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$\bullet$ the points $p 1, p 2,\ldots, p n$ are coplanar and no three of them are collinear,$\bullet$ each of the $n$ line segments intersects at least one of the other line segments at a point other than an endpoint,$\bullet$ all of the angles at $p 1, p 2,\ldots, p n$ are congruent,$\bullet$ all of the $n$ line segments $p 2p 3,\ldots, p np 1$ are congruent, and$\bullet$ 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?