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 math
n=int(input())
if math.sqrt(n)==int(math.sqrt(n)):
      print(int(math.sqrt(n))*4)
else:
      l=[]
      x=int(math.sqrt(n))
      for i in range(x,x+2):
            for j in range(x,x+2):
                  if i*j>=n:
                        l.append(2*i+2*j)
      print(min(l))