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:
from math import sqrt
N=int(input())
XY=[tuple(map(int,input().split())) for _ in range(N)]

def calc(r):
  lst=[]
  for i in range(N-1):
    x1=XY[i][0]
    y1=XY[i][1]
    for j in range(i+1,N):
      x2=XY[j][0]
      y2=XY[j][1]
      diff=sqrt((x1-x2)**2+(y1-y2)**2)
      if diff>2*r:
        return False
      
      h=sqrt(r**2-diff**2/4)
      if x1==x2:
        ny=(y1+y2)/2
        lst.append([x1-h,ny])
        lst.append([x1+h,ny])
      elif y1==y2:
        nx=(x1+x2)/2
        lst.append([nx,y1-h])
        lst.append([nx,y1+h])
      else:
        a=(y2-y1)/(x2-x1)
        b=-1/a
        size=sqrt(1+b**2)
        dx=h/size
        dy=dx*b
        nx=(x1+x2)/2
        ny=(y1+y2)/2
        lst.append([nx+dx,ny+dy])
        lst.append([nx-dx,ny-dy])
  nr=r+10**(-9)
  for x,y in lst:
    flag=True
    for X,Y in XY:
      tmp=(x-X)**2+(y-Y)**2
      if tmp>nr**2:
        flag=False
        break
    if flag:
      return True
  return False
l=0
r=1000
for i in range(100):
  mid=(l+r)/2
  if calc(mid):
    r=mid
  else:
    l=mid
print(r)