Given a positive integer K > 2, with prime
factorization:

K = p1^a1 * p2^a2 ... * pn^an

Compute the following:

S = a1*p1 + a2*p2 ... + an*pn.


Input
A list of 
Output
For each integer compute the super factor
sum and output it on a single line.

Example

Input:
6
7
Output:
5
7

Source: codechef | Difficulty: MEDIUM_HARD


Solutions: