Lazy Security Guard

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:

inputFormat

Input

Input will consist of a single integer N (1 ≤ N ≤ 106), the number of city blocks that must be enclosed by the route.

outputFormat

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:

样例

22

20

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