### 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

0)

 `4`
`Returns: 0`
 4 cannot be expressed as a product of 4 numbers all greater than 1.
1)

 `144`
`Returns: 1`
 144 = 4 x 2 x 3 x 6 The level of 4, 2, 3 and 6 is 0.
2)

 `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.
3)

 `1679616`
`Returns: 2`
 1679616 = 36 x 36 x 36 x 36 36 = 2 x 2 x 3 x 3

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10457

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13898&pm=10457

vexorian

#### Testers:

PabloGilberto , Andrew_Lazarev , ivan_metelsky

Math