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.*;
import java.io.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int N = sc.nextInt();
		
		long ans = 0;
		for (int k = 1; k <= N; k++) {
			ans += k * sum(N / k);
		}
		
		System.out.println(ans);
	}
	
	public static long sum(int N) {
		return (long) N * (N + 1) / 2;
	}
}