



from math import isclose, sqrt






def  lowerCamelCase_	(      lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float				)       ->							tuple[float, float, float]:

							'''simple docstring'''






							A      						=    point_y / 4 / point_x
							A      						=    2 * normal_gradient / (1 + normal_gradient * normal_gradient)
							A      						=    (1 - normal_gradient * normal_gradient) / (
							    1 + normal_gradient * normal_gradient
							)
							A      						=    (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
							A      						=    outgoing_gradient**2 + 4
							A      						=    2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
							A      						=    (point_y - outgoing_gradient * point_x) ** 2 - 100

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

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

							return next_x, next_y, outgoing_gradient






def  lowerCamelCase_	(      lowerCAmelCase__	:	float = 1.4			,	lowerCAmelCase__	:	float = -9.6				)       ->							int:

							'''simple docstring'''






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

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

							return num_reflections


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




import unittest

from diffusers.pipelines.pipeline_utils import is_safetensors_compatible



class        lowerCAmelCase__					(  unittest.TestCase       ):


				def __UpperCamelCase						(							self      :  List[str]       )		->     Any:
											A      						=    [
											    'safety_checker/pytorch_model.bin',
											    'safety_checker/model.safetensors',
											    'vae/diffusion_pytorch_model.bin',
											    'vae/diffusion_pytorch_model.safetensors',
											    'text_encoder/pytorch_model.bin',
											    'text_encoder/model.safetensors',
											    'unet/diffusion_pytorch_model.bin',
											    'unet/diffusion_pytorch_model.safetensors',
											]
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  str       )		->     List[Any]:
											A      						=    [
											    'unet/diffusion_pytorch_model.bin',
											    'unet/diffusion_pytorch_model.safetensors',
											]
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Any       )		->     Tuple:
											A      						=    [
											    'safety_checker/pytorch_model.bin',
											    'safety_checker/model.safetensors',
											    'vae/diffusion_pytorch_model.bin',
											    'vae/diffusion_pytorch_model.safetensors',
											    'text_encoder/pytorch_model.bin',
											    'text_encoder/model.safetensors',
											    'unet/diffusion_pytorch_model.bin',
											    # Removed: 'unet/diffusion_pytorch_model.safetensors',
											]
											self.assertFalse(is_safetensors_compatible(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Dict       )		->     Any:
											A      						=    [
											    'text_encoder/pytorch_model.bin',
											    'text_encoder/model.safetensors',
											]
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Optional[int]       )		->     List[str]:
											A      						=    [
											    'safety_checker/pytorch_model.bin',
											    'safety_checker/model.safetensors',
											    'vae/diffusion_pytorch_model.bin',
											    'vae/diffusion_pytorch_model.safetensors',
											    'text_encoder/pytorch_model.bin',
											    # Removed: 'text_encoder/model.safetensors',
											    'unet/diffusion_pytorch_model.bin',
											    'unet/diffusion_pytorch_model.safetensors',
											]
											self.assertFalse(is_safetensors_compatible(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  List[str]       )		->     List[str]:
											A      						=    [
											    'safety_checker/pytorch_model.fp16.bin',
											    'safety_checker/model.fp16.safetensors',
											    'vae/diffusion_pytorch_model.fp16.bin',
											    'vae/diffusion_pytorch_model.fp16.safetensors',
											    'text_encoder/pytorch_model.fp16.bin',
											    'text_encoder/model.fp16.safetensors',
											    'unet/diffusion_pytorch_model.fp16.bin',
											    'unet/diffusion_pytorch_model.fp16.safetensors',
											]
											A      						=    'fp16'
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Optional[Any]       )		->     Optional[Any]:
											A      						=    [
											    'unet/diffusion_pytorch_model.fp16.bin',
											    'unet/diffusion_pytorch_model.fp16.safetensors',
											]
											A      						=    'fp16'
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  int       )		->     Optional[int]:
											# pass variant but use the non-variant filenames
											A      						=    [
											    'unet/diffusion_pytorch_model.bin',
											    'unet/diffusion_pytorch_model.safetensors',
											]
											A      						=    'fp16'
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Any       )		->     List[str]:
											A      						=    [
											    'safety_checker/pytorch_model.fp16.bin',
											    'safety_checker/model.fp16.safetensors',
											    'vae/diffusion_pytorch_model.fp16.bin',
											    'vae/diffusion_pytorch_model.fp16.safetensors',
											    'text_encoder/pytorch_model.fp16.bin',
											    'text_encoder/model.fp16.safetensors',
											    'unet/diffusion_pytorch_model.fp16.bin',
											    # Removed: 'unet/diffusion_pytorch_model.fp16.safetensors',
											]
											A      						=    'fp16'
											self.assertFalse(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  Optional[Any]       )		->     Optional[int]:
											A      						=    [
											    'text_encoder/pytorch_model.fp16.bin',
											    'text_encoder/model.fp16.safetensors',
											]
											A      						=    'fp16'
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  List[str]       )		->     int:
											# pass variant but use the non-variant filenames
											A      						=    [
											    'text_encoder/pytorch_model.bin',
											    'text_encoder/model.safetensors',
											]
											A      						=    'fp16'
											self.assertTrue(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  List[str]       )		->     Optional[Any]:
											A      						=    [
											    'safety_checker/pytorch_model.fp16.bin',
											    'safety_checker/model.fp16.safetensors',
											    'vae/diffusion_pytorch_model.fp16.bin',
											    'vae/diffusion_pytorch_model.fp16.safetensors',
											    'text_encoder/pytorch_model.fp16.bin',
											    # 'text_encoder/model.fp16.safetensors',
											    'unet/diffusion_pytorch_model.fp16.bin',
											    'unet/diffusion_pytorch_model.fp16.safetensors',
											]
											A      						=    'fp16'
											self.assertFalse(is_safetensors_compatible(__UpperCamelCase						, variant=__UpperCamelCase       )       )