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 main():
    n=input()
    k=n**(0.5)
    if k-int(k)==0:
        print long(4*(k-1)+4)
    else:
        r=int(k)
        if r*(r+1)>=n:
            print long(2*(2*r-1)+4)
        else:
            print long(4*((r+1)-1)+4)
if __name__ == '__main__':
    main()