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())
sqr_lnt = math.floor(math.sqrt(n))
sqr_parameter = 4*sqr_lnt
#4
# 4print(sqr_parameter)
res = n - (sqr_lnt**2)

if res > sqr_lnt:
    res1 = res - sqr_lnt
    current_parameter = 2*(sqr_lnt+(sqr_lnt+1))
    new_parameter = 2*(res1 + 1) - 2*(res1)
    fin_parameter = current_parameter+ new_parameter    
elif res  == 0:
    fin_parameter  = 4*(sqr_lnt)
elif res < sqr_lnt:
    newer_parameter = 2*(res+1) - 2*(res)
    fin_parameter = sqr_parameter + newer_parameter
elif res == sqr_lnt:
    fin_parameter = 2*(sqr_lnt+(sqr_lnt+1))


print(fin_parameter)