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.*;
public class Main {

    private static int N;
    private static long[] divisors = new long[10000001];

    private static long result = 0;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

        N = Integer.parseInt(br.readLine());



        for (int i = 1; i <= 10000000; i++) {
            for (int j = 1; j <= 10000000 / i; j++) {
                if(i*j > 10000000)break;
                divisors[i * j]++;
            }
        }

        for(int i=1;i<=N;i++){
            result += divisors[i] * i;
        }
        System.out.println(result);


    }
}