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 sys import stdin, stdout

n = int(stdin.readline())

l, r = 0, n + 1
while r - l > 1:
    m = (r + l) >> 1
    
    if m * m > n:
        r = m
    else:
        l = m

if n > 1:
    ans = 8 + (l - 2) * 4
else:
    ans = 4

n -= l * l
for i in range(l):
    if not i:
        if n:
            ans += 2
            n -= 1
    else:
        if n:
            n -= 1

for i in range(l):
    if not i:
        if n:
            ans += 2
            n -= 1
    else:
        if n:
            n -= 1

stdout.write(str(ans))