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## 1953. Biggest Inscribed Ellipse

Time limit: 1.0 second
Memory limit: 64 MB
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.

### Input

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

### Output

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.

### Sample

inputoutput
```1 1 1
```
```0.000000 0.288675
```
Problem Author: Mikhail Rubinchik (idea by Pavel Ageev)
Problem Source: Ural FU contest. Kontur Cup. Petrozavodsk training camp. Winter 2013
Tags: none