
from math import isclose, sqrt






def        a_		(       __lowercase   :	int       ,					__lowercase   :	str       ,					__lowercase   :	Tuple ) ->  tuple[float, float, float]:
			_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 - 100

			_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(__a       ,					__a ) else x_plus
			_snake_case		=			point_y + outgoing_gradient * (next_x - point_x)

			return next_x, next_y, outgoing_gradient






def        a_		(       __lowercase   :	str = 1.4       ,					__lowercase   :	int = -9.6 ) ->  int:
			_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 (-0.0_1 <= point_x <= 0.0_1 and point_y > 0):
						_snake_case		=			next_point(__a       ,					__a       ,					__a )
						num_reflections += 1

			return num_reflections


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



'''simple docstring'''
import json
import pathlib
import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision, slow
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
		import torch

if is_vision_available():
		from PIL import Image

		from transformers import ConditionalDetrImageProcessor
class    lowercase	(							unittest.TestCase					):

		"""simple docstring"""

		def __init__(		self    ,   UpperCamelCase_    ,   UpperCamelCase_=7    ,   UpperCamelCase_=3    ,   UpperCamelCase_=30    ,   UpperCamelCase_=400    ,   UpperCamelCase_=True    ,   UpperCamelCase_=None    ,   UpperCamelCase_=True    ,   UpperCamelCase_=[0.5, 0.5, 0.5]    ,   UpperCamelCase_=[0.5, 0.5, 0.5]    ,   UpperCamelCase_=True    ,   UpperCamelCase_=1 / 255    ,   UpperCamelCase_=True    ,   ):

							'''simple docstring'''


							UpperCamelCase__   :Dict												= size if size is not None else {'''shortest_edge''': 18, '''longest_edge''': 1333}
							UpperCamelCase__   :str												= parent
							UpperCamelCase__   :List[Any]												= batch_size
							UpperCamelCase__   :Dict												= num_channels
							UpperCamelCase__   :str												= min_resolution
							UpperCamelCase__   :Optional[Any]												= max_resolution
							UpperCamelCase__   :int												= do_resize
							UpperCamelCase__   :Optional[Any]												= size
							UpperCamelCase__   :Tuple												= do_normalize
							UpperCamelCase__   :List[Any]												= image_mean
							UpperCamelCase__   :Dict												= image_std
							UpperCamelCase__   :Union[str, Any]												= do_rescale
							UpperCamelCase__   :Union[str, Any]												= rescale_factor
							UpperCamelCase__   :Union[str, Any]												= do_pad




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							return {
							    "do_resize": self.do_resize,
							    "size": self.size,
							    "do_normalize": self.do_normalize,
							    "image_mean": self.image_mean,
							    "image_std": self.image_std,
							    "do_rescale": self.do_rescale,
							    "rescale_factor": self.rescale_factor,
							    "do_pad": self.do_pad,
							}




		def     lowerCAmelCase__				(		self    ,   UpperCamelCase_    ,   UpperCamelCase_=False							):

							'''simple docstring'''


							if not batched:
												UpperCamelCase__   :List[str]												= image_inputs[0]
												if isinstance(UpperCamelCase_    ,   Image.Image							):
																	UpperCamelCase__					,				UpperCamelCase__   :List[str]												= image.size
												else:
																	UpperCamelCase__					,				UpperCamelCase__   :List[Any]												= image.shape[1], image.shape[2]
												if w < h:
																	UpperCamelCase__   :int												= int(self.size['''shortest_edge'''] * h / w							)
																	UpperCamelCase__   :Dict												= self.size['''shortest_edge''']
												elif w > h:
																	UpperCamelCase__   :int												= self.size['''shortest_edge''']
																	UpperCamelCase__   :Tuple												= int(self.size['''shortest_edge'''] * w / h							)
												else:
																	UpperCamelCase__   :str												= self.size['''shortest_edge''']
																	UpperCamelCase__   :str												= self.size['''shortest_edge''']

							else:
												UpperCamelCase__   :Any												= []
												for image in image_inputs:
																	UpperCamelCase__					,				UpperCamelCase__   :Dict												= self.get_expected_values([image]							)
																	expected_values.append((expected_height, expected_width)							)
												UpperCamelCase__   :List[Any]												= max(UpperCamelCase_    ,   key=lambda UpperCamelCase_							: item[0]							)[0]
												UpperCamelCase__   :Optional[int]												= max(UpperCamelCase_    ,   key=lambda UpperCamelCase_							: item[1]							)[1]

							return expected_height, expected_width



@require_torch
@require_vision
class    lowercase	(							A__	,		unittest.TestCase					):

		"""simple docstring"""

		_a     =				ConditionalDetrImageProcessor if is_vision_available() else None




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :List[Any]												= ConditionalDetrImageProcessingTester(self							)




		@property
		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							return self.image_processor_tester.prepare_image_processor_dict()




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :Tuple												= self.image_processing_class(**self.image_processor_dict							)
							self.assertTrue(hasattr(UpperCamelCase_    ,   '''image_mean'''							)							)
							self.assertTrue(hasattr(UpperCamelCase_    ,   '''image_std'''							)							)
							self.assertTrue(hasattr(UpperCamelCase_    ,   '''do_normalize'''							)							)
							self.assertTrue(hasattr(UpperCamelCase_    ,   '''do_resize'''							)							)
							self.assertTrue(hasattr(UpperCamelCase_    ,   '''size'''							)							)




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :Optional[int]												= self.image_processing_class.from_dict(self.image_processor_dict							)
							self.assertEqual(image_processor.size    ,   {'''shortest_edge''': 18, '''longest_edge''': 1333}							)
							self.assertEqual(image_processor.do_pad    ,   UpperCamelCase_							)

							UpperCamelCase__   :List[str]												= self.image_processing_class.from_dict(
							    self.image_processor_dict    ,   size=42    ,   max_size=84    ,   pad_and_return_pixel_mask=UpperCamelCase_							)
							self.assertEqual(image_processor.size    ,   {'''shortest_edge''': 42, '''longest_edge''': 84}							)
							self.assertEqual(image_processor.do_pad    ,   UpperCamelCase_							)




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							pass




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :Dict												= self.image_processing_class(**self.image_processor_dict							)
							# create random PIL images
							UpperCamelCase__   :List[str]												= prepare_image_inputs(self.image_processor_tester    ,   equal_resolution=UpperCamelCase_							)
							for image in image_inputs:
												self.assertIsInstance(UpperCamelCase_    ,   Image.Image							)

							# Test not batched input
							UpperCamelCase__   :Any												= image_processing(image_inputs[0]    ,   return_tensors='''pt'''							).pixel_values

							UpperCamelCase__					,				UpperCamelCase__   :str												= self.image_processor_tester.get_expected_values(UpperCamelCase_							)

							self.assertEqual(
							    encoded_images.shape    ,   (1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,   )

							# Test batched
							UpperCamelCase__					,				UpperCamelCase__   :str												= self.image_processor_tester.get_expected_values(UpperCamelCase_    ,   batched=UpperCamelCase_							)

							UpperCamelCase__   :List[str]												= image_processing(UpperCamelCase_    ,   return_tensors='''pt'''							).pixel_values
							self.assertEqual(
							    encoded_images.shape    ,   (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,   )




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :List[Any]												= self.image_processing_class(**self.image_processor_dict							)
							# create random numpy tensors
							UpperCamelCase__   :Any												= prepare_image_inputs(self.image_processor_tester    ,   equal_resolution=UpperCamelCase_    ,   numpify=UpperCamelCase_							)
							for image in image_inputs:
												self.assertIsInstance(UpperCamelCase_    ,   np.ndarray							)

							# Test not batched input
							UpperCamelCase__   :Union[str, Any]												= image_processing(image_inputs[0]    ,   return_tensors='''pt'''							).pixel_values

							UpperCamelCase__					,				UpperCamelCase__   :List[Any]												= self.image_processor_tester.get_expected_values(UpperCamelCase_							)

							self.assertEqual(
							    encoded_images.shape    ,   (1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,   )

							# Test batched
							UpperCamelCase__   :Union[str, Any]												= image_processing(UpperCamelCase_    ,   return_tensors='''pt'''							).pixel_values

							UpperCamelCase__					,				UpperCamelCase__   :str												= self.image_processor_tester.get_expected_values(UpperCamelCase_    ,   batched=UpperCamelCase_							)

							self.assertEqual(
							    encoded_images.shape    ,   (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,   )




		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :List[str]												= self.image_processing_class(**self.image_processor_dict							)
							# create random PyTorch tensors
							UpperCamelCase__   :Any												= prepare_image_inputs(self.image_processor_tester    ,   equal_resolution=UpperCamelCase_    ,   torchify=UpperCamelCase_							)
							for image in image_inputs:
												self.assertIsInstance(UpperCamelCase_    ,   torch.Tensor							)

							# Test not batched input
							UpperCamelCase__   :str												= image_processing(image_inputs[0]    ,   return_tensors='''pt'''							).pixel_values

							UpperCamelCase__					,				UpperCamelCase__   :Dict												= self.image_processor_tester.get_expected_values(UpperCamelCase_							)

							self.assertEqual(
							    encoded_images.shape    ,   (1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,   )

							# Test batched
							UpperCamelCase__   :List[str]												= image_processing(UpperCamelCase_    ,   return_tensors='''pt'''							).pixel_values

							UpperCamelCase__					,				UpperCamelCase__   :Optional[int]												= self.image_processor_tester.get_expected_values(UpperCamelCase_    ,   batched=UpperCamelCase_							)

							self.assertEqual(
							    encoded_images.shape    ,   (
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,   )




		@slow
		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :Optional[Any]												= Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
							with open('''./tests/fixtures/tests_samples/COCO/coco_annotations.txt'''    ,   '''r'''							) as f:
												UpperCamelCase__   :Optional[int]												= json.loads(f.read()							)

							UpperCamelCase__   :Any												= {'''image_id''': 39769, '''annotations''': target}

							# encode them
							UpperCamelCase__   :str												= ConditionalDetrImageProcessor.from_pretrained('''microsoft/conditional-detr-resnet-50'''							)
							UpperCamelCase__   :List[Any]												= image_processing(images=UpperCamelCase_    ,   annotations=UpperCamelCase_    ,   return_tensors='''pt'''							)

							# verify pixel values
							UpperCamelCase__   :List[str]												= torch.Size([1, 3, 800, 1066]							)
							self.assertEqual(encoding['''pixel_values'''].shape    ,   UpperCamelCase_							)

							UpperCamelCase__   :str												= torch.tensor([0.2796, 0.3138, 0.3481]							)
							self.assertTrue(torch.allclose(encoding['''pixel_values'''][0, 0, 0, :3]    ,   UpperCamelCase_    ,   atol=1e-4							)							)

							# verify area
							UpperCamelCase__   :str												= torch.tensor([5887.9600, 11250.2061, 489353.8438, 837122.7500, 147967.5156, 165732.3438]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''area''']    ,   UpperCamelCase_							)							)
							# verify boxes
							UpperCamelCase__   :Optional[Any]												= torch.Size([6, 4]							)
							self.assertEqual(encoding['''labels'''][0]['''boxes'''].shape    ,   UpperCamelCase_							)
							UpperCamelCase__   :Optional[Any]												= torch.tensor([0.5503, 0.2765, 0.0604, 0.2215]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''boxes'''][0]    ,   UpperCamelCase_    ,   atol=1e-3							)							)
							# verify image_id
							UpperCamelCase__   :List[Any]												= torch.tensor([39769]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''image_id''']    ,   UpperCamelCase_							)							)
							# verify is_crowd
							UpperCamelCase__   :int												= torch.tensor([0, 0, 0, 0, 0, 0]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''iscrowd''']    ,   UpperCamelCase_							)							)
							# verify class_labels
							UpperCamelCase__   :List[str]												= torch.tensor([75, 75, 63, 65, 17, 17]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''class_labels''']    ,   UpperCamelCase_							)							)
							# verify orig_size
							UpperCamelCase__   :Tuple												= torch.tensor([480, 640]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''orig_size''']    ,   UpperCamelCase_							)							)
							# verify size
							UpperCamelCase__   :Union[str, Any]												= torch.tensor([800, 1066]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''size''']    ,   UpperCamelCase_							)							)




		@slow
		def     lowerCAmelCase__				(		self							):

							'''simple docstring'''


							UpperCamelCase__   :List[str]												= Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
							with open('''./tests/fixtures/tests_samples/COCO/coco_panoptic_annotations.txt'''    ,   '''r'''							) as f:
												UpperCamelCase__   :Tuple												= json.loads(f.read()							)

							UpperCamelCase__   :List[str]												= {'''file_name''': '''000000039769.png''', '''image_id''': 39769, '''segments_info''': target}

							UpperCamelCase__   :Any												= pathlib.Path('''./tests/fixtures/tests_samples/COCO/coco_panoptic'''							)

							# encode them
							UpperCamelCase__   :List[Any]												= ConditionalDetrImageProcessor(format='''coco_panoptic'''							)
							UpperCamelCase__   :Dict												= image_processing(images=UpperCamelCase_    ,   annotations=UpperCamelCase_    ,   masks_path=UpperCamelCase_    ,   return_tensors='''pt'''							)

							# verify pixel values
							UpperCamelCase__   :str												= torch.Size([1, 3, 800, 1066]							)
							self.assertEqual(encoding['''pixel_values'''].shape    ,   UpperCamelCase_							)

							UpperCamelCase__   :Optional[int]												= torch.tensor([0.2796, 0.3138, 0.3481]							)
							self.assertTrue(torch.allclose(encoding['''pixel_values'''][0, 0, 0, :3]    ,   UpperCamelCase_    ,   atol=1e-4							)							)

							# verify area
							UpperCamelCase__   :Tuple												= torch.tensor([147979.6875, 165527.0469, 484638.5938, 11292.9375, 5879.6562, 7634.1147]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''area''']    ,   UpperCamelCase_							)							)
							# verify boxes
							UpperCamelCase__   :Any												= torch.Size([6, 4]							)
							self.assertEqual(encoding['''labels'''][0]['''boxes'''].shape    ,   UpperCamelCase_							)
							UpperCamelCase__   :List[Any]												= torch.tensor([0.2625, 0.5437, 0.4688, 0.8625]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''boxes'''][0]    ,   UpperCamelCase_    ,   atol=1e-3							)							)
							# verify image_id
							UpperCamelCase__   :List[str]												= torch.tensor([39769]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''image_id''']    ,   UpperCamelCase_							)							)
							# verify is_crowd
							UpperCamelCase__   :Union[str, Any]												= torch.tensor([0, 0, 0, 0, 0, 0]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''iscrowd''']    ,   UpperCamelCase_							)							)
							# verify class_labels
							UpperCamelCase__   :str												= torch.tensor([17, 17, 63, 75, 75, 93]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''class_labels''']    ,   UpperCamelCase_							)							)
							# verify masks
							UpperCamelCase__   :Optional[Any]												= 822873
							self.assertEqual(encoding['''labels'''][0]['''masks'''].sum().item()    ,   UpperCamelCase_							)
							# verify orig_size
							UpperCamelCase__   :List[str]												= torch.tensor([480, 640]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''orig_size''']    ,   UpperCamelCase_							)							)
							# verify size
							UpperCamelCase__   :List[Any]												= torch.tensor([800, 1066]							)
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''size''']    ,   UpperCamelCase_							)							)