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.*;
public class Main {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long f[]=new long[10000005];
		for(int i=1;i<10000005;i++) {
			for(int j=i;j<10000005;j+=i) {
				if(j%i==0) {
					f[j]++;
				}
			}
		}
		long sum=0;
		for(int i=1;i<=n;i++) {
			sum+=i*f[i];
		}
		System.out.println(sum);
	}
	
	

}