### Problem Statement

Given an int, N, return the number of ways to represent N as the sum of 4 non-negative perfect cubes. Do not count different permutations of the same 4 cubes more than once. For example, (0,0,0,1) is the same as (1,0,0,0).

### Definition

 Class: CubeSum Method: count Parameters: int Returns: int Method signature: int count(int N) (be sure your method is public)

### Constraints

-N will be between 1 and 100,000,000, inclusive.

### Examples

0)

 `1`
`Returns: 1`
 Keep in mind that 0 is a perfect cube so 1 can be represented as 0+0+0+1
1)

 `4`
`Returns: 1`
 1+1+1+1 = 4
2)

 `2072`
`Returns: 4`
 ```0 + 1 + 7*7*7* + 12*12*12 = 0 + 1 + 343 + 1728 = 2072 0 + 7*7*7 + 9*9*9 + 10*10*10 = 0 + 343 + 729 + 1000 = 2072 2*2*2 + 4*4*4 + 10*10*10 + 10*10*10 = 8 + 64 + 1000 + 1000 = 2072 4*4*4 + 4*4*4 + 6*6*6 + 12*12*12 = 64 + 64 + 216 + 1728 = 2072 ```
3)

 `456`
`Returns: 0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=3083

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5885&pm=3083

lars2520

#### Testers:

PabloGilberto , Yarin , vorthys

Math