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.util.function.*;
import java.lang.*;
import java.io.*;


public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();

        long ans = 0;
        for(int n=1; n<=N; n++){
            long num = N/n;
            /*n, 2n, 3n, ..., num*n == (1+num) * num / 2*/
            ans += n * (1+num) * num / 2;
        } 
        System.out.println(ans);
        
    }
}