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Points:
20 (partial)

Time limit:
2.0s

Memory limit:
64M

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##### Balkan Olympiad in Informatics: 2011 Day 1, Problem 1

We will consider a convex polygon with vertices. We wish to find the maximum radius such that two circles of radius can be placed entirely inside the polygon without overlapping.

#### Input Specificiation

The first line of input contains the number . Each of the next lines contains a pair of integers , – representing the coordinates of the th point, separated by a space.

#### Output Specification

You should output a single number – the desired radius. Output with a precision of 3 decimals. You will pass a test if the output differs from the true answer by at most 0.001.

#### Constraints

- The points are given in trigonometric (anti-clockwise) order.
- For of tests
- For of tests

#### Sample Input 1

```
4
0 0
1 0
1 1
0 1
```

#### Sample Output 1

`0.293`

#### Explanation for Sample Output 1

The maximum radius is obtained when the centers of the two circles are placed on one of the square's diagonals. The radius can be calculated exactly and it is

#### Sample Input 2

```
4
0 0
3 0
3 1
0 1
```

#### Sample Output 2

`0.500`

#### Sample Input 3

```
6
0 0
8 0
8 6
4 8
2 8
0 4
```

#### Sample Output 3

`2.189`

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