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.*;
class Main{
  public static void main(String[] args){
Scanner sc=new Scanner(System.in);
     long n=sc.nextLong();
    long a[]=new long[(int)n+1];
    Arrays.fill(a,1);
    for(int i=2;i<=n;i++){
for(int j=i;j<=n;j+=i){    //O(logN)
a[j]++;
}
    }
    long sum=0;
    for(int i=1;i<=n;i++){
sum+=(i*a[i]);
    }
    System.out.println(sum);
  }
}