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 itertools

N = int(input())
XY = [tuple(map(int,input().split())) for _ in range(N)]

def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
  d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
  x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
  y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
  r = ((x - x1) ** 2 + (y - y1) ** 2) ** 0.5
  return x, y, r

def check_line(x1,y1,x2,y2,x3,y3):
  if x1 == x2 == x3:
    return True
  elif y1 == y2 == y3:
    return True
  elif (y2-y1)*(x3-x1) == (y3-y1)*(x2-x1):
    return True
  else:
    return False

def check_r(x,y,r):
  res = True
  for i in range(N):
    x1,y1 = XY[i]
    if ((x-x1)**2+(y-y1)**2)**0.5 > r:
      res = False
      break
  return res

mnr = float('inf')

for i,j in list(itertools.combinations(range(N),2)):
  x1,y1 = XY[i]
  x2,y2 = XY[j]
  x = (x1+x2)/2
  y = (y1+y2)/2
  r = (((x2-x1)**2+(y2-y1)**2)**0.5)/2
  if check_r(x,y,r) and mnr > r:
    mnr = r    

for i,j,k in list(itertools.combinations(range(N),3)):
  x1,y1 = XY[i]
  x2,y2 = XY[j]
  x3,y3 = XY[k]
  if check_line(x1,y1,x2,y2,x3,y3):
    continue
  x,y,r = get_circle_center_and_radius(x1,y1,x2,y2,x3,y3)
  if check_r(x,y,r) and mnr > r:
    mnr = r

print(mnr)