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);
		long N = Integer.parseInt(sc.next());
		long ret = 0;
		int i = 2;
		while (true) {
			int step = i / 2;
			long start = (i + 1) / 2 * step;
			if (start > N)
				break;
			long end = N / step * step;
			ret += (start + end) * ((end - start) / step + 1) / 2;
			i += 1;
		}
		System.out.println(ret);
	}
}