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>
import bisect
pre=[0]*1000001
for i in xrange(1,1000001):
    pre[i]=i*i
n=int(raw_input())
ind=bisect.bisect_right(pre,n)
ind=ind-1
rem=n-pre[ind]
l,b=ind,ind
while rem>ind:
    b+=1
    rem=rem-ind
if rem==0:
    peri=2*(l+b)
else:
    peri=(2*(l+b))+2
print peri
