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.
//make sure to make new file!
import java.io.*;
import java.util.*;
//race against danny solving a rubik's cube
public class D520{
   
   public static void main(String[] args)throws IOException{
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter out = new PrintWriter(System.out);
      
      int n = Integer.parseInt(f.readLine());

      int N = 100005;
      
      long[] answer = new long[N];
      
      answer[2] = 0L;
      
      for(int k = 3; k < N; k++){
         answer[k] += answer[k-1];
         
         //get factors
         for(int j = 2; j*j <= k; j++){
            if(k%j == 0){
               answer[k] += k/j;
               if(j*j != k)
                  answer[k] += j;
            }
         }
      }
      
      out.println(answer[n]*4);
         
      
      

      
      
      
      
      
      out.close();
   }
   
      
}