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()
{
	int	N;
	cin >> N;
	int64_t	sum = 0;
	for (int i = 1; i < N + 1; ++i) {
		for (int j = i; j < N + 1; j += i) {
			sum += j;
		}
	}
	cout << sum << endl;
}