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 sc = new Scanner(System.in);
		int N = sc.nextInt();
		long A[] = new long[N+1];
		long result=0;
		for (int i=1;i<=N;i++) {
			for (int j=1;j*i<=N;j++) {
				A[j*i]++;
			}
		}
		for (int i=1;i<=N;i++) {
			result +=i*A[i];
		}
		System.out.println(result);
	}
}