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