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 scan = new Scanner(System.in);
    long n = scan.nextLong();
    long sum = 0;
    for (long i=1;i<=n;i++){
      sum += get(i,n);
    }
    System.out.println(sum);
  }

  public static long get(long a, long b){
    long g = (long) b/a;
    long c = (long) (g+1)*g*a/2;
    return c;
  }
}