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: Wrong Answer)

import sys
import numpy as np

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

N = ir()
XY = np.array([lr() for _ in range(N)])
X = XY[:, 0]
Y = XY[:, 1]
# 円の中心
cen_X = (X.max() + X.min()) / 2
cen_Y = (Y.max() + Y.min()) / 2
# 2分探索
def check(R):
    bool = True
    for x, y in XY:
        if (cen_X - x) ** 2 + (cen_Y - y) ** 2 > R ** 2:
            bool = False
    return bool

left = 0 #NG
right = 1000 #OK
while right > left + 0.0000000001:
    mid = (left + right) / 2
    if check(mid):
        right = mid
    else:
        left = mid

print(right)
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