Lich Sandro investigates the magic of fire. He is standing in the
center of a huge square hall with floor space 1030 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:
The input contains the radius of the fire circle R > 0.
This is an integer not exceeding 109.
Output the number of damaged slabs.
This problem is the same as “Fire Circle
” but with bigger limitations.
Problem Author: Alexander Ipatov