P5150 Birthday Gift

wyh is about to have a birthday, and hke and ljc plan to give him a birthday present.

wyh has a lucky number $n$. Now hke plans to give him a gift with thoughtfulness value $a$, and ljc plans to give him a gift with thoughtfulness value $b$. Together, their gifts have thoughtfulness value $\operatorname{lcm}(a,b)$, where $\operatorname{lcm}$ denotes the least common multiple. wyh receives this combined gift. If the thoughtfulness value of the gift wyh receives is exactly $n$, he will be happy. How many ways are there to give gifts that make wyh happy?

A positive integer $n$.

An integer representing the answer.

### Sample Explanation These $9$ ways are: $(1,6),(2,6),(3,6),(6,6),(2,3),(3,2),(6,1),(6,2),(6,3)$. ### Constraints For $30\%$ of the testdata, $n \leq 1000$. For $100\%$ of the testdata, $n \leq 10^{16}$. Translated by ChatGPT 5