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 math
import itertools

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

if N == 2:
  x1,y1 = l[0]
  x2,y2 = l[1]
  print( 0.5 * math.hypot(x1-x2,y1-y2))
  
else:
  ans = float("INF")
  l_ = itertools.combinations(l,3)
  for points in l_:
    a,b = points[0]
    c,d = points[1]
    e,f = points[2]
    
    if (e-a)*(b-d) == (c-a)*(b-f):
      continue
    else:
      aa = a * a
      bb = b * b
      cc = c * c
      dd = d * d
      ee = e * e
      ff = f * f

      py = ((e - a) * (aa + bb - cc - dd) - (c - a) * (aa + bb - ee- ff)) / (2 * (e - a)*(b - d) - 2 * (c - a) * (b - f))

      px = (2 * (b - f) * py - aa - bb + ee + ff) / (2 * (e - a)) \
          if (c == a) else (2 * (b - d) * py - aa - bb + cc + dd) / (2 * (c - a))

      r = math.hypot(px - a, py - b) + 10**(-7)
    flag = 1
    for point in l:
      if flag:
        s,t = point
        if math.hypot(px - s, py - t) > r:
          flag = 0
    if flag:
      ans = min(r,ans)
      
  l_ = itertools.combinations(l,2)
  for points in l_:
    a,b = points[0]
    c,d = points[1]
    
    
    px,py = (a+c)/2,(b+d)/2

    r = math.hypot(px - a, py - b) + 10**(-7)
    flag = 1
    for point in l:
      if flag:
        s,t = point
        if math.hypot(px - s, py - t) > r:
          flag = 0
    if flag:
      ans = min(r,ans)
    
  print(ans)