Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.

Input

Input will consist of a single integer N (1 ≤ N ≤ 106), the number of city blocks that must be enclosed by the route.

Output

Print the minimum perimeter that can be achieved.

Examples

Input

4


Output

8


Input

11


Output

14


Input

22


Output

20

Note

Here are some possible shapes for the examples:

<image>
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n, i;
  cin >> n;
  int ans = 1000000000, temp;
  for (i = 1; i <= n; i++) {
    temp = (n / i) + ((n % i) ? 1 : 0);
    ans = min(ans, 2 * (i + temp));
  }
  cout << ans << '\n';
  return 0;
}
