Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in PYTHON3):

Solution:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


from math import sqrt
eps = 10**-10
# eps = sys.float_info.epsilon
def crosscl(cx, cy, r, x1, y1, x2, y2):
    xd = x2 - x1; yd = y2 - y1
    X = x1 - cx; Y = y1 - cy
    a = xd**2 + yd**2
    b = xd * X + yd * Y
    c = X**2 + Y**2 - r**2
    # D = 0の時は1本で、D < 0の時は存在しない
    D = (b**2 - a*c)
    if D<0:
        return None, None
    s1 = (-b + sqrt(D)) / a
    s2 = (-b - sqrt(D)) / a
    return (x1 + xd*s1, y1 + yd*s1), (x1 + xd*s2, y1 + yd*s2)

def crosscc(x1,y1,r1,x2,y2,r2):
    k = -2*(x1-x2)
    l = -2*(y1-y2)
    m = x1**2 - x2**2 + y1**2 - y2**2 - r1**2 + r2**2
    if k==0:
        p1 = (0, -m/l)
        p2 = (100, -m/l)
    elif l==0:
        p1 = (-m/k, 0)
        p2 = (-m/k, 100)
    else:
        p1 = (0, -m/l)
        p2 = (1, -(m+k)/l)
    return crosscl(x1,y1,r1,*p1,*p2)

N = int(input())
xy = [None]*N
for i in range(N):
    x,y = map(int, input().split())
    xy[i] = (x,y)
def sub(r):
    kouho = xy[:]
    for i in range(N):
        for j in range(i+1, N):
            p1, p2 = crosscc(xy[i][0], xy[i][1], r, xy[j][0], xy[j][1], r)
            if p1 is not None:
                kouho.append(p1)
                kouho.append(p2)
    ans = False
#     print(kouho)
    for k in kouho:
        for x,y in xy:
            if (k[0]-x)**2 + (k[1]-y)**2 <= (r**2) * (1+eps):
                pass
            else:
                break
        else:
            ans = True
    return ans
lb = 0
ub = 2000
while abs(lb-ub)>10**-8:
    mm = (lb+ub)/2
    if sub(mm):
        ub = mm
    else:
        lb = mm
print(ub)