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 <bits/stdc++.h>

using namespace std;

int main() {

	long long n;
	cin >> n;

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

	cout << res << endl;

	return 0;

}