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:
EPS=10**(-9)

def outercenter(z1,z2,z3):
    w=(z1-z2)*z3.conjugate()+(z2-z3)*z1.conjugate()+(z3-z1)*z2.conjugate()
    if w==0:
        return (False,0,0)
    else:
        W=(z1-z2)*abs(z3)**2+(z2-z3)*abs(z1)**2+(z3-z1)*abs(z2)**2
        return (True,W/w,abs(z1-W/w))

def is_in_circle(c,r,z):
    return r+EPS>abs(z-c)

N=int(input())
z=[0 for i in range(0,N)]
for i in range(0,N):
    x,y=map(int,input().split())
    z[i]=complex(x,y)

ans=float('inf')
for i in range(0,N-1):
    for j in range(i+1,N):
        mid=(z[i]+z[j])/2
        r=abs(z[i]-mid)
        for k in range(0,N):
            if not is_in_circle(mid,r,z[k]):
                break
        else:
            ans=min(ans,r)

for i in range(0,N-2):
    for j in range(i+1,N-1):
        for k in range(j+1,N):
            info=outercenter(z[i],z[j],z[k])
            if info[0]:
                c=info[1]
                r=info[2]
                for l in range(0,N):
                    if not is_in_circle(c,r,z[l]):
                        break
                else:
                    ans=min(ans,r)

print(ans)