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.Scanner;


public class Main {

	public static void main(String[] args)  {
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		int MAX = 10000000;
		int[] cnt = new int[MAX+1];  
		
		Long ans = 0l;
		for(int i = 1 ; i <= n ; i++) {
			int value =  i;
			while(MAX >= value) {
				cnt[value]++;
				value += i;
			}
			
			Long tmp = (long) i;
			Long tmp2 = (long) cnt[i];
			ans += tmp * tmp2;
		}
		System.out.println(ans);
	}
}