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;

long long n, m = 0, k;

int main()
{
	cin >> n;

	for (int i = 1; i <= n; i++) {
		k = n / i;
		m += i * k * (k + 1) / 2;
	}
	
	cout << m << endl;
}