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.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;

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

}