Competitions

# 2013 Petrozavodsk, February 2

# Biggest Inscribed Ellipse

**Definition**. If **F _{1}**,

**F**are two points and

_{2}**R**is a positive number such that

**2R**>

**|F**, then an ellipse can be defined as a set of all points

_{1}F_{2}|**M**such that

**|F**≤

_{1}M| + |F_{2}M|**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 _{1}F_{2}|** and

**R**, which describe the requested ellipse. The answer must be given with absolute or relative error not exceeding

**10**. It is guaranteed that the answer is unique.

^{−6}Input example #1

1 1 1

Output example #1

0.0000000000 0.2886751346