


import copy
import inspect

from transformers.testing_utils import require_torch, torch_device
from transformers.utils.backbone_utils import BackboneType

@require_torch
class      __snake_case				:
					SCREAMING_SNAKE_CASE_		:       Optional[Any]								=			()
					SCREAMING_SNAKE_CASE_		:       Tuple								=			True
					def 	a			(						self       :						Union[str, Any]  )							->					Any:



											'''simple docstring'''





											__magic_name__					=      self.config_class

											# test default config
											__magic_name__					=      config_class()
											self.assertIsNotNone(_lowerCAmelCase  )
											__magic_name__					=      ['stem'] + [F'''stage{idx}''' for idx in range(1	,      len(config.depths  ) + 1  )]
											self.assertEqual(config.stage_names	,      _lowerCAmelCase  )
											self.assertTrue(set(config.out_features  ).issubset(set(config.stage_names  )  )  )

											# Test out_features and out_indices are correctly set
											# out_features and out_indices both None
											__magic_name__					=      config_class(out_features=_lowerCAmelCase	,      out_indices=_lowerCAmelCase  )
											self.assertEqual(config.out_features	,      [config.stage_names[-1]]  )
											self.assertEqual(config.out_indices	,      [len(config.stage_names  ) - 1]  )

											# out_features and out_indices both set
											__magic_name__					=      config_class(out_features=['stem', 'stage1']	,      out_indices=[0, 1]  )
											self.assertEqual(config.out_features	,      ['stem', 'stage1']  )
											self.assertEqual(config.out_indices	,      [0, 1]  )

											# Only out_features set
											__magic_name__					=      config_class(out_features=['stage1', 'stage3']  )
											self.assertEqual(config.out_features	,      ['stage1', 'stage3']  )
											self.assertEqual(config.out_indices	,      [1, 3]  )

											# Only out_indices set
											__magic_name__					=      config_class(out_indices=[0, 2]  )
											self.assertEqual(config.out_features	,      [config.stage_names[0], config.stage_names[2]]  )
											self.assertEqual(config.out_indices	,      [0, 2]  )

											# Error raised when out_indices do not correspond to out_features
											with self.assertRaises(_lowerCAmelCase  ):
																	__magic_name__					=      config_class(out_features=['stage1', 'stage2']	,      out_indices=[0, 2]  )
					def 	a			(						self       :						Optional[int]  )							->					Any:



											'''simple docstring'''





											__magic_name__		,      __magic_name__					=      self.model_tester.prepare_config_and_inputs_for_common()

											for model_class in self.all_model_classes:
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	__magic_name__					=      inspect.signature(model.forward  )
																	# signature.parameters is an OrderedDict => so arg_names order is deterministic
																	__magic_name__					=      [*signature.parameters.keys()]
																	__magic_name__					=      ['pixel_values']
																	self.assertListEqual(arg_names[:1]	,      _lowerCAmelCase  )
					def 	a			(						self       :						str  )							->					Tuple:



											'''simple docstring'''





											__magic_name__		,      __magic_name__					=      self.model_tester.prepare_config_and_inputs_for_common()

											for model_class in self.all_model_classes:
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	self.assertEqual(len(model.channels  )	,      len(config.out_features  )  )
																	__magic_name__					=      model.num_features
																	__magic_name__					=      [config.stage_names.index(_lowerCAmelCase  ) for feat in config.out_features]
																	__magic_name__					=      [num_features[idx] for idx in out_indices]
																	self.assertListEqual(model.channels	,      _lowerCAmelCase  )

																	__magic_name__					=      copy.deepcopy(_lowerCAmelCase  )
																	__magic_name__					=      None
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	self.assertEqual(len(model.channels  )	,      1  )
																	self.assertListEqual(model.channels	,      [num_features[-1]]  )

																	__magic_name__					=      copy.deepcopy(_lowerCAmelCase  )
																	__magic_name__					=      None
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	self.assertEqual(len(model.channels  )	,      1  )
																	self.assertListEqual(model.channels	,      [num_features[-1]]  )
					def 	a			(						self       :						List[str]  )							->					Any:



											'''simple docstring'''





											__magic_name__		,      __magic_name__					=      self.model_tester.prepare_config_and_inputs_for_common()

											for model_class in self.all_model_classes:
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	model.to(_lowerCAmelCase  )
																	model.eval()
																	__magic_name__					=      model(**_lowerCAmelCase  )

																	self.assertEqual(len(result.feature_maps  )	,      len(config.out_features  )  )
																	self.assertEqual(len(model.channels  )	,      len(config.out_features  )  )
																	self.assertEqual(len(result.feature_maps  )	,      len(config.out_indices  )  )
																	self.assertEqual(len(model.channels  )	,      len(config.out_indices  )  )

																	# Check output of last stage is taken if out_features=None, out_indices=None
																	__magic_name__					=      copy.deepcopy(_lowerCAmelCase  )
																	__magic_name__					=      None
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	model.to(_lowerCAmelCase  )
																	model.eval()
																	__magic_name__					=      model(**_lowerCAmelCase  )

																	self.assertEqual(len(result.feature_maps  )	,      1  )
																	self.assertEqual(len(model.channels  )	,      1  )

																	__magic_name__					=      copy.deepcopy(_lowerCAmelCase  )
																	__magic_name__					=      None
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	model.to(_lowerCAmelCase  )
																	model.eval()
																	__magic_name__					=      model(**_lowerCAmelCase  )

																	self.assertEqual(len(result.feature_maps  )	,      1  )
																	self.assertEqual(len(model.channels  )	,      1  )

																	# Check backbone can be initialized with fresh weights
																	__magic_name__					=      copy.deepcopy(_lowerCAmelCase  )
																	__magic_name__					=      False
																	__magic_name__					=      model_class(_lowerCAmelCase  )
																	model.to(_lowerCAmelCase  )
																	model.eval()
																	__magic_name__					=      model(**_lowerCAmelCase  )
					def 	a			(						self       :						int  )							->					Optional[int]:



											'''simple docstring'''





											__magic_name__		,      __magic_name__					=      self.model_tester.prepare_config_and_inputs_for_common()

											for backbone_class in self.all_model_classes:
																	__magic_name__					=      backbone_class(_lowerCAmelCase  )

																	self.assertTrue(hasattr(_lowerCAmelCase	,      'backbone_type'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'stage_names'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'num_features'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'out_indices'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'out_features'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'out_feature_channels'  )  )
																	self.assertTrue(hasattr(_lowerCAmelCase	,      'channels'  )  )

																	self.assertIsInstance(backbone.backbone_type	,      _lowerCAmelCase  )
																	# Verify num_features has been initialized in the backbone init
																	self.assertIsNotNone(backbone.num_features  )
																	self.assertTrue(len(backbone.channels  ) == len(backbone.out_indices  )  )
																	self.assertTrue(len(backbone.stage_names  ) == len(backbone.num_features  )  )
																	self.assertTrue(len(backbone.channels  ) <= len(backbone.num_features  )  )
																	self.assertTrue(len(backbone.out_feature_channels  ) == len(backbone.stage_names  )  )







					def 	a			(						self       :						Optional[Any]  )							->					Optional[Any]:



											'''simple docstring'''





											__magic_name__		,      __magic_name__					=      self.model_tester.prepare_config_and_inputs_for_common()
											__magic_name__					=      inputs_dict['pixel_values'].shape[0]

											for backbone_class in self.all_model_classes:
																	__magic_name__					=      backbone_class(_lowerCAmelCase  )
																	backbone.to(_lowerCAmelCase  )
																	backbone.eval()

																	__magic_name__					=      backbone(**_lowerCAmelCase  )

																	# Test default outputs and verify feature maps
																	self.assertIsInstance(outputs.feature_maps	,      _lowerCAmelCase  )
																	self.assertTrue(len(outputs.feature_maps  ) == len(backbone.channels  )  )
																	for feature_map, n_channels in zip(outputs.feature_maps	,      backbone.channels  ):
																							self.assertTrue(feature_map.shape[:2]	,      (batch_size, n_channels)  )
																	self.assertIsNone(outputs.hidden_states  )
																	self.assertIsNone(outputs.attentions  )

																	# Test output_hidden_states=True
																	__magic_name__					=      backbone(**_lowerCAmelCase	,      output_hidden_states=_lowerCAmelCase  )
																	self.assertIsNotNone(outputs.hidden_states  )
																	self.assertTrue(len(outputs.hidden_states  )	,      len(backbone.stage_names  )  )
																	for hidden_state, n_channels in zip(outputs.hidden_states	,      backbone.channels  ):
																							self.assertTrue(hidden_state.shape[:2]	,      (batch_size, n_channels)  )

																	# Test output_attentions=True
																	if self.has_attentions:
																							__magic_name__					=      backbone(**_lowerCAmelCase	,      output_attentions=_lowerCAmelCase  )
																							self.assertIsNotNone(outputs.attentions  )





from itertools import count
from math import asin, pi, sqrt
def 				UpperCamelCase_	(					__snake_case      :    float  )->   float:




						'''simple docstring'''
						return (
						    (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
						) / 4
def 				UpperCamelCase_	(					__snake_case      :    int  )->   float:




						'''simple docstring'''
						__magic_name__					=      (circles_number + 1 - sqrt(2 * circles_number  )) / (
						    2 * (circles_number**2 + 1)
						)
						__magic_name__					=      circles_number * intersection_y

						__magic_name__					=      intersection_x * intersection_y / 2
						__magic_name__					=      circle_bottom_arc_integral(
						    1 / 2  ) - circle_bottom_arc_integral(__snake_case  )

						return triangle_area + concave_region_area
def 				UpperCamelCase_	(					__snake_case      :    float = 1 / 10_00  )->   int:




						'''simple docstring'''
						__magic_name__					=      (1 - pi / 4) / 4

						for n in count(1  ):
												if concave_triangle_area(__snake_case  ) / l_section_area < fraction:
																		return n

						return -1


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

