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<bits/stdc++.h>
using namespace std;

typedef long long int ll;

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