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:
n=int(input())
xy=[list(map(int,input().split()))for _ in range(n)]
def gaisin(a,b,c,d,e,f):
  if (a-c)*(d-f)==(c-e)*(b-d):return ["ng"]
  aa=a**2
  bb=b**2
  cc=c**2
  dd=d**2
  ee=e**2
  ff=f**2
  py=((e-a)*(aa+bb-cc-dd)-(c-a)*(aa+bb-ee-ff))/(2*((e-a)*(b-d)-(c-a)*(b-f)))
  if a==c:px=(2*(b-f)*py-aa-bb+ee+ff)/(2*(e-a))
  else:px=(2*(b-d)*py-aa-bb+cc+dd)/(2*(c-a))
  return ["ok",px,py]
pxy=[]
for i in range(n-2):
  for j in range(i+1,n-1):
    for k in range(j+1,n):
      x1,y1=xy[i]
      x2,y2=xy[j]
      x3,y3=xy[k]
      gai=gaisin(x1,y1,x2,y2,x3,y3)
      if len(gai)==1:continue
      _,px,py=gai
      pxy.append([px,py])
for i in range(n-1):
  for j in range(i+1,n):
    x1,y1=xy[i]
    x2,y2=xy[j]
    px=(x1+x2)/2
    py=(y1+y2)/2
    pxy.append([px,py])
ans=10**10
for px,py in pxy:
  ans=min(ans,max(((px-x)**2+(py-y)**2)**(0.5)for x,y in xy))
print(ans)