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 < 100 integers, one on each line, all less than 2*10^19.

Output

For each integer compute the super factor sum and output it on a single line.

Example

Input:
6
7

Output:
5
7