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();
      long[] div = new long[n];
      
      
      for(int i=1;i<n+1;i++){
        for(int j=1;j*i<n+1;j++){
          div[i-1] += i*j;
        }
      }
      
      long ans = 0;
      for(int i=1;i<n+1;i++){
        ans += div[i-1];
      }
      System.out.println(ans);
	}
}