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>
import java.util.Scanner;

public class Codechef {

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt(), n1 = 0, n2 = 0, n3 = 0, x1 = 0, x2 = 0;
        int x = (int) Math.sqrt(n);
        if (x * x == n) {
            System.out.println(x * 4);
        } else {
            x2 = x * 4;//12
            x1 = x * x;//9
            n1 = n - x1;//2
            x2 = x2 - n1;
            if (n1 <= x) {
                System.out.println(x2 + n1 + 2);
            } else {
                n2 = n1 / 2;
                n3 = n1 - n2;
                n2 = n2 + 2;
                n3 = n3 + 2;
                System.out.println(x2 + n2 + n3);
            }

        }
    }

}
