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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.*;
import java.util.*;


public class Main {
    public static void main(String[] args) throws Exception {
        
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        long ans = 0;

        for(int i=1;i<=n;i++) {
            long amari = n%i;
            long syou = n/i;
            
            ans+=(i+n-amari)*syou/2;
        }
        
        System.out.println(ans);
        
    }
}