No Story

Time Limit : 1 sec, Memory Limit : 65536 KB
Japanese version is here

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 (ab) 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

  • 1 ≤ L ≤ 1012

Sample Input

12
9
2
0

Output for the Sample Input

8
3
2

Source: University of Aizu Programming Contest , Aizu-Wakamatsu, Japan, 2010-05-29
Problem Setter:  Takashi Tayama