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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# N**3 * log(1500000000)
N = int(input())
XY = [list(map(int, input().split())) for _ in range(N)]
# N = 50
# XY = [(0, i) for i in range(N)]

def distance(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    d = (abs(x1-x2)**2 + abs(y1-y2)**2) ** (1/2)
    return d
def mid_p(p1, p2):
    x1, y1 = p1
    x2, y2 = p2
    m = (x1+x2)/2, (y1+y2)/2
    return m
def is_in_circle(a, center, radius):
    r = all(distance(a_i, center) <= radius for a_i in a)
    return r

min_num = 10**18
for i, p1 in enumerate(XY):
    for j, p2 in enumerate(XY):
        center = mid_p(p1, p2)
        ok = 1500
        ng = 0
        while ok-ng > 10**-7:
            mid = (ok+ng) / 2
            if is_in_circle(XY, center, mid):
                ok = mid
            else:
                ng = mid
        min_num = min(min_num, ok)

print(min_num)