A11433. Symmetric Projections
编程题
普及/提高-
知识点
题目描述
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 $P$ .
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 $P$ .
输入格式
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 $x_{i}$ and $y_{i}$ ( $-10^{6}<=x_{i},y_{i}<=10^{6}$ ) — the coordinates of the points. It is guaranteed that no two points coincide.
Each of the next $n$ lines contains two integers $x_{i}$ and $y_{i}$ ( $-10^{6}<=x_{i},y_{i}<=10^{6}$ ) — the coordinates of the points. It is guaranteed that no two points coincide.
输出格式
If there are infinitely many good lines, print -1.
Otherwise, print single integer — the number of good lines.
Otherwise, print single integer — the number of good lines.
输入输出样例
输入 #1
3 1 2 2 1 3 3
输出 #1
3
输入 #2
2 4 3 1 2
输出 #2
-1
说明/提示
Picture to the first sample test:
In the second sample, any line containing the origin is good.
In the second sample, any line containing the origin is good.