Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

D. Fun with Integers
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a positive integer $$$n$$$ greater or equal to $$$2$$$. For every pair of integers $$$a$$$ and $$$b$$$ ($$$2 \le |a|, |b| \le n$$$), you can transform $$$a$$$ into $$$b$$$ if and only if there exists an integer $$$x$$$ such that $$$1 < |x|$$$ and ($$$a \cdot x = b$$$ or $$$b \cdot x = a$$$), where $$$|x|$$$ denotes the absolute value of $$$x$$$.

After such a transformation, your score increases by $$$|x|$$$ points and you are not allowed to transform $$$a$$$ into $$$b$$$ nor $$$b$$$ into $$$a$$$ anymore.

Initially, you have a score of $$$0$$$. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?

Input

A single line contains a single integer $$$n$$$ ($$$2 \le n \le 100\,000$$$) — the given integer described above.

Output

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print $$$0$$$.

Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note

In the first example, the transformations are $$$2 \rightarrow 4 \rightarrow (-2) \rightarrow (-4) \rightarrow 2$$$.

In the third example, it is impossible to perform even a single transformation.