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 scan = new Scanner(System.in);

                int N = scan.nextInt();

                long count = 0;

                for (long i = 1; i <= N; i++) {
                	long position = i;
                	while (position <= N) {
                		count += position;
                		position += i;
                	}
                }

                System.out.println(count);

                scan.close();

        }
}