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 PyPy2 (5.6.0) (judge verdict: Accepted)

#
#   Bad python template TM
#
#       Zeyu, 2019
#

from sys import stdin, stdout, setrecursionlimit

input = stdin.readline
flush = stdout.flush

# setrecursionlimit(1000000)

############################################################

OUT = []


def write(item, sep=""):
    if type(item) is int or type(item) is long:
        OUT.append(str(item))
    elif type(item) is float:
        OUT.append("%.9f" % item)
    elif type(item) is list or type(item) is tuple:
        if len(item) == 0:
            OUT.append(" ")
        elif type(item[0]) is int:
            OUT.append(sep.join(map(str, item)))
        else:
            OUT.append(sep.join(item))
    else:
        OUT.append(item)


def PRINT(sep="\n"):
    print(sep.join(OUT))


GI = lambda: int(input())
GS = lambda: input().rstrip()

gi = lambda: list(map(int, input().split()))
gs = lambda: input().split()

digits = lambda i: list(map(int, str(i)))

############################################################

n = GI()
pts = [gi() for i in range(n)]
while len(pts) < 3:
    pts.append(pts[-1])
    n+=1
def getDist(x,y,z):
    xa,ya = pts[x]
    xb,yb = pts[y]
    xc,yc = pts[z]

    a = pow((xb - xc)**2 + (yb - yc)**2, 0.5)
    b = pow((xa - xc)**2 + (ya - yc)**2, 0.5)
    c = pow((xb - xa)**2 + (yb - ya)**2, 0.5)
    s = (a + b + c) / 2.0
    a,b,c = sorted([a,b,c])
    if s == 0 or a*a + b*b - c*c <= 0:
        return c / 2.0
    return a*b*c / 4.0 / pow(s*(s-a)*(s-b)*(s-c), 0.5)



m = -1
for i in range(n):
    for j in range(i + 1, n):
        for k in range(j + 1, n):
            m = max(m, getDist(i, j, k))
print "%.7f" % m