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 math


def min_radius(k, x, y):
    dis = [0] * k

    center_x = (min(x) + max(x)) / float(2)
    center_y = (min(y) + max(y)) / float(2)

    for i in range(k):
        dis[i] = math.sqrt(math.pow(center_x - x[i], float(2)) + math.pow(center_y - y[i], float(2)))

    return max(dis)


k = int(input())

x = [0] * k
y = [0] * k

for i in range(k):
    x[i], y[i] = map(int, input().split(' '))

print("{:.12f}".format(min_radius(k, x, y)))