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.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    int[] numOfDivisor = new int[n + 1];
    for (int i = 1; i <= n; i++) {
      for (int k = i; k <= n; k += i) {
        numOfDivisor[k]++;
      }
    }
    long ans = 0;
    for (int i = 1; i <= n; i++) {
      ans += (long) i * numOfDivisor[i];
    }
    pw.println(ans);
  }
}