Define a regular n-pointed star to be the union of n line segments \overline{P_{1} P_{2}}, \overline{P_{2} P_{3}}, \ldots, \overline{P_{n} P_{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 \overline{P_{1} P_{2}}, \overline{P_{2} P_{3}}, \ldots, \overline{P_{n} P_{1}} are congruent, and
- the path P_{1} P_{2} \ldots P_{n} P_{1} turns counterclockwise at an angle of less than 180^{\circ} 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?