Biggest Inscribed Ellipse

Definition. If F_1, F_2 are two points and R is a positive number such that 2R > |F_1F_2|, then an ellipse can be defined as a set of all points M such that |F_1M| + |F_2M| ≤ 2R.

Your task is to inscribe an ellipse of the biggest possible area into the given triangle.

Input

The input contains three integers a, b, c: lengths of the triangle’s sides (1 ≤ a ≤ b ≤ c ≤ 1000; c < a + b).

Output

Output numbers |F_1F_2| 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.

Examples