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 10⁻⁶. It is guaranteed that the answer is unique.