


from math import isclose, sqrt
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     snake_case					=    point_y / 4 / point_x
     snake_case					=    2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     snake_case					=    (1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     snake_case					=    (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
     snake_case					=    outgoing_gradient**2 + 4
     snake_case					=    2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     snake_case					=    (point_y - outgoing_gradient * point_x) ** 2 - 1_00

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

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

     return next_x, next_y, outgoing_gradient
def       UpperCAmelCase__						(UpperCamelCase_ = 1.4							,UpperCamelCase_ = -9.6    ):



     """simple docstring"""






     snake_case					=    0
     snake_case					=    first_x_coord
     snake_case					=    first_y_coord
     snake_case					=    (10.1 - point_y) / (0.0 - point_x)

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

     return num_reflections


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








import warnings

from ...utils import logging
from .image_processing_beit import BeitImageProcessor


_SCREAMING_SNAKE_CASE      :			List[str]      				=   logging.get_logger(__name__)

class   A__ (   snake_case__     ):







    """simple docstring"""

    def __init__(	self      , *__snake_case      , **__snake_case   ):
         warnings.warn(
             '''The class BeitFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please'''
             ''' use BeitImageProcessor instead.'''      , __snake_case      , )
         super().__init__(*__snake_case      , **__snake_case   )




