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;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
using pcc = pair<char, char>;
using pdd = pair<double, double>;
using vi = vector<int>;
using vs = vector<string>;
using vll = vector<ll>;
using vpii = vector<pii>;
using vc = vector<char>;
using vd = vector<double>;
int main(int argc, char* argv[]) {
  ll n, ans = 0, i;
  scanf("%lld%*c", &(n));
  for (i = 2; i <= n; i++) {
    if (n / i > 1) ans += ((n / i) - 1) * i;
  }
  cout << ans * 4 << endl;
  return 0;
}
