180 degrees at each vertex. There are no regular 3-pointed, 4-pointed, or 6-pointed stars. All regular 5-pointed stars are similar, but there are two non-similar regular 7-pointed stars. How many non-similar regular 1000-pointed stars are there?

(第二十二届AIME1 2004 第8题)