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 approach_sum_squares(n):
    i = 1
    s = 1
    for d in range(3, n, 2):
        s += d
        if s > n:
            break
        i += 1
    return i

def min_perim(n):
    k = approach_sum_squares(n)
    n -= k*k
    picks = 4 * k
    if n == 0:
        return picks
    if n <= k:
        return picks + 2
    if n > k:
        return picks + 4

if __name__ == "__main__":
    n = int(input().strip())
    print(min_perim(n))
