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>

def main():

	n = int(raw_input())

	sq = 1000

	while sq >= 0:
		if sq*sq <= n:
			break
		sq-=1

	sol = 4 * sq

	rs = n - sq * sq

	if rs > sq:
		sol += 4
	
	if rs > 0 and rs <= sq:
		sol += 2

	print sol


	return 0

if __name__ == '__main__':
	main()