题目描述
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.
Constraints
- 1 ≤ L ≤ 1012
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.
Example
Input
12
9
2
0
Output
8
3
2
输入格式
见题面
输出格式
见题面
样例输入
12
9
2
0
样例输出
8
3
2