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 n;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  int x = sqrt(n);
  int r = n - x * x;
  if (!r) {
    cout << 4 * x;
    return 0;
  }
  if (r <= x)
    cout << 4 * x + 2;
  else
    cout << 4 * x + 4;
  return 0;
}
