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.*;

public class Main {


    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int sq = (int) Math.sqrt(n);

        if (Math.pow(sq, 2) == n) {
            p(sq * 4);
        } else {
            boolean up = (Math.pow(sq, 2) + Math.pow(sq + 1, 2)) / 2 <= n;
            if (up) {
                p((sq + 1) * 4);
            } else {
                int v = n - (int)Math.pow(sq, 2);
                int add = v / sq + (v % sq == 0 ? 0 : 1);
                p(sq * 4 + add * 2);
            }
        }
    }


    static void p(Object str) {
        System.out.println(str);
    }

    public static void pa(int[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

    public static void pi(Object[] objs) {
        String str = "";
        for (Object obj : objs) {
            str += obj.toString() + " ";
        }
        p(str);
    }

}

