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>
n = int(input())

if n == 1:
    print(4)
elif n == 2:
    print(6)
elif n == 3:
    print(8)
else:
    i = 2
    while i * i < n:
        i += 1
    
    if (i * i > n):
        i -= 1
    
    c = 4 * i
    d = n - i * i
    
    
    if (d > 0):
        l = d // i
        if d % i == 0:
            c += l * 2
        else:
            c += (l + 1) * 2
    
    print(c)
    