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>
from math import sqrt, floor, ceil


def min_route(n):
    ls, us = floor(sqrt(n)), ceil(sqrt(n))
    p1 = 4 * ls + 2
    p2 = 4 * us
    # print(n, p1, p2)
    if ls < n - ls ** 2:
        return p2
    return min(p1, p2)

def main():
    n = int(input().strip())
    print(min_route(n))


if __name__ == '__main__':
    main()
