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.Scanner;

public class Main {

    public static void main(String[] args) {
	// write your code here

        Scanner scan = new Scanner(System.in);
   long N=scan.nextLong();
long p=0;
long n=0;
 for(long i=1;i<=N;i++){
     n=N/i;
     p=p+i*n*(n+1)/2;
 }
System.out.println(p);
    }
}