# Problem J: No Story

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*.

## Input

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

## Output

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

## Constraints

## Sample Input

12
9
2
0

## Output for the Sample Input

8
3
2