P4388 Princess Fu's Rectangle

Princess Fu did poorly in the monthly exam and felt very upset.

To vent her anger, she made a large number of scarecrows. Every day, Princess Fu arranges some scarecrows into an $ R*C $ rectangle, with one scarecrow on each cell of the grid. Then she stands at the top-left corner and shoots an arrow toward the bottom-right corner of the rectangle. Princess Fu is an excellent archer; she can pierce through any number of scarecrows. Any scarecrow on a cell that the arrow passes through is destroyed. Seeing the ruined scarecrows makes Princess Fu a little happier. However, making scarecrows costs a lot of money, so Princess Fu does not want to destroy too many scarecrows. Therefore, each day she chooses to destroy exactly $ N $ scarecrows. Princess Fu is also fickle; she wants to see a different rectangle arrangement each day. Rectangles are considered up to rotation, i.e., $ R\times C $ and $ C\times R $ are equivalent. She easily computed the number of arrangements, and decided to make things difficult for you. Unwilling to admit defeat, you decide to write a program to compute this number and submit it as your answer to Princess Fu.

The input consists of a single line with one integer $ N $ ($ 1\le N\le 10^6 $), representing the number of scarecrows destroyed each time.

Output a single integer representing the total number of arrangements.

Sample explanation:  For $ 40\% $ of the testdata, $ 1 \le N \le 10^4 $. For $ 100\% $ of the testdata, $ 1 \le N \le 10^6 $. Translated by ChatGPT 5