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 $*P*$.

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 $*x*_{*i*}$ and $*y*_{*i*}$ ($- 10^{6}  ≤  *x*_{*i*},  *y*_{*i*}  ≤  10^{6}$) — the coordinates of the points. It is guaranteed that no two points coincide.

Output

If there are infinitely many good lines, print -1.

Otherwise, print single integer — the number of good lines.

Note

Picture to the first sample test:

In the second sample, any line containing the origin is good.