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 {
    static List<Integer> sosu;
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        long sum = 0;
        for(long i=1;i<=T;i++){
            final long bai = (long)(T/i);
            final long cap = bai * i;
            sum += (cap+i) * (cap/i) / 2;
        }
        System.out.println(sum);
    }

}