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;
const int N = 1e5 + 6, MODM = 1e9 + 7;
const long long INF = 1e18 + 9;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  int x = (int)sqrt(n);
  int c = x * x;
  int ans = 4 * x;
  for (int i = 0; i < n - c; ++i) {
    --ans;
    if (i % x == 0)
      ans += 3;
    else {
      --ans;
      ans += 2;
    }
  }
  cout << ans << "\n";
  return 0;
}
