import copy
import inspect

from transformers.testing_utils import require_torch, torch_device
from transformers.utils.backbone_utils import BackboneType
@require_torch
class 	_a  :



	"""simple docstring"""



	__SCREAMING_SNAKE_CASE              =					()
	__SCREAMING_SNAKE_CASE              =					True


	def __lowerCAmelCase      (   self       ):
		_lowercase   =self.config_class

		# test default config
		_lowercase   =config_class()
		self.assertIsNotNone(lowerCAmelCase_       )
		_lowercase   =["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
		_lowercase   =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
		_lowercase   =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
		_lowercase   =config_class(out_features=["stage1", "stage3"]       )
		self.assertEqual(config.out_features       ,  ["stage1", "stage3"]       )
		self.assertEqual(config.out_indices       ,  [1, 3]       )

		# Only out_indices set
		_lowercase   =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_       ):
			_lowercase   =config_class(out_features=["stage1", "stage2"]       ,  out_indices=[0, 2]       )


	def __lowerCAmelCase      (   self       ):
		_lowercase   ,  _lowercase   =self.model_tester.prepare_config_and_inputs_for_common()

		for model_class in self.all_model_classes:
			_lowercase   =model_class(lowerCAmelCase_       )
			_lowercase   =inspect.signature(model.forward       )
			# signature.parameters is an OrderedDict => so arg_names order is deterministic
			_lowercase   =[*signature.parameters.keys()]
			_lowercase   =["pixel_values"]
			self.assertListEqual(arg_names[:1]       ,  lowerCAmelCase_       )


	def __lowerCAmelCase      (   self       ):
		_lowercase   ,  _lowercase   =self.model_tester.prepare_config_and_inputs_for_common()

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

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

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


	def __lowerCAmelCase      (   self       ):
		_lowercase   ,  _lowercase   =self.model_tester.prepare_config_and_inputs_for_common()

		for model_class in self.all_model_classes:
			_lowercase   =model_class(lowerCAmelCase_       )
			model.to(lowerCAmelCase_       )
			model.eval()
			_lowercase   =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
			_lowercase   =copy.deepcopy(lowerCAmelCase_       )
			_lowercase   =None
			_lowercase   =model_class(lowerCAmelCase_       )
			model.to(lowerCAmelCase_       )
			model.eval()
			_lowercase   =model(**lowerCAmelCase_       )

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

			_lowercase   =copy.deepcopy(lowerCAmelCase_       )
			_lowercase   =None
			_lowercase   =model_class(lowerCAmelCase_       )
			model.to(lowerCAmelCase_       )
			model.eval()
			_lowercase   =model(**lowerCAmelCase_       )

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

			# Check backbone can be initialized with fresh weights
			_lowercase   =copy.deepcopy(lowerCAmelCase_       )
			_lowercase   =False
			_lowercase   =model_class(lowerCAmelCase_       )
			model.to(lowerCAmelCase_       )
			model.eval()
			_lowercase   =model(**lowerCAmelCase_       )


	def __lowerCAmelCase      (   self       ):
		_lowercase   ,  _lowercase   =self.model_tester.prepare_config_and_inputs_for_common()

		for backbone_class in self.all_model_classes:
			_lowercase   =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 __lowerCAmelCase      (   self       ):
		_lowercase   ,  _lowercase   =self.model_tester.prepare_config_and_inputs_for_common()
		_lowercase   =inputs_dict["pixel_values"].shape[0]

		for backbone_class in self.all_model_classes:
			_lowercase   =backbone_class(lowerCAmelCase_       )
			backbone.to(lowerCAmelCase_       )
			backbone.eval()

			_lowercase   =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
			_lowercase   =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:
				_lowercase   =backbone(**lowerCAmelCase_       ,  output_attentions=lowerCAmelCase_       )
				self.assertIsNotNone(outputs.attentions       )










from itertools import count
from math import asin, pi, sqrt
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return (
        (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
    ) / 4
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(circles_number + 1 - sqrt(2 * circles_number		)) / (
        2 * (circles_number**2 + 1)
    )
    a__  			=							circles_number * intersection_y

    a__  			=							intersection_x * intersection_y / 2
    a__  			=							circle_bottom_arc_integral(
        1 / 2		) - circle_bottom_arc_integral(UpperCAmelCase_		)

    return triangle_area + concave_region_area
def 							__lowerCAmelCase			(UpperCAmelCase_ = 1 / 1_000		):
    a__  			=							(1 - pi / 4) / 4

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

    return -1


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






