Definition. If F1, F2 are two points and R
is a positive number such that 2R > |F1F2|, then an ellipse
can be defined as a set of all points M such that |F1M| + |F2M| ≤ 2R.
Your task is to inscribe an ellipse of the biggest possible area into
the given triangle.
The input contains three integers a, b, c:
lengths of the triangle’s sides
(1 ≤ a ≤ b ≤ c ≤ 1000; c < a + b).
Output numbers |F1F2| and R, which describe the requested ellipse.
The answer must be given with absolute or relative error not exceeding
It is guaranteed that the answer is unique.
1 1 1
Problem Author: Mikhail Rubinchik (idea by Pavel Ageev)
Problem Source: Ural FU contest. Kontur Cup. Petrozavodsk training camp. Winter 2013