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.util.*;
import java.lang.*;
public class Main {
	PrintWriter out;
    StringTokenizer st;
    BufferedReader br;
 	
 	class Pair implements Comparable<Pair>
	{
	    int f;
	    int s;
 
	    Pair(int t, int r) {
	       f = t;
	       s = r;
	    }
	    public int compareTo(Pair p)
	    {
	    	if(this.f!=p.f)
	    		return this.f-p.f;
 
	    	return this.s-p.s;
	    }
 	}
 // 	class Sort implements Comparator<String> 
	// { 
	//     public int compare(String a, String b) 
	//     { 
	//     	return (a+b).compareTo(b+a);
	//     } 
	// }
 
	String ns() {
        while (st == null || !st.hasMoreElements()) {
 
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    String nextLine() throws Exception {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            throw new Exception(e.toString());
        }
        return str;
    }
 
    int nextInt() {
        return Integer.parseInt(ns());
    }
 
    long nextLong() {
        return Long.parseLong(ns());
    }
 
    double nextDouble() {
        return Double.parseDouble(ns());
    }
	
	int upperBound(long a[],long key)
	{
		int l=0,r=a.length-1;
		int i=-1;
 
		while(l<=r)
		{
			int mid=(l+r)/2;
 
			if(a[mid]<key)
				l=mid+1;
 
			else{
				i=mid;	
				r=mid-1;
			}
			
		}
		return i;
	}
	int lowerBound(Pair[] a , long key)
	{
		int l = 0, r = a.length- 1;
		int i = -1;
 	
		while(l<=r)
		{
			int mid=(l+r)/2;
 
			if(a[mid].f<key)
			{
				i=mid;
				l=mid+1;	
			}
 
			else
				r=mid-1;
			
		}
		return i;
	}
 
	long power(long x,long y)
	{
	    long ans=1;
	    
	    while(y!=0)
	    {
	        if(y%2==1) ans=(ans*x)%mod;
	        x=(x*x)%mod;
	        y/=2;
	    }
	    return ans%mod;
	}
	
 
	int mod= 1000000007;
	long gcd(long x ,long y)
	{
		if(y==0)
			return x;
		return gcd(y,x%y);
	}
 
	// ArrayList a[];
	// int vis[],cnt=0;
	// void dfs(int ver)
	// {
	// 	ArrayList<Integer> l=a[ver];
	// 	if(l.size()==1)
	// 		cnt++;
	// 	for(int v:l)
	// 	{
	// 		if(vis[v]==0){
	// 			vis[v]=vis[ver]+1;
	// 			dfs(v);
	// 		}
	// 	}
	// }
 
 	int countSetBits(long n) 
    { 
        int count = 0; 
        while (n > 0) { 
            n &= (n - 1); 
            count++; 
        } 
        return count; 
    }
    int max; 
    int spf[]; 

    void sieve() 
    { 
    	spf = new int[max];
        spf[1] = 1; 
        for (int i = 2; i < max; i++) 
        	spf[i] = i;

        for (int i = 4; i < max; i += 2) 
            spf[i] = 2; 
       
        for (int i = 3; i * i < max; i++) 
        {  
            if (spf[i] == i) 
            { 
                for (int j = i * i; j < max; j += i){ 
                	if (spf[j] == j) 
                        spf[j] = i; 
                }
            } 
        } 
        // out.println(Arrays.toString(spf));
    } 

    long getFactorization(int x) 
    { 
    	HashMap<Integer,Integer> map = new HashMap<>(); 
        while (x != 1) 
        { 
            if(map.containsKey(spf[x]))
            	map.replace(spf[x], map.get(spf[x]) + 1);
            else
            	map.put(spf[x], 1); 
            x = x / spf[x]; 
        } 
        long ans = 1;
        for(Map.Entry<Integer,Integer> m : map.entrySet())
        {
        	ans *= (m.getValue() + 1);
        }
        return ans; 
    } 

	void solve() throws IOException{
		int n = nextInt();
		max = n + 1;
		sieve();
		long ans = 0;
		for(int i = 1; i <= n; i++){
			ans += i * 1l * getFactorization(i);
		}
		out.println(ans);
	}
 
 
	
    void run() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
		solve();
		out.flush();
 
		out.close();
	}
 
	public static void main(String args[]) throws IOException {
		new Main().run();
	}
  
}