#P886F. Symmetric Projections
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ID: 4069
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Symmetric Projections
No submission language available for this problem.
Description
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 in respect of point P.
The 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.
If there are infinitely many good lines, print -1.
Otherwise, print single integer — the number of good lines.
Input
The 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.
Output
If there are infinitely many good lines, print -1.
Otherwise, print single integer — the number of good lines.
Samples
3
1 2
2 1
3 3
3
2
4 3
1 2
-1
Note
Picture to the first sample test:
In the second sample, any line containing the origin is good.