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.Arrays;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    //int end = (int)Math.sqrt(n) + 1;
    int end = n / 2;
    int[] cntOfDivisors = new int[n + 1];
    Arrays.fill(cntOfDivisors, 2);
    cntOfDivisors[0] = 0;
    cntOfDivisors[1] = 1;
    for(int i = 2; i <= end; i++){
      int t = 2;
      while(i * t <= n){
        cntOfDivisors[i * t]++;
        t++;
      }
    }
    long answer = 0;
    for(int i = 1; i <= n; i++){
      answer += cntOfDivisors[i] * (long)i;
    }
    System.out.println(answer);
  }
}