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) {
	Scanner s = new Scanner(System.in);
	int N = s.nextInt();
	int[] div = new int[N+1];
	for(int i = 1; i <= N; i++){
		for(int j = i; j <= N; j=j+i){
			div[j]++;
		}
	}

	long sum = 0;
	for(int i = 1; i <= N; i++){
		sum += (long)i*(long)div[i];
	}

	System.out.println(sum);
    
  }
}