Fun with Integers
Description
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?
A single line contains a single integer $n$ ($2 \le n \le 100\,000$) — the given integer described above.
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 $0$.
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 $0$.
Samples
4
8
6
28
2
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.