You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ 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 ≤ n ≤ 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 → 4 → (-2) → (-4) → 2.

In the third example, it is impossible to perform even a single transformation.
import java.io.*;
import java.util.*;

public class FunWithIntegers
{
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

    public void go()
    {
        int n = in.nextInt();
        long count = 0;
        for (int i = 2; i <= n; i++)
        {
            for (int j = 2; j*i <= n; j++)
            {
                count += j;
            }
        }
        out.println(count*4);

        out.flush();
        in.close();
    }

    public static void main(String[] args)
    {
        new FunWithIntegers().go();
    }
}