



'''simple docstring'''




import unittest

import numpy as np

from transformers import RobertaConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
						from transformers.models.roberta.modeling_flax_roberta import (
						    FlaxRobertaForCausalLM,
						    FlaxRobertaForMaskedLM,
						    FlaxRobertaForMultipleChoice,
						    FlaxRobertaForQuestionAnswering,
						    FlaxRobertaForSequenceClassification,
						    FlaxRobertaForTokenClassification,
						    FlaxRobertaModel,
						)






class 						_UpperCamelCase  (							unittest.TestCase    ):


			'''simple docstring'''

			def __init__(							self     : List[str]							,     lowerCAmelCase__     : Optional[Any]							,     lowerCAmelCase__     : List[str]=1_3							,     lowerCAmelCase__     : Union[str, Any]=7							,     lowerCAmelCase__     : Tuple=True							,     lowerCAmelCase__     : str=True							,     lowerCAmelCase__     : List[str]=True							,     lowerCAmelCase__     : int=True							,     lowerCAmelCase__     : Tuple=9_9							,     lowerCAmelCase__     : Union[str, Any]=3_2							,     lowerCAmelCase__     : Any=5							,     lowerCAmelCase__     : str=4							,     lowerCAmelCase__     : Optional[Any]=3_7							,     lowerCAmelCase__     : List[str]="gelu"							,     lowerCAmelCase__     : List[str]=0.1							,     lowerCAmelCase__     : Optional[Any]=0.1							,     lowerCAmelCase__     : List[str]=5_1_2							,     lowerCAmelCase__     : str=1_6							,     lowerCAmelCase__     : Optional[int]=2							,     lowerCAmelCase__     : int=0.02							,     lowerCAmelCase__     : Optional[int]=4							,     ):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		List[Any]           =		parent
					__SCREAMING_SNAKE_CASE       :		Dict           =		batch_size
					__SCREAMING_SNAKE_CASE       :		List[str]           =		seq_length
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		is_training
					__SCREAMING_SNAKE_CASE       :		List[str]           =		use_attention_mask
					__SCREAMING_SNAKE_CASE       :		List[Any]           =		use_token_type_ids
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		use_labels
					__SCREAMING_SNAKE_CASE       :		Dict           =		vocab_size
					__SCREAMING_SNAKE_CASE       :		Any           =		hidden_size
					__SCREAMING_SNAKE_CASE       :		int           =		num_hidden_layers
					__SCREAMING_SNAKE_CASE       :		List[str]           =		num_attention_heads
					__SCREAMING_SNAKE_CASE       :		List[Any]           =		intermediate_size
					__SCREAMING_SNAKE_CASE       :		str           =		hidden_act
					__SCREAMING_SNAKE_CASE       :		Tuple           =		hidden_dropout_prob
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		attention_probs_dropout_prob
					__SCREAMING_SNAKE_CASE       :		List[str]           =		max_position_embeddings
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		type_vocab_size
					__SCREAMING_SNAKE_CASE       :		Tuple           =		type_sequence_label_size
					__SCREAMING_SNAKE_CASE       :		Dict           =		initializer_range
					__SCREAMING_SNAKE_CASE       :		Dict           =		num_choices

			def UpperCamelCase__					(							self     : Optional[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		ids_tensor([self.batch_size, self.seq_length]							,     self.vocab_size						)

					__SCREAMING_SNAKE_CASE       :		List[Any]           =		None
					if self.use_attention_mask:
							__SCREAMING_SNAKE_CASE       :		Tuple           =		random_attention_mask([self.batch_size, self.seq_length]						)

					__SCREAMING_SNAKE_CASE       :		Dict           =		None
					if self.use_token_type_ids:
							__SCREAMING_SNAKE_CASE       :		str           =		ids_tensor([self.batch_size, self.seq_length]							,     self.type_vocab_size						)

					__SCREAMING_SNAKE_CASE       :		Dict           =		RobertaConfig(
					    vocab_size=self.vocab_size							,     hidden_size=self.hidden_size							,     num_hidden_layers=self.num_hidden_layers							,     num_attention_heads=self.num_attention_heads							,     intermediate_size=self.intermediate_size							,     hidden_act=self.hidden_act							,     hidden_dropout_prob=self.hidden_dropout_prob							,     attention_probs_dropout_prob=self.attention_probs_dropout_prob							,     max_position_embeddings=self.max_position_embeddings							,     type_vocab_size=self.type_vocab_size							,     is_decoder=lowerCAmelCase__							,     initializer_range=self.initializer_range							,     )

					return config, input_ids, token_type_ids, attention_mask

			def UpperCamelCase__					(							self     : List[str]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		int           =		self.prepare_config_and_inputs()
					__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Tuple           =		config_and_inputs
					__SCREAMING_SNAKE_CASE       :		Dict           =		{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": attention_mask}
					return config, inputs_dict



			def UpperCamelCase__					(							self     : Optional[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Any           =		self.prepare_config_and_inputs()
					__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Dict           =		config_and_inputs

					__SCREAMING_SNAKE_CASE       :		Any           =		True
					__SCREAMING_SNAKE_CASE       :		Tuple           =		floats_tensor([self.batch_size, self.seq_length, self.hidden_size]						)
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		ids_tensor([self.batch_size, self.seq_length]							,     vocab_size=2						)

					return (
					    config,
					    input_ids,
					    token_type_ids,
					    encoder_hidden_states,
					    encoder_attention_mask,
					)






@require_flax
class 						_UpperCamelCase  (							lowerCamelCase__    ,					unittest.TestCase    ):


			'''simple docstring'''

			_A      :		Union[str, Any]			    =		True

			_A      :		List[Any]			    =		(
			    (
			        FlaxRobertaModel,
			        FlaxRobertaForCausalLM,
			        FlaxRobertaForMaskedLM,
			        FlaxRobertaForSequenceClassification,
			        FlaxRobertaForTokenClassification,
			        FlaxRobertaForMultipleChoice,
			        FlaxRobertaForQuestionAnswering,
			    )
			    if is_flax_available()
			    else ()
			)

			def UpperCamelCase__					(							self     : Any						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Dict           =		FlaxRobertaModelTester(self						)



			@slow
			def UpperCamelCase__					(							self     : Dict						):





					"""simple docstring"""






					for model_class_name in self.all_model_classes:
							__SCREAMING_SNAKE_CASE       :		List[Any]           =		model_class_name.from_pretrained("""roberta-base"""							,     from_pt=lowerCAmelCase__						)
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		model(np.ones((1, 1)						)						)
							self.assertIsNotNone(lowerCAmelCase__						)




'''simple docstring'''




from math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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