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 itertools
import math

def circle(points):

    x1 = xy[points[0]][0]
    y1 = xy[points[0]][1]
    x2 = xy[points[1]][0]
    y2 = xy[points[1]][1]
    x3 = xy[points[2]][0]
    y3 = xy[points[2]][1]

    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d != 0:
        x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
        y = -(((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2))) / d
        r = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)

    else:
        r = 0
        x = 0
        y = 0

    center = [x, y]
    radius = r

    return center, radius


def check(center, radius):
    flag = 0
    for i in range(n):
        if (xy[i][0] - center[0]) ** 2 + (xy[i][1] - center[1]) ** 2 > radius ** 2:
            break
    else:
        flag = 1

    return flag


n = int(input())
xy = []
for i in range(n):
    xy.append([int(i) for i in input().split()])

ans = float("inf")
for i in itertools.combinations(range(0, n), 2):
    r = math.sqrt((xy[i[0]][0] - xy[i[1]][0]) ** 2 + (xy[i[0]][1] - xy[i[1]][1]) ** 2) / 2
    x = (xy[i[0]][0] + xy[i[1]][0]) / 2
    y = (xy[i[0]][1] + xy[i[1]][1]) / 2
    flag = check([x, y], r)
    if flag == 1:
        ans = min(ans, r)

else:
    for i in itertools.combinations(range(0, n), 3):
        center, radius = circle(i)
        flag = check(center, radius)
        if flag == 1:
            ans = min(ans, radius)

print(ans)