### Problem Statement

A line of symmetry is a line through the cartesian plane such that if you reflect everything from one side of the line to the other, you still have the same image. For example, if the x-axis is a line of symmetry, it means that for every point (x,y) there is also a point (x,-y).

Your task is, given a list of points, determine how many such lines exist.

### Definition

 Class: Symmetry Method: countLines Parameters: String[] Returns: int Method signature: int countLines(String[] points) (be sure your method is public)

### Constraints

-Each element of points will be formatted as a list of x,y pairs "<x1> <y1> <x2> <y2> <x3> <y3> ...", where there is exactly one space between every two terms, and both <xi> and <yi> are integers.
-<xi> and <yi> will both be between -10,000 and 10,000, inclusive.
-Each point will be unique.
-There will be between 2 and 200 points, inclusive.

### Examples

0)

 `{"1 1 1 -1 -1 1 -1 -1"}`
`Returns: 4`
 This looks something like this (where '-' and '|' represent the axes, and '*' represents a point): ``` | | * | * | --------+-------- | * | * | | ``` There are 4 lines of symmetry. Both axes are lines of symmetry, as are the line y = x and y = -x.
1)

 `{"0 0 2 1 0 5 -2 4"}`
`Returns: 2`
2)

 `{"0 100 100 0","0 0 100 100","51 52"}`
`Returns: 0`
3)

 `{"0 0","100 0","50 87"}`
`Returns: 1`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=924

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4355&pm=924

lars2520

Geometry