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<iostream>
using namespace std;
int N;
long ans;
int main()
{
	cin>>N;
	for(int i=1;i<=N;i++)
	{
		for(int j=i;j<=N;j+=i)ans+=j;
	}
	cout<<ans<<endl;
}