Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides 
and 
.
and .Our goal in this exercise is to write a function that outputs the maximum number of unique pythagorean triangles that can fit inside a circle of radius R, with overlaps are allowed.
For example if 
, the following unique pythagorean triangles can fit inside the circle: , , 
, 
, 
, and 
. Hence, for , the function should return 6.
, the following unique pythagorean triangles can fit inside the circle: , , , , , and . Hence, for , the function should return 6.--------------------
NOTE: Unique means that congruent triangles, even if rotated or reflected, are counted only once.
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