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.Scanner;

public class Main {

    public static final int MOD = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        long ans = 0;
        long[] num = new long[n + 1];
        for (long i = 2; i <= n; i++) {
            for (int j = 1; i * j <= n; j++) {
                num[(int)i * j]++;
            }
        }
        for (int i = 2; i <= n; i++) {
            ans += (num[i] + 1) * i;
        }
        System.out.println(ans + 1);
    }
}