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();

        long[] array = new long[n];
        Arrays.fill(array, 1);

        for (int i = 2; i <= n; i++) {
            int count = 0;
            int index;
            while ((index = ++count * i) <= n) {
                array[index - 1]++;
            }
        }

        long ans = 0;
        for (int i = 0; i < n; i++) {
            ans += array[i] * (i + 1);
        }

        System.out.println(ans);
    }
}