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()
{
  int64_t n;
  cin >> n;

  int64_t ans = 0;

  for (int64_t i = 1; i <= n; i++) {
    int64_t m = n / i;
    ans += m * (m + 1) / 2 * i;
  }

  cout << ans << endl;
}