Refactoring | Topcoder Archive

Problem Statement

You have been hired to do some refactoring. You are not really sure what that is, but you think it has something to do with factoring a number multiple times.

Recall that a factorization of a positive integer n is a collection of at least two positive integers, each larger than one, whose product is n. Note that the order of the numbers in a factorization is ignored, so 2*12 and 12*2 represent the same factorization of 24. In fact, 24 has precisely 6 valid factorizations: 2*2*2*3, 2*2*6, 2*3*4, 2*12, 3*8, and 4*6.

To prepare for your job, write a program that, given an int n, returns the number of unique factorizations of n.

Definition

Class:: Refactoring
Method:: refactor
Parameters:: int
Returns:: int
Method signature:: int refactor(int n)
(be sure your method is public)

Constraints

n will be between 2 and 2,000,000,000 inclusive.

Examples

```
24
```
```
Returns: 6
```
This is the example from the problem statement.
```
9973
```
```
Returns: 0
```
9973 is a prime number, so there are no valid factorizations of 9973.
```
9240
```
```
Returns: 295
```
```
1916006400
```
```
Returns: 7389115
```
The number of factorizations will never be larger than this.

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