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.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    void solve(Scanner sc, PrintWriter pw) {
        long N = sc.nextLong();
        long result = 0;
        for (long k = 1; k <= N; k++) {
            result += (N / k) * (1 + N / k) * k / 2;
        }
        pw.println(result);
    }
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        new Main().solve(sc, pw);
        pw.flush();
        pw.close();
        sc.close();
    }
}