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.io.*;
import java.lang.*;
import java.util.*;

public class D1062 {
    public static void main(String[] args) throws IOException{
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int k = Integer.parseInt(st.nextToken());
        f.close();
        long ans = 0;
        for(int n = 4; n <= k; n++){
            for (long i=2; i<=Math.sqrt(n); i++)
            {
                if (n%i==0)
                {
                    if (n/i == i) {
                        ans+=4*i;
                    }
                    else {
                        ans+=4*i;
                        ans+=4*(n/i);
                    }
                }
            }
        }



        System.out.println(ans);
    }

}