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:
def calc1(x1,y1,x2,y2,x3,y3):
  a=x1-x2
  b=y1-y2
  c=x2-x3
  d=y2-y3
  if a*d-b*c==0:
    return [0,0,0]
  x4=(d*((x1**2+y1**2)-(x2**2+y2**2))-b*((x2**2+y2**2)-(x3**2+y3**2)))/(2*(a*d-b*c))
  y4=(-c*((x1**2+y1**2)-(x2**2+y2**2))+a*((x2**2+y2**2)-(x3**2+y3**2)))/(2*(a*d-b*c))
  r=((x1-x4)**2+(y1-y4)**2)**0.5
  return [x4,y4,r]
def calc2(x1,y1,x2,y2):
  r=(((x2-x1)**2+(y2-y1)**2)**0.5)/2
  return [(x1+x2)/2,(y1+y2)/2,r]

eps=10**(-9)
n=int(input())
arr=[list(map(int,input().split())) for _ in range(n)]
ans=10**18
for i in range(n):
  for j in range(i+1,n):
    for k in range(j+1,n):
      cx,cy,r=calc1(arr[i][0],arr[i][1],arr[j][0],arr[j][1],arr[k][0],arr[k][1])
      for l in range(n):
        tx,ty=arr[l]
        if ((cx-tx)**2+(cy-ty)**2)>r**2+eps:
          break
      else:
        ans=min(ans,r)
for i in range(n):
  for j in range(i+1,n):
    cx,cy,r=calc2(arr[i][0],arr[i][1],arr[j][0],arr[j][1])
    for k in range(n):
      tx,ty=arr[k]
      if ((cx-tx)**2+(cy-ty)**2)>r**2+eps:
        break
    else:
      ans=min(ans,r)
print(ans)