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);
        
        long n = Integer.parseInt(sc.next());
        
        long ans = n*(n+1)/2;
        for(int i=2; i<=(int)1e7; i++){
            //System.out.println(ans);
            long tmp = n/i;
            tmp = tmp*(tmp+1)/2*i;
            ans += tmp;
        }
        
        System.out.println(ans);
    }
    
}