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.*;

public class Main {
    public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int N = sc.nextInt();
	int[] f = new int[N+1];
	for (int i=2;i<=N;i++) {
	    for (int j=1;i*j<=N;j++) {
		f[i*j]++;
	    }
	}
	long count = 0;
	for (int i=1;i<=N;i++) {
	    count += (long)i * (long)(f[i]+1);
	}
	System.out.print(count);
    }
}