Define a regular $n$-pointed star to be a union of $n$ lines segments $P_1P_2, P_2P_3, ..., P_nP_1$ such that $\bullet$ the points $P_1,P_2,...,P_n$ 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 $P_1, P_2,..., P_n$ are congruent , $\bullet$ all of the $n$ line segments $P_1P_2, P_2P_3, ..., P_nP_1$ are congruent, and $\bullet$ the path $P_1P_2...P_nP_1$ turns counterclockwise at an angle less than $180^o$ at each vertex. There are no regular $3$-pointed, $4$-pointed, or $6$-pointed stars. All regular $5$-pointed star are similar, but there are two non-similar regular $7$-pointed stars. Find all possible values of $n$ such that there are exactly $29$ non-similar regular $n$-pointed stars.