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
 *
 * @author silviase
 */
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);
        DSumOfDivisors solver = new DSumOfDivisors();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSumOfDivisors {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            long sum = 0;

            for (long i = 1; i <= n; i++) {
                long t = n / i;
                sum += t * (t + 1) / 2 * i;
            }

            out.println(sum);
        }

    }
}