Problem: For a positive integer X, let f(X) be the number of positive divisors of X.

Given a positive integer N, find \sum_{K=1}^N K\times f(K).

Constraints

* 1 \leq N \leq 10^7

Input

Input is given from Standard Input in the following format:


N


Output

Print the value \sum_{K=1}^N K\times f(K).

Examples

Input

4


Output

23


Input

100


Output

26879


Input

10000000


Output

838627288460105

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
class Main
{
  public static void findDivisors(long[] a,int n)
  {
    for(int i=1;i<=n;i++)
    {
      for(int j=i;j<=n;j+=i)
        a[j]++;
    }
  }
  public static void main(String args[])
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
   // double max=Math.pow(10,7);
    long[] a=new long[n+1];
    //Arrays.fill(a,0);
    findDivisors(a,n);
    long ans=0;
    for(int i=1;i<=n;i++)
    {
      ans=ans+(i*a[i]);
    }
    System.out.println(ans);
  }
}