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 LazySecurityGuard {

    public static void main(String[] args) {
        Scanner cs = new Scanner(System.in);
        int n = cs.nextInt();
        int x = (int) Math.sqrt(n);
        int y = x + 1;
        if(x * y > n){
            y--;
        }
        int z = n - x * y;
        long ans;
        if(z==0){
            ans = x * 2 + y * 2;
        } else {
            ans = x * 2 + y * 2 + 2;
            
        }        
        System.out.println(ans);
    }

}
