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) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] arr = new int[n+1];
		for(int i = 1; i <= n ; ++i) {
			for(int j = i; j <= n; j += i) {
				++arr[j];
			}
		}

		long ans = 0;
		for(int i = 1; i <= n; ++i) 
			ans += ( (long)i * arr[i]);

			System.out.println(ans);


	}
}