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.*;
import java.io.*;
public class Main {

	public static void main(String[] args)throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		long k =Long.parseLong(br.readLine());
		long ans=0;
		//y=k/i i.e. maximum number not exceeding k.
		for(long i=1; i<=k; i++) ans+=((k/i)*((k/i)+1)*i/2);
		System.out.println(ans);
	}
	
	
}