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.*;
import java.math.*;
import java.util.*;
public class Main { //FILTER PRIMES
 
	public static void main(String[] args) { 
		FastScanner input = new FastScanner();
		PrintWriter w = new PrintWriter(System.out);
		long ans = 0;
		long N = input.nextLong();
		long[] cnts = new long[(int)(N+1)];
		for (long f = 1; f <= N; f++) {
			for (long s = f; s <= N; s+=f) {
				cnts[(int)s]++;
			}
		}
		for (int i = 1; i <= N; i++) {
			ans+=cnts[i]*i;
		}
		//CODE
		w.println(ans);
		w.flush();
	}
	public static long GCD(long a, long b) {
		if (a==0||b==0) return Math.max(a,b);
		return GCD(Math.min(a, b),Math.max(a, b)%Math.min(a, b));
	}
	public static long FastExp(long base, long exp, long mod) {
		long ans=1;
		while (exp>0) {
			if (exp%2==1) ans*=base;
			exp/=2;
			base*=base;
			base%=mod;
			ans%=mod;
		}
		return ans;
	}
	public static long ModInv(long num,long mod) {return FastExp(num,mod-2,mod);}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}