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.
//package Graphs;

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;
import java.util.Scanner;

public class M1062D {
    public static Scanner enter = new Scanner(System.in);
    public static Random random = new Random();
    public static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) {
        int n=enter.nextInt();
        eratosfen pr=new eratosfen(n);
        pr.fillSieve();
        long ans=0;
        //System.out.println(Arrays.toString(pr.primes));
        for (int i = 2; i <=n ; i++) {
            ans+=(long)2*(2+n/i)*(n/i-1);
        }
        System.out.println(ans);

    }
}

class eratosfen {
    boolean[] primes;
    public eratosfen(int n) {
        primes=new boolean[n+1];
    }
    public void fillSieve() {
        Arrays.fill(primes, true);
        primes[0] = false;
        primes[1] = false;
        for (int i = 2; i < primes.length; ++i) {
            if (primes[i]) {
                for (int j = 2; i * j < primes.length; ++j) {
                    primes[i * j] = false;
                }
            }
        }
    }
}