Symmetric Projections

2000ms

262144K

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.

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 ( - 10⁶ ≤ x_i, y_i ≤ 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.

Sample Input:

Sample Output:

Sample Input:

2
4 3
1 2

Sample Output:

-1

Note:

Picture to the first sample test:

$\text{[math]}$

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

Informação

Provedor Codeforces

Código CF886F