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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long a[] = new long[n+1];
        Arrays.fill(a,1);
        
        for(int i=2;i<=n;i++){
            for(int j=1;;j++){
                if(i*j <= n){
                    a[i*j]++;
                }else{
                    break;
                }
            }
        }
        
        long sum = 0;
        for(int i = 1;i<=n;i++){
            sum += i*a[i];
        }
        
        System.out.println(sum);
    }
}

class Monmo {
}