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.*;

public class Main {

	public static void main(String[] args) {

		// 入力
		Scanner sc = new Scanner(System.in);
		long n = new Integer(Integer.parseInt(sc.next()));

		long result = 0;
		for (long i = 1; i <= n; i++) {
			long kosuu = n / i;
			result += (i + (i * kosuu)) * kosuu / 2;
		}

		System.out.println(result);

	}
}