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 <stdio.h>

int n;

int main()
{
	scanf ("%d", &n);

	long long a = 0;
	for (int i = 1; i <= n; i++){
		long long c = n / i;
		a += c * (c + 1) / 2 * i;
	}

	printf ("%lld\n", a);
	return 0;

}