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 blocks {

	public static void main(String[] args) {
Scanner sc = new Scanner(System.in); 
        
		int n = sc.nextInt();
		int t=1;
		while(t*t<=n) {
			t+=1;
		}
        t-=1;
        int per=0;
        if((n-(t*t))%t==0) {
            per = (4*t)+(((n-(t*t))/t)*2);	
        }
        
        else { per = (4*t)+(((n-(t*t))/t)*2)+2;}
        System.out.println(per);
        //System.out.println(t);

	}

}
