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())
l = [[0, 0] for _ in range(n)]
for i in range(n):
  x, y = map(int, input().split())
  l[i][0] = x
  l[i][1] = y

import math
if n == 2:
  r = math.sqrt((l[1][0]-l[0][0])**2+(l[1][1]-l[0][1])**2)/2
  print(r)
  exit()

ans = float('inf')
import itertools
combs = list(itertools.combinations(range(n), 3))
for comb in combs:
  x0, y0 = l[comb[0]]
  x1, y1 = l[comb[1]]
  x2, y2 = l[comb[2]]
  
  a = x1 - x0
  b = y1 -y0
  p = (x1**2-x0**2+y1**2-y0**2)/2
  
  c = x2 - x0  
  d = y2 -y0
  q = (x2**2-x0**2+y2**2-y0**2)/2
  
  if a*d - b*c == 0:
    continue
  xc = (p*d-q*b)/(a*d-b*c)
  yc = (-p*c+q*a)/(a*d-b*c)
  r = math.sqrt((x0-xc)**2+(y0-yc)**2)
  for i in range(n):
    x, y = l[i]
    if math.sqrt((x-xc)**2+(y-yc)**2) > r:
      break
  else:
    ans = min(ans, r)

combs = list(itertools.combinations(range(n), 2))
for comb in combs:
  x0, y0 = l[comb[0]]
  x1, y1 = l[comb[1]]
  xc = (x0+x1)/2
  yc = (y0+y1)/2
  r = math.sqrt((x0-xc)**2+(y0-yc)**2)
  for i in range(n):
    x, y = l[i]
    if math.sqrt((x-xc)**2+(y-yc)**2) > r:
      break
  else:
    ans = min(ans, r)
print(ans)