Execution time limit is 1 second Runtime memory usage limit is 128 megabytes Let n=p1a1p2a2...pkak(p1<p2<...<pk) be a factorization of positive integer n.
Find the value of a1+a2+...+ak.
Input
One positive integer n(1<n≤109).
Output
Find the factorization of n and print the value of a1+a2+...+ak.
Examples
For example, 72=23⋅32. The answer is a1+a2=3+2=5.