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()
{
  uint64_t n, r = 0;
  cin >> n;
  for (uint64_t i = 1; i <= n; i++)
  {
    r += (n / i) * ((n - (n % i)) + i) / 2;
  }
  cout << r << endl;
}