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 void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();

            final int M = (int) 1e7;
            long[] numDivisors = new long[M + 1];
            for (int divisor = 1; divisor <= M; divisor++) {
                for (int j = divisor; j <= M; j += divisor) {
                    numDivisors[j]++;
                }
            }

            long sum = 0;
            for (int k = 1; k <= N; k++) {
                sum += k * numDivisors[k];
            }
            System.out.println(sum);
        }
    }
}