10832: ABC151 - F - Enclose All
[Creator : ]
Description
Given are $N$ points $(x_i, y_i)$ in a two-dimensional plane.
Find the minimum radius of a circle such that all the points are inside or on it.
Find the minimum radius of a circle such that all the points are inside or on it.
Input
Input is given from Standard Input in the following format:
```
$N$
$x_1$ $y_1$
$:$
$x_N$ $y_N$
```
```
$N$
$x_1$ $y_1$
$:$
$x_N$ $y_N$
```
Output
Print the minimum radius of a circle such that all the $N$ points are inside or on it.
Your output will be considered correct if the absolute or relative error from our answer is at most $10^{-6}$.
Your output will be considered correct if the absolute or relative error from our answer is at most $10^{-6}$.
Constraints
- $2 \leq N \leq 50$
- $0 \leq x_i \leq 1000$
- $0 \leq y_i \leq 1000$
- The given $N$ points are all different.
- The values in input are all integers.
- $0 \leq x_i \leq 1000$
- $0 \leq y_i \leq 1000$
- The given $N$ points are all different.
- The values in input are all integers.
Sample 1 Input
2
0 0
1 0
Sample 1 Output
0.500000000000000000
Both points are contained in the circle centered at $(0.5,0)$ with a radius of $0.5$.
Sample 2 Input
3
0 0
0 1
1 0
Sample 2 Output
0.707106781186497524
Sample 3 Input
10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9
Sample 3 Output
6.726812023536805158
If the absolute or relative error from our answer is at most $10^{-6}$, the output will be considered correct.