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

def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
    """
    3点を通る円の中心と半径を取得
    """
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    if d == 0:
      return (0, 0), 0
    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 = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
    return (x, y), r
  
N = int(input())
XY = [list(map(int, input().split())) for _ in range(N)]
answer = []
if N == 2:
  xy1, xy2 = XY
  x1, y1 = xy1
  x2, y2 = xy2
  answer.append(((x2 - x1)**2 + (y2 - y1)**2)**0.5 / 2)
else:
  for i in range(N):
    xi, yi = XY[i]
    for j in range(i + 1, N):
      xj, yj = XY[j]      
      r = ((xi - xj)**2 + (yi - yj)**2)**0.5/2
      x0, y0 = ((xi + xj) / 2, (yi + yj) / 2)
      flag = 1
      for ii in range(N):
        xii, yii = XY[ii]
        if ((x0 - xii)**2 + (y0 - yii)**2)**0.5 > r:
          flag = 0
          break
      if flag:
        answer.append(r)

  for i in range(N):
    xi, yi = XY[i]
    for j in range(i + 1, N):
      xj, yj = XY[j]
      for k in range(j + 1, N):
        xk, yk = XY[k]
        xy0, r = get_circle_center_and_radius(xi, yi, xj, yj, xk, yk)
        x0, y0 = xy0
        
        if r:
          flag = 1
          for ii in range(N):
            xii, yii = XY[ii]
            if ((x0 - xii)**2 + (y0 - yii)**2)**0.5 > r:
              flag = 0
              break
          if flag:
            answer.append(r)
print(min(answer))