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.util.*;
public class Main {
 
  public static void main(String[] args) { 
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int[] arr = new int[n + 1];
      Arrays.fill(arr, 2);
      arr[1]--;
      for(int i = 2; i * 2 <= n; i++) {
        for(int j = i * 2; j <= n; j += i)
          arr[j]++;
      }
      long sum = 0;

      for(int i = 1; i <= n; i++)
        sum += ((long)arr[i] * i);
      System.out.println(sum);
  }
}