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.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;
 
public  class realfast implements Runnable {
    private static final int INF = (int) 1e9;
 
    public  void solve() throws IOException 
    {
     int n = readInt();
     int parent[]= new int[n+1];  
     for(int i=2;i<=n;i++)
      parent[i]=i;

     long val[]= new long[n+1];
     for(int i=2;i<=n;i++)
     {
      for(int j=2*i;j<=n;j=j+i)
      {
        val[j]= val[j]+4*(j/i); 
        union(parent,i,j);	
      } 	
     }
     
     
     long arr[]= new long[n+1];
     for(int i=2;i<=n;i++)
     {
     	int par1 = find(parent,i);
     	arr[par1]= arr[par1]+val[i];
     }
     
     long max=0;

     for(int i =2;i<=n;i++)
     {
      if(find(parent,i)==i)
      max=Math.max(max, arr[i]);	
     }
     out.println(max);


    }
    public int find(int parent[], int i)
    {
     if(parent[i]==i)
     return i;
     parent[i]= find(parent,parent[i]);
     return parent[i];	
    }
    public void union(int parent[], int i , int j)
    {
     int par1= find(parent,i);
     int par2= find(parent,j);
     if(par1==par2)
     return ;
     if(par1<par2)
     parent[par2]= par1;
     else
     parent[par1]= par2;
    	
    }


    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v ;
    int val;
    edge(int u1, int v1 , int val1)
    {
       this.u=u1;
       this.v=v1;
       this.val=val1;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}