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 D1062 
{
    public static void main(String args[])throws IOException
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        if(n<=3)
            System.out.println(0);
        else
        {
            long sum=0;
            for(int i=2;i<=n/2;i++)
            {
                long t=n/i;
                long p=t*(t+1);
                p=p/2;
                p--;
                sum=sum+(p*4);
            }
            System.out.println(sum);
        }
    }
}
