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 math

def f(a,b,x,y):
    ans=math.sqrt( (a-x)*(a-x) + (b-y)*(b-y) )
    return ans

def circumcenter(ax,ay,bx,by,cx,cy):
    d = 2 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by))
    if d==0:
        return (-1,-1)
    ux = ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) * (cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d
    uy = ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) * (ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d
    return (ux, uy)

n=int(input())
x=[]
y=[]
for i in range(n):
    u,v=map(int,input().split())
    x.append(u)
    y.append(v)
if n==2:
    ans=f(x[0],y[0],x[1],y[1])/2
    print("%0.12f"%ans)
else:
    radius=20000
    for i in range(n):
        for j in range(i+1,n):
            for k in range(j+1,n):

                a,b=circumcenter(x[i],y[i],x[j],y[j],x[k],y[k])
                if a==-1 and b==-1:
                    continue
                r=f(a,b,x[i],y[i])

                ff=1
                for l in range(n):
                    if f(a,b,x[l],y[l])>r:
                        ff=0
                        break
                if ff:
                    radius=min(radius,r)
    for i in range(n):
        for j in range(i+1,n):
            a=(x[i]+x[j])/2
            b=(y[i]+y[j])/2
            r=f(x[i],y[i],x[j],y[j])/2
            ff=1
            for k in range(n):
                if f(a,b,x[k],y[k])>r:
                    ff=0
                    break
            if ff:
                radius=min(r,radius)
    print("%0.12f"%radius)