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>
#include <vector>

int main()
{
	int n;
	std::cin >> n;
	long long res = 0;
	for (int i = 1; i <= n; i++)
		for (int j = i; j <= n; j += i)
			res += j;

	std::cout << res << std::endl;
}