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>

typedef long long ll;

int main(void)
{
	ll n, i, ans = 0;

	scanf("%lld", &n);

	for (i = 1; i <= n; i++)
		ans += (n / i + 1) * (n / i) / 2 * i;

	printf("%lld", ans);
	return 0;
}