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 CPP):

Solution:
#include<cstdio>
using namespace std;

#define ll long long
int n;

int main()
{
	scanf("%d",&n);
	
	ll ans=0;
	for (int i=1 ; i<=n ; i++)
	{
		ll x=n/i;
		ans+=x*(x+1)/2*i; 
	} 
	
	printf("%lld",ans);
	return 0;
 }