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:
//package ABC172;
import java.util.*;
import java.lang.*;
import java.io.*;

class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		
		long ans=0;
		
		long[] div=new long[n+1];
		
		for(int i=1;i<=n;i++)
		{
			for(int j=1;j*i<=n;j++)
			{
				div[i*j]++;
			}
		}
		
		for(int i=1;i<=n;i++)
		{
			ans=ans+(long)(i*div[i]);
		}
		System.out.println(ans);
	}

}