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 scanner = new Scanner(System.in);
		int number = scanner.nextInt();
		long result = 0l;
		for(int i = 1; i <= number; i++) {
			int temporal = number / i;
			long add = 1l * temporal * (temporal + 1) / 2 * i;
			result += add;			
		}
		System.out.println(result);
		
	}
}