F. Symmetric Projectionstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 in respect of point P.InputThe first line contains a single integer n (1 ≤ n ≤ 2000) — the number of points in the set.Each of the next n lines contains two integers xi and yi ( - 106  ≤  xi,  yi  ≤  106) — the coordinates of the points. It is guaranteed that no two points coincide.OutputIf there are infinitely many good lines, print -1.Otherwise, print single integer — the number of good lines.ExamplesInput31 22 13 3Output3Input24 31 2Output-1NotePicture to the first sample test: In the second sample, any line containing the origin is good.
Input31 22 13 3
Output3
['geometry', '*2900']