### Problem Statement

Given a list of points return how many unique isoceles right triangles use 3 of those points as corners. An isoceles right triangle has 2 sides of equal length and a single right angle (90 degrees). Two isoceles triangles are unique if they differ by at least one point.

### Definition

 Class: Isoceles Method: howMany Parameters: int[], int[] Returns: int Method signature: int howMany(int[] xs, int[] ys) (be sure your method is public)

### Notes

-xs[K] is the x-coordinate of the Kth point and ys[K] is the y-coordinate of the Kth point

### Constraints

-xs will contain between 3 and 50 elements inclusive
-ys will contain between 3 and 50 elements inclusive
-xs and ys will contain the same number of elements
-Each element of xs will be between -1000000 and 1000000 inclusive
-Each element of ys will be between -1000000 and 1000000 inclusive
-There will be no duplicate points

### Examples

0)

 `{0,1,2}` `{0,10,0}`
`Returns: 0`
1)

 `{0,0,5,5}` `{0,5,0,5}`
`Returns: 4`
 There are four right isoceles triangles in a square.
2)

 `{-1000000,1000000,0}` `{0,0,1000000}`
`Returns: 1`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1169

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4371&pm=1169

brett1479

#### Testers:

alexcchan , lbackstrom

#### Problem categories:

Brute Force, Geometry