Problem:
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}.

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.

Solution in Python (3.4.3) (judge verdict: Accepted)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# 2点の直径または3点の外心をテスト

import itertools
import numpy as np

N = int(readline())
m = map(int,read().split())
Z = [x + y * 1j for x,y in zip(m,m)]

def find_O(z0,z1,z2):
    z1 -= z0; z2 -= z0
    if abs((z1 * z2.conjugate()).imag) < 0.5:
        # 同一直線上
        return None
    num = z1 * z2 * (z1-z2).conjugate()
    den = z1.conjugate() * z2
    den -= den.conjugate()
    return (num / den) + z0

A = []
for comb in itertools.combinations(Z,3):
    O = find_O(*comb)
    if O is None:
        continue
    A.append(O)
    
for z1,z2 in itertools.combinations(Z,2):
    O = (z1 + z2) / 2
    A.append(O)

Z = np.array(Z); A = np.array(A)

answer = np.abs((Z[:,None] - A[None,:])).max(axis = 0).min()
print(answer)