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.*;
import java.io.*;

class Main{
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st  = new StringTokenizer(br.readLine());

        int N = Integer.parseInt(st.nextToken());
        
        long ans=0;

        for (int i=1; i<=N; i++) {
            long Y = (long)Math.floor(N/i);
            ans+=(Y)*(Y+1)*i/2;
        }

        System.out.println(ans);

    }

}