You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.

After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.

Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?

Input

A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.

Output

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.

Examples

Input

4


Output

8

Input

6


Output

28

Input

2


Output

0

Note

In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.

In the third example, it is impossible to perform even a single transformation.
import java.util.*;
import java.math.*;
import java.io.*;

public class CF1062D {
	// A Josh/Billy Collab (mostly Josh)
	final int MAX = 111111;
	public CF1062D() {
		Scanner scan = new Scanner(System.in);
		int n = Integer.parseInt(scan.next()); // ?
		long res = 0;
		for(int i = 2 ; i <= n ; i++) {
			Set<Integer> set = new HashSet<>();
			for(int j = 2 ; j * j <= n ; j++) {
				if(i % j == 0 && (i / j) != 1) {
					set.add(j);
					set.add(i / j);
				}
			}
			for(int x : set)
				res += 4 * (i / x);
		}
		System.out.println(res);
	}
	public static void main(String[] args) { new CF1062D(); }
}
