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 Problem {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        final int N = scanner.nextInt();
        if (N == 1) {
            System.out.println(4);
            return;
        }
        final long K = Math.round(Math.sqrt(N));
        int perimeter = 0;
        int i = 0;
        perimeter += K + 2;
        i += K;
        while (i < N) {
            if (N - i <= K) {
                perimeter += 2 + K;
                i += N - i;
            } else {
                perimeter += 2;
                i += K;
            }
        }
        System.out.println(perimeter);
    }
}
