


import unittest

from transformers import MraConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_torch_available():
   import torch

   from transformers import (
       MraForMaskedLM,
       MraForMultipleChoice,
       MraForQuestionAnswering,
       MraForSequenceClassification,
       MraForTokenClassification,
       MraModel,
   )
   from transformers.models.mra.modeling_mra import MRA_PRETRAINED_MODEL_ARCHIVE_LIST



class        a					:





     def __init__(    self					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				Dict=2    ,	SCREAMING_SNAKE_CASE_					:				Dict=8    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]=True    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]=True    ,	SCREAMING_SNAKE_CASE_					:				Optional[int]=True    ,	SCREAMING_SNAKE_CASE_					:				Tuple=True    ,	SCREAMING_SNAKE_CASE_					:				str=99    ,	SCREAMING_SNAKE_CASE_					:				str=16    ,	SCREAMING_SNAKE_CASE_					:				List[Any]=5    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]=2    ,	SCREAMING_SNAKE_CASE_					:				Any=36    ,	SCREAMING_SNAKE_CASE_					:				Any="gelu"    ,	SCREAMING_SNAKE_CASE_					:				List[str]=0.0    ,	SCREAMING_SNAKE_CASE_					:				Tuple=0.0    ,	SCREAMING_SNAKE_CASE_					:				int=512    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]=16    ,	SCREAMING_SNAKE_CASE_					:				Tuple=2    ,	SCREAMING_SNAKE_CASE_					:				Dict=0.02    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]=3    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]=4    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]=None    ,	):
        __lowerCamelCase:				Optional[int]     =	parent
        __lowerCamelCase:				Optional[int]     =	batch_size
        __lowerCamelCase:				Optional[int]     =	seq_length
        __lowerCamelCase:				str     =	is_training
        __lowerCamelCase:				Tuple     =	use_input_mask
        __lowerCamelCase:				Optional[int]     =	use_token_type_ids
        __lowerCamelCase:				Optional[Any]     =	use_labels
        __lowerCamelCase:				List[str]     =	vocab_size
        __lowerCamelCase:				Optional[Any]     =	hidden_size
        __lowerCamelCase:				List[str]     =	num_hidden_layers
        __lowerCamelCase:				Union[str, Any]     =	num_attention_heads
        __lowerCamelCase:				Optional[int]     =	intermediate_size
        __lowerCamelCase:				str     =	hidden_act
        __lowerCamelCase:				Dict     =	hidden_dropout_prob
        __lowerCamelCase:				Optional[Any]     =	attention_probs_dropout_prob
        __lowerCamelCase:				Union[str, Any]     =	max_position_embeddings
        __lowerCamelCase:				str     =	type_vocab_size
        __lowerCamelCase:				List[str]     =	type_sequence_label_size
        __lowerCamelCase:				Dict     =	initializer_range
        __lowerCamelCase:				List[str]     =	num_labels
        __lowerCamelCase:				int     =	num_choices
        __lowerCamelCase:				Tuple     =	scope





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

        __lowerCamelCase:				int     =	None
        if self.use_input_mask:
           __lowerCamelCase:				int     =	random_attention_mask([self.batch_size, self.seq_length]							)

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

        __lowerCamelCase:				int     =	None
        __lowerCamelCase:				Tuple     =	None
        __lowerCamelCase:				List[Any]     =	None
        if self.use_labels:
           __lowerCamelCase:				Tuple     =	ids_tensor([self.batch_size]    ,	self.type_sequence_label_size							)
           __lowerCamelCase:				Union[str, Any]     =	ids_tensor([self.batch_size, self.seq_length]    ,	self.num_labels							)
           __lowerCamelCase:				Dict     =	ids_tensor([self.batch_size]    ,	self.num_choices							)

        __lowerCamelCase:				int     =	self.get_config()

        return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[Any]							):
        return MraConfig(
            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=SCREAMING_SNAKE_CASE_    ,	initializer_range=self.initializer_range    ,	)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any							):
        __lowerCamelCase:				int     =	self.get_config()
        __lowerCamelCase:				int     =	300
        return config





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[Any]							):
        (
            (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     
        ):				Tuple     =	self.prepare_config_and_inputs()

        __lowerCamelCase:				Union[str, Any]     =	True
        __lowerCamelCase:				Optional[int]     =	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,
            token_type_ids,
            input_mask,
            sequence_labels,
            token_labels,
            choice_labels,
            encoder_hidden_states,
            encoder_attention_mask,
        )





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				List[Any]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]							):
        __lowerCamelCase:				Tuple     =	MraModel(config=SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Optional[int]     =	model(SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_							)
        __lowerCamelCase:				Dict     =	model(SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_							)
        __lowerCamelCase:				Tuple     =	model(SCREAMING_SNAKE_CASE_							)
        self.parent.assertEqual(result.last_hidden_state.shape    ,	(self.batch_size, self.seq_length, self.hidden_size)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				List[str]    ,	SCREAMING_SNAKE_CASE_					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Any    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	):
        __lowerCamelCase:				Any     =	True
        __lowerCamelCase:				Any     =	MraModel(SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				List[Any]     =	model(
            SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	encoder_hidden_states=SCREAMING_SNAKE_CASE_    ,	encoder_attention_mask=SCREAMING_SNAKE_CASE_    ,	)
        __lowerCamelCase:				Optional[Any]     =	model(
            SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	encoder_hidden_states=SCREAMING_SNAKE_CASE_    ,	)
        __lowerCamelCase:				List[Any]     =	model(SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_							)
        self.parent.assertEqual(result.last_hidden_state.shape    ,	(self.batch_size, self.seq_length, self.hidden_size)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				List[str]    ,	SCREAMING_SNAKE_CASE_					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				Any    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Dict							):
        __lowerCamelCase:				Optional[Any]     =	MraForMaskedLM(config=SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Optional[Any]     =	model(SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	labels=SCREAMING_SNAKE_CASE_							)
        self.parent.assertEqual(result.logits.shape    ,	(self.batch_size, self.seq_length, self.vocab_size)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				int    ,	SCREAMING_SNAKE_CASE_					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]							):
        __lowerCamelCase:				Any     =	MraForQuestionAnswering(config=SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Optional[int]     =	model(
            SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	start_positions=SCREAMING_SNAKE_CASE_    ,	end_positions=SCREAMING_SNAKE_CASE_    ,	)
        self.parent.assertEqual(result.start_logits.shape    ,	(self.batch_size, self.seq_length)							)
        self.parent.assertEqual(result.end_logits.shape    ,	(self.batch_size, self.seq_length)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				List[str]    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]							):
        __lowerCamelCase:				int     =	self.num_labels
        __lowerCamelCase:				str     =	MraForSequenceClassification(SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Any     =	model(SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	labels=SCREAMING_SNAKE_CASE_							)
        self.parent.assertEqual(result.logits.shape    ,	(self.batch_size, self.num_labels)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				Dict    ,	SCREAMING_SNAKE_CASE_					:				List[Any]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Any    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Union[str, Any]							):
        __lowerCamelCase:				Optional[Any]     =	self.num_labels
        __lowerCamelCase:				List[str]     =	MraForTokenClassification(config=SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Union[str, Any]     =	model(SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	labels=SCREAMING_SNAKE_CASE_							)
        self.parent.assertEqual(result.logits.shape    ,	(self.batch_size, self.seq_length, self.num_labels)							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				str    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				Dict							):
        __lowerCamelCase:				Tuple     =	self.num_choices
        __lowerCamelCase:				Optional[Any]     =	MraForMultipleChoice(config=SCREAMING_SNAKE_CASE_							)
        model.to(SCREAMING_SNAKE_CASE_							)
        model.eval()
        __lowerCamelCase:				Optional[int]     =	input_ids.unsqueeze(1							).expand(-1    ,	self.num_choices    ,	-1							).contiguous()
        __lowerCamelCase:				int     =	token_type_ids.unsqueeze(1							).expand(-1    ,	self.num_choices    ,	-1							).contiguous()
        __lowerCamelCase:				List[Any]     =	input_mask.unsqueeze(1							).expand(-1    ,	self.num_choices    ,	-1							).contiguous()
        __lowerCamelCase:				Dict     =	model(
            SCREAMING_SNAKE_CASE_    ,	attention_mask=SCREAMING_SNAKE_CASE_    ,	token_type_ids=SCREAMING_SNAKE_CASE_    ,	labels=SCREAMING_SNAKE_CASE_    ,	)
        self.parent.assertEqual(result.logits.shape    ,	(self.batch_size, self.num_choices)							)







     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        __lowerCamelCase:				int     =	self.prepare_config_and_inputs()
        (
            (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     (
            __lowerCamelCase
        )   ,     
        ):				Any     =	config_and_inputs
        __lowerCamelCase:				int     =	{"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": input_mask}
        return config, inputs_dict



@require_torch
class        a					(			_UpperCAmelCase     ,unittest.TestCase   ):
     UpperCAmelCase__ :  Tuple						      =	(
         (
             MraModel,
             MraForMaskedLM,
             MraForMultipleChoice,
             MraForQuestionAnswering,
             MraForSequenceClassification,
             MraForTokenClassification,
         )
         if is_torch_available()
         else ()
     )
     UpperCAmelCase__ :  Union[str, Any]						      =	False
     UpperCAmelCase__ :  List[str]						      =	False
     UpperCAmelCase__ :  List[Any]						      =	False
     UpperCAmelCase__ :  str						      =	False

     UpperCAmelCase__ :  Union[str, Any]						      =	()





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[Any]							):
        __lowerCamelCase:				Dict     =	MraModelTester(self							)
        __lowerCamelCase:				int     =	ConfigTester(self    ,	config_class=SCREAMING_SNAKE_CASE_    ,	hidden_size=37							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        self.config_tester.run_common_tests()





     def  SCREAMING_SNAKE_CASE__       (    self					:				List[Any]							):
        __lowerCamelCase:				int     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				List[Any]							):
        __lowerCamelCase:				str     =	self.model_tester.prepare_config_and_inputs()
        for type in ["absolute", "relative_key", "relative_key_query"]:
           __lowerCamelCase:				Optional[int]     =	type
           self.model_tester.create_and_check_model(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any							):
        __lowerCamelCase:				List[str]     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_masked_lm(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[int]							):
        __lowerCamelCase:				int     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_multiple_choice(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Union[str, Any]							):
        __lowerCamelCase:				Optional[int]     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_question_answering(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        __lowerCamelCase:				Optional[Any]     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_sequence_classification(*SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[Any]							):
        __lowerCamelCase:				List[Any]     =	self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_for_token_classification(*SCREAMING_SNAKE_CASE_							)





     @slow
     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        for model_name in MRA_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
           __lowerCamelCase:				Optional[Any]     =	MraModel.from_pretrained(SCREAMING_SNAKE_CASE_							)
           self.assertIsNotNone(SCREAMING_SNAKE_CASE_							)







     @unittest.skip(reason="""MRA does not output attentions"""							)
     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        return



@require_torch
class        a					(			unittest.TestCase   ):





     @slow
     def  SCREAMING_SNAKE_CASE__       (    self					:				int							):
        __lowerCamelCase:				List[Any]     =	MraModel.from_pretrained("""uw-madison/mra-base-512-4"""							)
        __lowerCamelCase:				Tuple     =	torch.arange(256							).unsqueeze(0							)

        with torch.no_grad():
           __lowerCamelCase:				List[str]     =	model(SCREAMING_SNAKE_CASE_							)[0]

        __lowerCamelCase:				List[str]     =	torch.Size((1, 256, 768)							)
        self.assertEqual(output.shape    ,	SCREAMING_SNAKE_CASE_							)

        __lowerCamelCase:				Union[str, Any]     =	torch.tensor(
            [[[-0.0140, 0.0830, -0.0381], [0.1546, 0.1402, 0.0220], [0.1162, 0.0851, 0.0165]]]							)

        self.assertTrue(torch.allclose(output[:, :3, :3]    ,	SCREAMING_SNAKE_CASE_    ,	atol=1E-4							)							)





     @slow
     def  SCREAMING_SNAKE_CASE__       (    self					:				Dict							):
        __lowerCamelCase:				int     =	MraForMaskedLM.from_pretrained("""uw-madison/mra-base-512-4"""							)
        __lowerCamelCase:				Tuple     =	torch.arange(256							).unsqueeze(0							)

        with torch.no_grad():
           __lowerCamelCase:				Optional[int]     =	model(SCREAMING_SNAKE_CASE_							)[0]

        __lowerCamelCase:				Optional[int]     =	50265

        __lowerCamelCase:				int     =	torch.Size((1, 256, vocab_size)							)
        self.assertEqual(output.shape    ,	SCREAMING_SNAKE_CASE_							)

        __lowerCamelCase:				Dict     =	torch.tensor(
            [[[9.2595, -3.6038, 11.8819], [9.3869, -3.2693, 11.0956], [11.8524, -3.4938, 13.1210]]]							)

        self.assertTrue(torch.allclose(output[:, :3, :3]    ,	SCREAMING_SNAKE_CASE_    ,	atol=1E-4							)							)







     @slow
     def  SCREAMING_SNAKE_CASE__       (    self					:				Dict							):
        __lowerCamelCase:				Optional[Any]     =	MraForMaskedLM.from_pretrained("""uw-madison/mra-base-4096-8-d3"""							)
        __lowerCamelCase:				List[str]     =	torch.arange(4096							).unsqueeze(0							)

        with torch.no_grad():
           __lowerCamelCase:				Any     =	model(SCREAMING_SNAKE_CASE_							)[0]

        __lowerCamelCase:				Tuple     =	50265

        __lowerCamelCase:				List[str]     =	torch.Size((1, 4096, vocab_size)							)
        self.assertEqual(output.shape    ,	SCREAMING_SNAKE_CASE_							)

        __lowerCamelCase:				Optional[int]     =	torch.tensor(
            [[[5.4789, -2.3564, 7.5064], [7.9067, -1.3369, 9.9668], [9.0712, -1.8106, 7.0380]]]							)

        self.assertTrue(torch.allclose(output[:, :3, :3]    ,	SCREAMING_SNAKE_CASE_    ,	atol=1E-4							)							)






import math



def     __lowerCAmelCase						(							snake_case	:    int )       ->							bool:
   __lowerCamelCase:				Dict     =	math.loga(math.sqrt(4 * positive_integer + 1 ) / 2 + 1 / 2 )

   return exponent == int(snake_case )



def     __lowerCAmelCase						(							snake_case	:    float = 1 / 12345 )       ->							int:
   __lowerCamelCase:				str     =	0
   __lowerCamelCase:				Optional[Any]     =	0

   __lowerCamelCase:				str     =	3
   while True:
      __lowerCamelCase:				int     =	(integer**2 - 1) / 4
      # if candidate is an integer, then there is a partition for k
      if partition_candidate == int(snake_case ):
         __lowerCamelCase:				Union[str, Any]     =	int(snake_case )
         total_partitions += 1
         if check_partition_perfect(snake_case ):
            perfect_partitions += 1
      if perfect_partitions > 0:
         if perfect_partitions / total_partitions < max_proportion:
            return int(snake_case )
      integer += 1


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


