CF1062D.Fun with Integers

普及/提高-

通过率：0%

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题目描述

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?

输入格式

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

输出格式

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 $0$ .

输入输出样例

输入#1
```
4
```
输出#1
```
8
```
输入#2
```
6
```
输出#2
```
28
```
输入#3
```
2
```
输出#3
```
0
```

说明/提示

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.

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