### Problem Statement

NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.

Taro and Hanako are playing Bunny Puzzle. There are several bunnies standing on a line. You are given a int[] bunnies, where each element is the initial position of a single bunny.

They must perform the following routine exactly once:
1. Choose two different bunnies A and B, located at points a and b, respectively.
2. A jumps over B and lands at point 2*b-a.

The jump is not allowed if another bunny is already at point 2*b-a.

The jump is also not allowed if A jumps over more than one bunny.

Return the number of different ways in which Taro and Hanako can choose the pair of bunnies A and B. "A jumps over B" and "B jumps over A" are considered to be different.

### Definition

 Class: BunnyPuzzle Method: theCount Parameters: int[] Returns: int Method signature: int theCount(int[] bunnies) (be sure your method is public)

### Constraints

-bunnies will contain between 2 and 50 elements, inclusive.
-Each element of bunnies will be between -10^6 and 10^6, inclusive.
-bunnies will be sorted in strictly ascending order.

### Examples

0)

 `{5, 8}`
`Returns: 2`
 There are two possible moves: A bunny jumps from 5 to 11 A bunny jumps from 8 to 2
1)

 `{-1, 0, 1}`
`Returns: 2`
 There are two possible moves: A bunny jumps from 0 to -2 A bunny jumps from 0 to 2
2)

 `{0, 1, 3}`
`Returns: 3`
 There are three possible moves: A bunny jumps from 0 to 2 A bunny jumps from 1 to -1 A bunny jumps from 1 to 5
3)

 `{-677, -45, -2, 3, 8, 29, 384, 867}`
`Returns: 7`
4)

 `{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}`
`Returns: 2`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10740

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14148&pm=10740

rng_58

#### Testers:

PabloGilberto , misof , ivan_metelsky

#### Problem categories:

Simple Search, Iteration