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 numpy as np
def cir(x1, y1, x2, y2, x3, y3):
    """
    3点を通る円の中心と半径を取得
    """
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d==0:
        return None
    x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / (1.0*d)
    y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / (-d*1.0)
    r = ((x - x1) ** 2 + (y - y1) ** 2)**0.5
    return [[x, y], r]
n=int(input())
l=[]
for i in range(n):
    l.append(list(map(float,input().split())))
ans=10**10
for i in range(n):
    for j in range(n):
        for k in range(n):
            if i<j<k:
                z=cir(l[i][0],l[i][1],l[j][0],l[j][1],l[k][0],l[k][1])
                if z:
                    f=0
                    x=z[0][0]
                    y=z[0][1]
                    r=z[1]
                    for m in l:
                        if ((m[0]-x)**2+(m[1]-y)**2)**0.5<=r:
                            f+=1
                    if f==n:
                        ans=min(ans,r)
def cir2(p,q):
    x1=p[0]
    y1=p[1]
    x2=q[0]
    y2=q[1]
    return [(x1+x2)*0.5,(y1+y2)*0.5,(((x1-x2)**2+(y1-y2)**2)**0.5)*0.5]
for i in range(n):
    for j in range(n):
        if i<j:
            z=cir2(l[i],l[j])
            x=z[0]
            y=z[1]
            r=z[2]
            f=0
            for m in l:
                if ((x-m[0])**2+(y-m[1])**2)**0.5<=r:
                    f+=1
            if f==n:
                ans=min(ans,r)
print(ans)