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:

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import java.util.Scanner;

public class LazyGuard {

    public static void main(String[] args) {
        
        Scanner scanner = new Scanner(System.in);
        int num = scanner.nextInt();
        
        double middle = ((int) Math.sqrt(num)) + 0.5;
        double index = 0;
        
        if (Math.sqrt(num) < middle) { //round up
            index = Math.floor(Math.sqrt(num));
        }
        else {
            index = Math.ceil(Math.sqrt(num));
        }
        
        int parameter = (int) index * 4;
        
        if ((index * index) < num) {
            parameter += 2;
        }
        
        System.out.println(parameter);
        
        scanner.close();
    }
}
