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;

int main() {
	long long n, ans = 0;
	cin >> n;
	for (int a = 1; a*a <= n; a++) {
		ans += a*a + a * (n/a-a) * (a+1+n/a);
	}
	cout << ans << endl;
	return 0;
}