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 ans = 0;
  for(long long i = 1; i <= n; i++) ans += (i * (n/i) * (1 + n/i))/2;
	cout << ans;
  return 0;
}