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.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		Scanner stdIn = new Scanner(System.in);
		int N = stdIn.nextInt();
		ArrayList<Integer> f = new ArrayList<Integer>();
		
		long ans = 0;
		
		for(int i = 1; i <= N; i ++) {
			long Y = (int) Math.floor((double) N / i);
			ans += Y * (Y + 1) * i / 2;
		}
		
		System.out.println(ans);
		
	}
}