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:

Solution:

#include <bits/stdc++.h>

using namespace std;

int main() {
int n;
scanf("%d", &n);
int ans = (int) 1e9;
for (int a = 1; a <= n; a++) {
int b = (n + a - 1) / a;
ans = min(ans, 2 * (a + b));
}
printf("%d\n", ans);
return 0;
}