You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.

After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.

Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?

Input

A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.

Output

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.

Examples

Input

4


Output

8

Input

6


Output

28

Input

2


Output

0

Note

In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.

In the third example, it is impossible to perform even a single transformation.
#include <bits/stdc++.h>
using namespace std;
void play() {
  long long n;
  cin >> n;
  long long summ = 0;
  long long totscore = 0;
  for (long long k = 4; k < n + 1; ++k) {
    long long score = 0;
    for (long long a = 2; a < ceil(sqrt(n + 2)); ++a) {
      if (a * a > k) {
        break;
      }
      if (k % a == 0) {
        score += k / a;
        if (a != k / a) {
          score += a;
        }
      }
    }
    totscore += score * 4;
  }
  cout << totscore << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) {
    play();
  }
  return 0;
}
