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.math.*;
public class Main {
	public static void main(String[] args){
		
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		
		long[] num = new long[10000002];
		
		for (int i = 0; i<num.length;i++)
		{num[i]=0;}
	
		for (int i = 1; i<num.length;i++)
		{
			int i2 = i;
			while(i2 < 10000001)
			{
				num[i2]++;
				i2 += i;	
			}
		}
		
		long ans = 0;
		
		for (int i = 1; i < (N+1) ;i++)
		{
          long temp = i*num[i];
			ans += temp;
			}
		System.out.println(ans);
   
        }
		
	}