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USU Junior Contest, October 2006

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B. Fire Circle

Time limit: 1.0 second
Memory limit: 64 MB
Lich Sandro investigates the magic of fire. He is standing in the center of a huge square hall with floor space one million square kilometers. The floor of the hall is paved with square 1 × 1 meter stone slabs. When Sandro waves his staff, a fire circle of radius R meters springs up around him. The center of the circle coincides with the center of the hall and is located at the point of contact of four slabs. Sandro wants to calculate the number of slabs damaged by the fire. A slab is assumed to be damaged if it has at least two common points with the fire circle. The figure shows as an example the slabs damaged by the fire circle of radius 4:
Problem illustration

Input

The input contains the radius of the fire circle R > 0. This is an integer not exceeding 105.

Output

Output the number of damaged slabs.

Samples

inputoutput
2
16
4
60
Problem Author: Alexander Ipatov
Problem Source: XIII-th USU Junior Contest, October 2006
To submit the solution for this problem go to the Problem set: 1490. Fire Circle