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>
int main() {
  long n, i, d, a, m;
  scanf("%ld", &n);
  for (i = 0; i <= 1000; i++) {
    d = n - i * i;
    if (d <= 0) {
      a = i;
      break;
    }
  }
  if (a * (a - 1) - n >= 0) {
    m = 2 * (2 * a - 1);
    printf("%ld", m);
  } else {
    m = 4 * a;
    printf("%ld", m);
  }
  return 0;
}
