




"""simple docstring"""






import unittest

import numpy as np

from transformers import BertConfig, 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.bert.modeling_flax_bert import (
			    FlaxBertForMaskedLM,
			    FlaxBertForMultipleChoice,
			    FlaxBertForNextSentencePrediction,
			    FlaxBertForPreTraining,
			    FlaxBertForQuestionAnswering,
			    FlaxBertForSequenceClassification,
			    FlaxBertForTokenClassification,
			    FlaxBertModel,
			)






class lowerCAmelCase__      (	unittest.TestCase		):






			'''simple docstring'''



			def __init__(    self    , lowercase    , lowercase=13    , lowercase=7    , lowercase=True    , lowercase=True    , lowercase=True    , lowercase=True    , lowercase=99    , lowercase=32    , lowercase=5    , lowercase=4    , lowercase=37    , lowercase="gelu"    , lowercase=0.1    , lowercase=0.1    , lowercase=512    , lowercase=16    , lowercase=2    , lowercase=0.02    , lowercase=4    , ):
							_lowerCamelCase	:     Tuple       =       parent
							_lowerCamelCase	:     str       =       batch_size
							_lowerCamelCase	:     Dict       =       seq_length
							_lowerCamelCase	:     Dict       =       is_training
							_lowerCamelCase	:     Optional[int]       =       use_attention_mask
							_lowerCamelCase	:     str       =       use_token_type_ids
							_lowerCamelCase	:     Optional[int]       =       use_labels
							_lowerCamelCase	:     Optional[int]       =       vocab_size
							_lowerCamelCase	:     str       =       hidden_size
							_lowerCamelCase	:     List[Any]       =       num_hidden_layers
							_lowerCamelCase	:     int       =       num_attention_heads
							_lowerCamelCase	:     List[str]       =       intermediate_size
							_lowerCamelCase	:     List[str]       =       hidden_act
							_lowerCamelCase	:     Union[str, Any]       =       hidden_dropout_prob
							_lowerCamelCase	:     Optional[Any]       =       attention_probs_dropout_prob
							_lowerCamelCase	:     int       =       max_position_embeddings
							_lowerCamelCase	:     Any       =       type_vocab_size
							_lowerCamelCase	:     Union[str, Any]       =       type_sequence_label_size
							_lowerCamelCase	:     Optional[int]       =       initializer_range
							_lowerCamelCase	:     List[Any]       =       num_choices
			def    A_       (    self    ):
							_lowerCamelCase	:     Optional[int]       =       ids_tensor([self.batch_size, self.seq_length]    , self.vocab_size    )

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

							_lowerCamelCase	:     str       =       None
							if self.use_token_type_ids:
											_lowerCamelCase	:     Optional[Any]       =       ids_tensor([self.batch_size, self.seq_length]    , self.type_vocab_size    )

							_lowerCamelCase	:     Tuple       =       BertConfig(
							    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=lowercase    , initializer_range=self.initializer_range    , )

							return config, input_ids, token_type_ids, attention_mask
			def    A_       (    self    ):
							_lowerCamelCase	:     Tuple       =       self.prepare_config_and_inputs()
							_lowerCamelCase,					_lowerCamelCase,					_lowerCamelCase,					_lowerCamelCase	:     int       =       config_and_inputs
							_lowerCamelCase	:     Tuple       =       {'input_ids': input_ids, 'token_type_ids': token_type_ids, 'attention_mask': attention_mask}
							return config, inputs_dict






			def    A_       (    self    ):
							_lowerCamelCase	:     List[str]       =       self.prepare_config_and_inputs()
							_lowerCamelCase,					_lowerCamelCase,					_lowerCamelCase,					_lowerCamelCase	:     Optional[Any]       =       config_and_inputs

							_lowerCamelCase	:     Optional[Any]       =       True
							_lowerCamelCase	:     Union[str, Any]       =       floats_tensor([self.batch_size, self.seq_length, self.hidden_size]    )
							_lowerCamelCase	:     List[Any]       =       ids_tensor([self.batch_size, self.seq_length]    , vocab_size=2    )

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






@require_flax
class lowerCAmelCase__      (	lowercase,      unittest.TestCase		):






			'''simple docstring'''



			lowerCamelCase__ =     True

			lowerCamelCase__ =     (
			    (
			        FlaxBertModel,
			        FlaxBertForPreTraining,
			        FlaxBertForMaskedLM,
			        FlaxBertForMultipleChoice,
			        FlaxBertForQuestionAnswering,
			        FlaxBertForNextSentencePrediction,
			        FlaxBertForSequenceClassification,
			        FlaxBertForTokenClassification,
			        FlaxBertForQuestionAnswering,
			    )
			    if is_flax_available()
			    else ()
			)
			def    A_       (    self    ):
							_lowerCamelCase	:     Dict       =       FlaxBertModelTester(self    )






			@slow
			def    A_       (    self    ):
							# Only check this for base model, not necessary for all model classes.
							# This will also help speed-up tests.
							_lowerCamelCase	:     Dict       =       FlaxBertModel.from_pretrained('bert-base-cased'    )
							_lowerCamelCase	:     Any       =       model(np.ones((1, 1)    )    )
							self.assertIsNotNone(lowercase    )





"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt







def 	_snake_case     (							lowercase__						):
				_lowerCamelCase	:     int       =       int(number**0.5						)
				return number == sq * sq







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						):
				_lowerCamelCase	:     int       =       x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				_lowerCamelCase	:     int       =       x_den * y_den * z_den
				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
				top //= hcf
				bottom //= hcf
				return top, bottom







def 	_snake_case     (							lowercase__ = 35						):
				_lowerCamelCase	:     set       =       set()
				_lowerCamelCase	:     int
				_lowerCamelCase	:     Fraction       =       Fraction(0						)
				_lowerCamelCase	:     tuple[int, int]

				for x_num in range(1				,       order + 1						):
								for x_den in range(x_num + 1				,       order + 1						):
												for y_num in range(1				,       order + 1						):
																for y_den in range(y_num + 1				,       order + 1						):
																				# n=1
																				_lowerCamelCase	:     int       =       x_num * y_den + x_den * y_num
																				_lowerCamelCase	:     List[Any]       =       x_den * y_den
																				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								_lowerCamelCase	:     Optional[Any]       =       add_three(
																								    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																								unique_s.add(lowercase__						)

																				# n=2
																				_lowerCamelCase	:     Tuple       =       (
																				    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																				)
																				_lowerCamelCase	:     Dict       =       x_den * x_den * y_den * y_den
																				if is_sq(lowercase__						) and is_sq(lowercase__						):
																								_lowerCamelCase	:     Dict       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     Optional[Any]       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     List[Any]       =       gcd(lowercase__				,       lowercase__						)
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												_lowerCamelCase	:     Union[str, Any]       =       add_three(
																												    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																												unique_s.add(lowercase__						)

                    # n=-1
																				_lowerCamelCase	:     List[str]       =       x_num * y_num
																				_lowerCamelCase	:     int       =       x_den * y_num + x_num * y_den
																				_lowerCamelCase	:     Dict       =       gcd(lowercase__				,       lowercase__						)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								_lowerCamelCase	:     List[str]       =       add_three(
																								    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																								unique_s.add(lowercase__						)

																				# n=2
																				_lowerCamelCase	:     Tuple       =       x_num * x_num * y_num * y_num
																				_lowerCamelCase	:     List[str]       =       (
																				    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																				)
																				if is_sq(lowercase__						) and is_sq(lowercase__						):
																								_lowerCamelCase	:     Optional[int]       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     Optional[int]       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     Dict       =       gcd(lowercase__				,       lowercase__						)
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												_lowerCamelCase	:     int       =       add_three(
																												    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																												unique_s.add(lowercase__						)

				for num, den in unique_s:
								total += Fraction(lowercase__				,       lowercase__						)

				return total.denominator + total.numerator


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