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.io.PrintWriter;

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