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

def f(p,q):
    num=0
    for ppp,qqq in xy:
        num=max(num,(p-ppp)**2+(q-qqq)**2)
    return num

inf=float("inf")
N=int(input())
xy=[list(map(int,input().split())) for i in range(N)]
ans=inf
if N==2:
    x=(xy[0][0]+xy[1][0])/2
    y=(xy[0][1]+xy[1][1])/2
    p,q=xy[0]
    num=(x-p)**2+(y-q)**2
    print(num**0.5)
    sys.exit()
for i in range(N-2):
    for j in range(i+1,N-1):
        for k in range(j+1,N):
            p,q=xy[i]
            r,s=xy[j]
            v,w=xy[k]
            a=2*v-2*r
            b=2*w-2*s
            c=v**2+w**2-r**2-s**2
            d=2*p-2*r
            e=2*q-2*s
            f=p**2+q**2-r**2-s**2
            if a*e==b*d:
                num=0
            else:
                x=(c*e-b*f)/(a*e-b*d)
                y=(c*d-a*f)/(b*d-a*e)
                num=0
                for ppp,qqq in xy:
                    num=max(num,(x-ppp)**2+(y-qqq)**2)
                ans=min(ans,num)
            x,y=(p+r)/2,(q+s)/2
            num=0
            for ppp,qqq in xy:
                num=max(num,(x-ppp)**2+(y-qqq)**2)
            ans=min(ans,num)
            x,y=(p+v)/2,(q+w)/2
            num=0
            for ppp,qqq in xy:
                num=max(num,(x-ppp)**2+(y-qqq)**2)
            ans=min(ans,num)
            x,y=(r+v)/2,(s+w)/2
            num=0
            for ppp,qqq in xy:
                num=max(num,(x-ppp)**2+(y-qqq)**2)
            ans=min(ans,num)
print(ans**0.5)