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 Main() {
        Scanner scanner = new Scanner(System.in);
        long N = scanner.nextLong();

        long R = (N+1L)*N-1L;

        for (long i = 2; 2*i <= N; i++) {
            R += (((N/i)*i+i*2L)*((N-i)/i))/2L;
        }

        System.out.println(R);
    }

    public static void main(String[] args) {
        new Main();
    }
}