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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {

  static long n, ans;
  static long[] a, b, asum, bsum;

  public static void main(String[] args) throws Exception {

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);

    String[] in = br.readLine().split(" ");
    n = Long.parseLong(in[0]);

    br.close();

    ans = 0;
    for (long i = 1; i <= n; i++) {
      for (long j = i; j <= n; j += i) {
        ans += j;
      }
    }

    out.println(ans);

    out.flush();

  }
}