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.io.*;
import java.math.BigInteger;

public class Main
{
    static final long mod=(int)1e9+7;
    public static void main(String[] args) throws Exception
    {
    	FastReader in=new FastReader();
    	PrintWriter pw=new PrintWriter(System.out);
    	int n=in.nextInt();
    	long ans=0;
    	for(int i=2;2*i<=n;i++)
    	{
    		ans+=i*(n/i-1);
    	}
    	ans*=4;
    	pw.print(ans);
    	pw.flush();
    }
}

class pair
{
	int f,s;
}

class FastReader
{
    BufferedReader br;
    StringTokenizer st;
 
    public FastReader()
    {
        br=new BufferedReader(new InputStreamReader(System.in));
    }
 
    public String next() throws IOException
    {
        if(st==null || !st.hasMoreElements())
        {
            st=new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
 
    public int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }
 
    public long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
}