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.io.*;
import java.util.*;
public class Main
{
	public static void main(String[] args) throws IOException
	{
	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    int n=Integer.parseInt(br.readLine());
	    long ans=0;
	    for(int i=1;i<=n;i++)
	    {
	        long temp=(long)n/i;
	        ans+=(long)temp*(temp+1)*i/2;
	    }
	    System.out.println(ans);
	}
}