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())

val = []
min_size = []

for i in range(math.trunc(math.sqrt(1000000))+1):
    val.append(i*(i-1)+1)
    min_size.append(4*i)
    val.append(i*i+1)
    min_size.append(4*i + 2)

last = 0

for idx in range(len(val)):
    if n < val[idx]:
        print(last)
        break
    else:
        last = min_size[idx]
