Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer *L*, how many pairs of positive integers *a*, *b* (*a* ≤ *b*) such that LCM(*a*, *b*) = *L* are there? Here, LCM(*a*, *b*) stands for the least common multiple of *a* and *b*.

For each dataset, an integer *L* is given in a line. Input terminates when *L* = 0.

For each dataset, output the number of pairs of *a* and *b*.

- 1 ≤
*L*≤ 10^{12}

12 9 2 0

8 3 2

Source: University of Aizu Programming Contest
, Aizu-Wakamatsu, Japan, 2010-05-29

Problem Setter: Takashi Tayama

Problem Setter: Takashi Tayama