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.

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}.

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.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

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

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

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

Sample Output 3

6.726812023536805158

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

见题面 Input 部分

见题面 Output 部分