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) {
		try (Scanner sc = new Scanner(System.in)) {
			int n = Integer.parseInt(sc.next());
			long[] arr = new long[n + 1];
			for (int i = 2; i <= n; i++) {
				int j = 1;
				int tmp = i * j;
				while (tmp <= n) {
					arr[tmp] += 1;
					j++;
					tmp = i * j;
				}
			}
			long ans = 0;
			for (int i = 1; i <= n; i++) {
				ans += i * (arr[i] + 1);
			}
			System.out.print(ans);
		}
	}
}