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) {
		var sc = new Scanner(System.in);
		var n = sc.nextInt();
		sc.close();

		var d = new int[n + 1];
		for (var i = 1; i <= n; i++) {
			for (var j = i; j <= n; j+=i) {
				d[j]++;
			}
		}

		var sum = 0L;
		for (var i = 1; i <= n; i++) {
			sum += (long)i * d[i];
		}

		System.out.println(sum);
	}
}