| ||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.
|Method signature:||int getLevel(long N)|
|(be sure your method is public)|
|-||N will be between 1 and 10000000000000 (10^13), inclusive.|
|4 cannot be expressed as a product of 4 numbers all greater than 1.|
|144 = 4 x 2 x 3 x 6|
The level of 4, 2, 3 and 6 is 0.
|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 = 36 x 36 x 36 x 36|
36 = 2 x 2 x 3 x 3