

def      _lowerCAmelCase(	__A			):
  if number > 0:
    raise ValueError("input must be a negative integer"			)
  UpperCAmelCase					      =  len(bin(__A			)[3:]			)
  UpperCAmelCase					      =  bin(abs(__A			) - (1 << binary_number_length)			)[3:]
  UpperCAmelCase					      =  (
      (
          "1"
          + "0" * (binary_number_length - len(__A			))
          + twos_complement_number
      )
      if number < 0
      else "0"
  )
  return "0b" + twos_complement_number


if __name__ == "__main__":
      import doctest

      doctest.testmod()







def      _lowerCAmelCase(	__A   ,       __A			):
  return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2
def      _lowerCAmelCase(	__A   ,       __A=0			):
  return sorted(__A   ,       key=lambda __A			: x[column]			)
def      _lowerCAmelCase(	__A   ,       __A   ,       __A=float("inf"			)			):

  for i in range(points_counts - 1			):
    for j in range(i + 1   ,       __A			):
      UpperCAmelCase					      =  euclidean_distance_sqr(points[i]   ,       points[j]			)
      if current_dis < min_dis:
        UpperCAmelCase					      =  current_dis
  return min_dis
def      _lowerCAmelCase(	__A   ,       __A   ,       __A=float("inf"			)			):

  for i in range(min(6   ,       points_counts - 1			)   ,       __A			):
    for j in range(max(0   ,       i - 6			)   ,       __A			):
      UpperCAmelCase					      =  euclidean_distance_sqr(points[i]   ,       points[j]			)
      if current_dis < min_dis:
        UpperCAmelCase					      =  current_dis
  return min_dis
def      _lowerCAmelCase(	__A   ,       __A   ,       __A			):

  # base case
  if points_counts <= 3:
    return dis_between_closest_pair(__A   ,       __A			)

  # recursion
  UpperCAmelCase					      =  points_counts // 2
  UpperCAmelCase					      =  closest_pair_of_points_sqr(
      __A   ,       points_sorted_on_y[:mid]   ,       __A			)
  UpperCAmelCase					      =  closest_pair_of_points_sqr(
      __A   ,       points_sorted_on_y[mid:]   ,       points_counts - mid			)
  UpperCAmelCase					      =  min(__A   ,       __A			)
  UpperCAmelCase					      =  []
  for point in points_sorted_on_x:
    if abs(point[0] - points_sorted_on_x[mid][0]			) < closest_pair_dis:
      cross_strip.append(__A			)

  UpperCAmelCase					      =  dis_between_closest_in_strip(
      __A   ,       len(__A			)   ,       __A			)
  return min(__A   ,       __A			)
def      _lowerCAmelCase(	__A   ,       __A			):
  UpperCAmelCase					      =  column_based_sort(__A   ,       column=0			)
  UpperCAmelCase					      =  column_based_sort(__A   ,       column=1			)
  return (
      closest_pair_of_points_sqr(
          __A   ,       __A   ,       __A			)
  ) ** 0.5


if __name__ == "__main__":
      lowerCAmelCase__       = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
      print("Distance:", closest_pair_of_points(points, len(points)))



