"""simple docstring"""


from math import isclose, sqrt






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   point_y / 4 / point_x
  _UpperCAmelCase    			=   2 * normal_gradient / (1 + normal_gradient * normal_gradient)
  _UpperCAmelCase    			=   (1 - normal_gradient * normal_gradient) / (
      1 + normal_gradient * normal_gradient
  )
  _UpperCAmelCase    			=   (sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

  # to find the next point, solve the simultaeneous equations:
  # y^2 + 4x^2 = 100
  # y - b = m * (x - a)
  # ==> A x^2 + B x + C = 0
  _UpperCAmelCase    			=   outgoing_gradient**2 + 4
  _UpperCAmelCase    			=   2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
  _UpperCAmelCase    			=   (point_y - outgoing_gradient * point_x) ** 2 - 1_00

  _UpperCAmelCase    			=   (
      -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
  ) / (2 * quadratic_term)
  _UpperCAmelCase    			=   (
      -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
  ) / (2 * quadratic_term)

  # two solutions, one of which is our input point
  _UpperCAmelCase    			=   x_minus if isclose(lowercase ,lowercase		) else x_plus
  _UpperCAmelCase    			=   point_y + outgoing_gradient * (next_x - point_x)

  return next_x, next_y, outgoing_gradient






def      __UpperCAmelCase       (      lowercase = 1.4 ,lowercase = -9.6		):







  """simple docstring"""
  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   first_x_coord
  _UpperCAmelCase    			=   first_y_coord
  _UpperCAmelCase    			=   (10.1 - point_y) / (0.0 - point_x)

  while not (-0.01 <= point_x <= 0.01 and point_y > 0):
    _UpperCAmelCase			,					_UpperCAmelCase			,					_UpperCAmelCase    			=   next_point(lowercase ,lowercase ,lowercase		)
    num_reflections += 1

  return num_reflections


if __name__ == "__main__":
    print(F'''{solution() = }''')

"""simple docstring"""


from transformers import BertTokenizerFast

from .custom_tokenization import CustomTokenizer


class 							a					(		lowerCAmelCase_ ):
    _snake_case  :	Dict  				=				CustomTokenizer
    pass
