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) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long ans = 0;
		int[] yn = new int[N+1];
		for(int i = 1; i <= N; i++)
			for(int k = 1; k <= N / i; k++)
				yn[i*k]++;
		for(int i = 1; i <= N; i++)
			ans += (long)i * yn[i];
		System.out.println(ans);
	}

}