F - Enclose All

Score : $600$ points

Problem Statement

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.

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.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$:$

$x_N$ $y_N$

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 $10^{-6}$.

2
0 0
1 0

0.500000000000000000

Both points are contained in the circle centered at $(0.5,0)$ with a radius of $0.5$.

3
0 0
0 1
1 0

0.707106781186497524

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

6.726812023536805158

If the absolute or relative error from our answer is at most $10^{-6}$, the output will be considered correct.