Problem2933--Blocked Points

2933: Blocked Points

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:

  • the Euclidean distance between A and B is one unit and neither A nor B is blocked;
  • or there is some integral point C, such that A is 4-connected with C, and C is 4-connected with B.

Let's assume that the plane doesn't contain blocked points. Consider all the integral points of the plane whose Euclidean distance from the origin is no more than n, we'll name these points special. Chubby Yang wants to get the following property: no special point is 4-connected to some non-special point. To get the property she can pick some integral points of the plane and make them blocked. What is the minimum number of points she needs to pick?

Input

The first line contains an integer n (0≤n≤4·107).

Output

Print a single integer − the minimum number of points that should be blocked.

Examples
Input
1
Output
4
Input
2
Output
8
Input
3
Output
16

Source/Category

 
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