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

def gaisin(a, b, c): #3点の外心を求める
  A = a[0] ** 2 + a[1] ** 2 - b[0] ** 2 - b[1] ** 2
  B = b[0] ** 2 + b[1] ** 2 - c[0] ** 2 - c[1] ** 2
  x = [2 * (b[0] - a[0]), 2 * (c[0] - b[0])]
  y = [2 * (b[1] - a[1]), 2 * (c[1] - b[1])]
  return renritu(x, y, [A, B])

def renritu(x, y, z): #連立方程式を解く
  k = x[1] * y[0] - x[0] * y[1]
  if k == 0: return False, 0, 0
  Cx = -(y[0] * z[1] - y[1] * z[0]) / k
  Cy = (x[0] * z[1] - x[1] * z[0]) / k
  return True, Cx, Cy

def nasu(a, b, c):
  f, Cx, Cy = gaisin(a, b, c)
  if f: return honyamorake(Cx, Cy)
  else: return 10 ** 10

def honya(x, y, Cx, Cy):
  return ((x - Cx) ** 2 + (y - Cy) ** 2) ** (1 / 2)

def honyaraka(a, b):
  Cx = (a[0] + b[0]) / 2
  Cy = (a[1] + b[1]) / 2
  return honyamorake(Cx, Cy)

def honyamorake(Cx, Cy):
  r = honya(xy[0][0], xy[0][1], Cx, Cy)
  for i in range(1, N):
    r = max(r, honya(xy[i][0], xy[i][1], Cx, Cy))
  return r

ans = 10 ** 10
for i in range(N - 2):
  for j in range(i + 1, N - 1):
    for k in range(j + 1, N):
      ans = min(ans, nasu(xy[i], xy[j], xy[k]))
for i in range(N - 1):
  for j in range(i + 1, N):
    ans = min(ans, honyaraka(xy[i], xy[j]))

print(ans)