Description

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.

Input Format

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 Format

Output a single integer representing the total number of arrangements.

4

4

Hint

Sample explanation:

For $40\%$ of the testdata, $1 \le N \le 10^4$.

For $100\%$ of the testdata, $1 \le N \le 10^6$.

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