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;
typedef long long ll;
const ll MAXN=1e7+7;
ll n,sum;
int main()
{
	cin>>n;
	sum=(1+n)*n/2;
	for(int i=2;i<=n;i++) sum+=(i+n/i*i)*(n/i)/2;
	cout<<sum<<endl;
	return 0;
}