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) {
		// TODO 自動生成されたメソッド・スタブ

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

		long ans = 0L;
		long[] array = new long[n+1];
		for(long j=1L;j<=n;j++) {
			for(long i=1;i*j<=n;i++) {
				array[(int) (i*j)] = array[(int) (i*j)] + 1L;
			}
		}
		for(long j=1L;j<=n;j++) {
			ans = ans + j*array[(int) j];
		}
		System.out.println(ans);
	}
}