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;
const long long int M = 2e5 + 10;
const long long int mod = 1e9 + 7;
const long long int infi = LLONG_MAX;
long long int ans, k, n, x, y, m, mymax = LLONG_MIN, mymin = LLONG_MAX, b, c, z,
                                  sum;
vector<long long int> v[M];
long long int sprime[M];
int main() {
  long long int i, j;
  scanf("%lld", &n);
  for (i = 2; i < n + 1; i++) {
    if (2 * i <= n) {
      x = n / i;
      ans = ans + (x * (x + 1)) / 2;
      ans--;
    }
  }
  ans *= 4;
  printf("%lld\n", ans);
  return 0;
}
