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.*;

 public class Main{
// taking inputs
static BufferedReader s1;
static BufferedWriter out;
static String read() throws IOException{String line="";while(line.length()==0){line=s1.readLine();continue;}return line;}
static int int_v (String s1){return Integer.parseInt(s1);}
static long long_v(String s1){return Long.parseLong(s1);}
static int[] int_arr() throws IOException{String[] a=read().split(" ");int[] b=new int[a.length];for(int i=0;i<a.length;i++){b[i]=int_v(a[i]);}return b;}
static long[] long_arr() throws IOException{String[] a=read().split(" ");long[] b=new long[a.length];for(int i=0;i<a.length;i++){b[i]=long_v(a[i]);}return b;}
static void assign(){s1=new BufferedReader(new InputStreamReader(System.in));out=new BufferedWriter(new OutputStreamWriter(System.out));}
static long Modpow(long a,long p,long m){long res=1;while(p>0){if((p&1)!=0){res=(res*a)%m;}p >>=1;a=(a*a)%m;}return res;}
static long Modmul(long a,long b,long m){return ((a%m)*(b%m))%m;}
static long ModInv(long a,long m){return Modpow(a,m-2,m);}
static long nck(int n,int r,long m){if(r>n){return 0l;}return Modmul(f[n],ModInv(Modmul(f[n-r],f[r],m),m),m);}
static long[] f;
//......................................@uthor_Alx..............................................
static void spf(int n, int[] spf){
        for(int i=2;i<=(int)Math.sqrt(n);i++){
          if(spf[i]!=0) continue;
          spf[i]=i;
          for(int j=i*i;j<=n;j+=i){
            if(spf[j]!=0) continue;
            spf[j]=i;
          }
        }
        for(int i=(int)Math.sqrt(n);i<=n;i++){
          if(spf[i]==0) spf[i]=i;
        }
    }
   public static void main(String[] args) throws  IOException{
	        		  assign();
	        		  	int n=int_v(read());
	        		  	int[] spf=new int[n+1];
	        		  	spf(n,spf);
	        		  	long res=1;
	        		  	for(int i=2;i<=n;i++){
	        		  		long tmp=1l,c=0l;int j=i;
	        		  		while(j>1){
	        		  			int p=spf[j];
	        		  			while(j%p==0){
	        		  				j/=p;
	        		  				c++;
	        		  			}
	        		  			tmp*=(c+1);
	        		  			c=0;
	        		  		}
	        		  		res+=tmp*i;
	        		  	}
	        		  	out.write((res)+"");
                      	out.flush();
	        		 
	}
}