CF886F Symmetric Projections

You are given a set of $ n $ points on the plane. A line containing the origin is called good, if projection of the given set to this line forms a symmetric multiset of points. Find the total number of good lines. Multiset is a set where equal elements are allowed. Multiset is called symmetric, if there is a point $ P $ on the plane such that the multiset is [centrally symmetric](https://en.wikipedia.org/wiki/Point_reflection) in respect of point $ P $ .

The first line contains a single integer $ n $ ( $ 1

If there are infinitely many good lines, print -1. Otherwise, print single integer — the number of good lines.

Picture to the first sample test:  In the second sample, any line containing the origin is good.