NumericalPerfectionLevel | Topcoder Archive

Problem Statement

It is a well known fact that of all numbers, the number 4 is the most relevant. Patterns related to the number 4 tend to appear everywhere. For example, the numerical perfection level is closely related to the number 4.

We define the perfection level of a positive integer N as k if N can be expressed as a product of 4 positive integers, each with a perfection level of at least (k-1), and cannot be expressed as a product of 4 positive integers, each with a perfection level greater than (k-1). There is one exception - if it is not possible to express N as a product of 4 positive integers all greater than 1, then the perfection level of N is 0.

Given a long N, return its perfection level.

Definition

Class:: NumericalPerfectionLevel
Method:: getLevel
Parameters:: long
Returns:: int
Method signature:: int getLevel(long N)
(be sure your method is public)

Constraints

N will be between 1 and 10000000000000 (10^13), inclusive.

Examples

```
4
```
```
Returns: 0
```
4 cannot be expressed as a product of 4 numbers all greater than 1.
```
144
```
```
Returns: 1
```
144 = 4 x 2 x 3 x 6 The level of 4, 2, 3 and 6 is 0.
```
1152
```
```
Returns: 1
```
One of many possible ways to express 1152 is: 1152 = 144 x 2 x 2 x 2 Although 144's level is 1, the remaining factors are of level 0. There is no way to express 1152 as a product of four level 1 numbers.
```
1679616
```
```
Returns: 2
```
1679616 = 36 x 36 x 36 x 36 36 = 2 x 2 x 3 x 3

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