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.Scanner;

public class D {
    public static void main(String[] aaaa) {
        Scanner scanner = new Scanner(System.in);

        /*int[] prime = new int[1000005];

        for (int i = 2; i * i < prime.length; i++) {
            for (int j = i; j * i < prime.length; j++) {
                prime[j * i] = 1;
            }
        }
        */

        int _ = scanner.nextInt();
        long ans = 0;
        //base
        for (int i = 2; i < _; i++) {
            //start
            for (int j = 2; j * i <= _; j++) {
                //if (i % 2 == 0 || j % 2 == 0) {
                    //int tmp = i * ((int) (Math.log(_ / j) / Math.log(i) + 0.000001));
                    int tmp = i;

                    //System.out.println(i + " " + j);
                    //System.out.println(tmp);
                    ans += 4 * tmp;
                //}
            }
        }
        System.out.println(ans);
    }
}
