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) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        
        // a(n) = Sum_{k=1..n} k/2 * floor(n/k) * floor(1 + n/k)
        
        long ans = 0;
        for (long k = 1; k <= n; k++) {
            long now = (n / k) * (1 + (n / k)) * k / 2;
            ans += now;
        }
        System.out.println(ans);
    }
}