Hyperbox | Topcoder Archive

Problem Statement

The boundary of a two-dimensional rectangle is one-dimensional (a collection of line segments), and we can measure its length.
The boundary of a three-dimensional box is two-dimensional (a collection of rectangles), and we can measure its area.
In the same sense, the boundary of a four-dimensional hyperbox is three-dimensional, and we can measure its volume.

You are given the int volume (in cubic meters). Return the number of distinct hyperboxes with positive integer sides (in meters) and this exact surface volume.

Two hyperboxes are distinct if they are not congruent. (In other words, they are distinct if we cannot rearrange the dimensions of one to get the dimensions of the other.)

Definition

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

Constraints

volume will be between 1 and 200,000,000, inclusive.

Examples

```
8
```
```
Returns: 1
```
The smallest possible hyperbox (i.e., the 1 x 1 x 1 x 1 hyperbox) is the only one with surface volume 8.
```
1234567
```
```
Returns: 0
```
There are no hyperboxes with integer sides and this exact surface volume.
```
120
```
```
Returns: 3
```
One of the three distinct hyperboxes with this surface volume has side lengths 1, 2, 2, and 7.
```
123456
```
```
Returns: 52
```

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