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) {
        try (Scanner sc = new Scanner(System.in)) {
            // in
            int N = Integer.parseInt(sc.next());
            int[] q = new int[N+1];
            long ans = 0L;

            for (int i = 1; i <= N; i++) {
                for (int j = i; j <= N; j += i) {
                    ans += j;
                }
            }
            System.out.println(ans);
        }
    }
}