Given $n$ integer points $(x_i, y_i)$ on a plane, projecting these $n$ points onto a line $l$ forms a multiset $E_l$ of $n$ points. A line $l$ passing through the origin is called "good" if there exists a point $P$ on the line such that $E_l$ is symmetric with respect to $P$.

A multiset of points on a line is symmetric with respect to $P$ if, after removing any points that coincide with $P$, the remaining points can be paired such that each pair is symmetric with respect to $P$.

Find the number of "good" lines.

Note that there may be infinitely many such lines, in which case you should output $-1$.

Input

The first line contains an integer $n$, representing the number of points.

The next $n$ lines each contain two integers $x_i, y_i$, representing the coordinates of the $i$-th point.

$1 \leq n \leq 2\,000$, $|x_i|, |y_i| \leq 10^6$. The data may contain coincident points.

Output

Output a single integer representing the number of "good" lines. If there are infinitely many, output $-1$.

Examples

Input 1

3
1 3
2 1
3 3

Output 1

3

Input 2

6
88 -27
115 34
-147 -298
-106 -229
-9 -128
212 135

Output 2

5

Input 3

2
6666 -2333
2333 6666

Output 3

-1

Subtasks

For subtask 1 ($10\%$), $n \leq 3$.

For subtask 2 ($20\%$), $n \leq 12$.

For subtask 3 ($20\%$), special property 1 is satisfied.

For subtask 4 ($50\%$), no special properties.

Special property 1: $n \geq 100$, there are at most 10 points outside the $y$-axis, then some distinct points are placed randomly on the positive $y$-axis, and their symmetric points with respect to the origin are placed on the negative $y$-axis.

For $100\%$ of the data, $1 \leq n \leq 2\,000$, $|x_i|, |y_i| \leq 10^6$. The data may contain coincident points.