Problem: For a positive integer X, let f(X) be the number of positive divisors of X.

Given a positive integer N, find \sum_{K=1}^N K\times f(K).

Constraints

* 1 \leq N \leq 10^7

Input

Input is given from Standard Input in the following format:


N


Output

Print the value \sum_{K=1}^N K\times f(K).

Examples

Input

4


Output

23


Input

100


Output

26879


Input

10000000


Output

838627288460105

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            out.println(findDivisors(N));
        }

        static long findDivisors(int n)
        {
            long[] div = new long[n + 1];
            for (int i = 1; i <= n; i++)
            {
                for (int j = 1; j * i <= n; j++)
                    div[i * j]++;
            }
            long sum = 0;
            for (int i = 1; i <= n; i++)
                sum += i * div[i];

            return sum;
        }

    }
}