Description

Consider the following Diophantine equation:

$$\frac{1}{x}~+~\frac{1}{y}~=~\frac{1}{n}~,(x,y,n~\in~\mathbb{N}^+)$$

Xiao G is very interested in the following question: for a given positive integer $n$, how many essentially different solutions satisfy the equation above? For example, when $n=4$, there are three essentially different solutions $(x~\leq~y)$:

$\frac{1}{5}+\frac{1}{20}~=~\frac{1}{4}$

$\frac{1}{6}+\frac{1}{12}~=~\frac{1}{4}$

$\frac{1}{8}+\frac{1}{8}~=~\frac{1}{4}$

Obviously, for larger $n$, it is meaningless to list all essentially different solutions. Can you help Xiao G quickly find, for a given $n$, the number of essentially different solutions to the equation above?

Input Format

One line with only one integer $n$.

Output Format

Output one line with one integer, representing the answer.

4

3

Hint

Constraints

For all testdata, it is guaranteed that $1 \leq n \leq 10^{14}$.

Translated by ChatGPT 5