






from __future__ import annotations

import unittest

from transformers import DebertaVaConfig, is_tf_available
from transformers.testing_utils import require_tf, slow

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
				import tensorflow as tf

				from transformers import (
				    TFDebertaVaForMaskedLM,
				    TFDebertaVaForQuestionAnswering,
				    TFDebertaVaForSequenceClassification,
				    TFDebertaVaForTokenClassification,
				    TFDebertaVaModel,
				)


class 							__a							:





		'''simple docstring'''



		def __init__(						self ,    UpperCamelCase__ ,    UpperCamelCase__=13 ,    UpperCamelCase__=7 ,    UpperCamelCase__=True ,    UpperCamelCase__=True ,    UpperCamelCase__=True ,    UpperCamelCase__=True ,    UpperCamelCase__=99 ,    UpperCamelCase__=32 ,    UpperCamelCase__=2 ,    UpperCamelCase__=4 ,    UpperCamelCase__=37 ,    UpperCamelCase__="gelu" ,    UpperCamelCase__=0.1 ,    UpperCamelCase__=0.1 ,    UpperCamelCase__=512 ,    UpperCamelCase__=16 ,    UpperCamelCase__=2 ,    UpperCamelCase__=0.02 ,    UpperCamelCase__=False ,    UpperCamelCase__=True ,    UpperCamelCase__="None" ,    UpperCamelCase__=3 ,    UpperCamelCase__=4 ,    UpperCamelCase__=None ,    ):
						SCREAMING_SNAKE_CASE_   :	Any													=   parent
						SCREAMING_SNAKE_CASE_   :	List[str]													=   batch_size
						SCREAMING_SNAKE_CASE_   :	str													=   seq_length
						SCREAMING_SNAKE_CASE_   :	Tuple													=   is_training
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   use_input_mask
						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   use_token_type_ids
						SCREAMING_SNAKE_CASE_   :	Tuple													=   use_labels
						SCREAMING_SNAKE_CASE_   :	int													=   vocab_size
						SCREAMING_SNAKE_CASE_   :	Tuple													=   hidden_size
						SCREAMING_SNAKE_CASE_   :	List[str]													=   num_hidden_layers
						SCREAMING_SNAKE_CASE_   :	Dict													=   num_attention_heads
						SCREAMING_SNAKE_CASE_   :	Dict													=   intermediate_size
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   hidden_act
						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   hidden_dropout_prob
						SCREAMING_SNAKE_CASE_   :	Tuple													=   attention_probs_dropout_prob
						SCREAMING_SNAKE_CASE_   :	Dict													=   max_position_embeddings
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   type_vocab_size
						SCREAMING_SNAKE_CASE_   :	List[str]													=   type_sequence_label_size
						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   initializer_range
						SCREAMING_SNAKE_CASE_   :	Dict													=   num_labels
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   num_choices
						SCREAMING_SNAKE_CASE_   :	int													=   relative_attention
						SCREAMING_SNAKE_CASE_   :	Tuple													=   position_biased_input
						SCREAMING_SNAKE_CASE_   :	List[str]													=   pos_att_type
						SCREAMING_SNAKE_CASE_   :	str													=   scope


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   ids_tensor([self.batch_size, self.seq_length] ,    self.vocab_size       )

						SCREAMING_SNAKE_CASE_   :	int													=   None
						if self.use_input_mask:
										SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   random_attention_mask([self.batch_size, self.seq_length]       )

						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   None
						if self.use_token_type_ids:
										SCREAMING_SNAKE_CASE_   :	List[str]													=   ids_tensor([self.batch_size, self.seq_length] ,    self.type_vocab_size       )

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

						SCREAMING_SNAKE_CASE_   :	str													=   DebertaVaConfig(
						    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 ,    relative_attention=self.relative_attention ,    position_biased_input=self.position_biased_input ,    initializer_range=self.initializer_range ,    return_dict=UpperCamelCase__ ,    )

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


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   TFDebertaVaModel(config=UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   {'input_ids': input_ids, 'attention_mask': input_mask, 'token_type_ids': token_type_ids}

						SCREAMING_SNAKE_CASE_   :	str													=   [input_ids, input_mask]
						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   model(UpperCamelCase__       )

						SCREAMING_SNAKE_CASE_   :	str													=   model(UpperCamelCase__       )

						self.parent.assertEqual(result.last_hidden_state.shape ,    (self.batch_size, self.seq_length, self.hidden_size)       )


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   TFDebertaVaForMaskedLM(config=UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Tuple													=   {
						    'input_ids': input_ids,
						    'attention_mask': input_mask,
						    'token_type_ids': token_type_ids,
						}
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   model(UpperCamelCase__       )
						self.parent.assertEqual(result.logits.shape ,    (self.batch_size, self.seq_length, self.vocab_size)       )


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	Any													=   self.num_labels
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   TFDebertaVaForSequenceClassification(config=UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	str													=   {
						    'input_ids': input_ids,
						    'attention_mask': input_mask,
						    'token_type_ids': token_type_ids,
						}

						SCREAMING_SNAKE_CASE_   :	Any													=   model(UpperCamelCase__       )
						self.parent.assertEqual(result.logits.shape ,    (self.batch_size, self.num_labels)       )


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   self.num_labels
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   TFDebertaVaForTokenClassification(config=UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	int													=   {
						    'input_ids': input_ids,
						    'attention_mask': input_mask,
						    'token_type_ids': token_type_ids,
						}
						SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   model(UpperCamelCase__       )
						self.parent.assertEqual(result.logits.shape ,    (self.batch_size, self.seq_length, self.num_labels)       )


		def   __snake_case			(						self ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__       ):
						SCREAMING_SNAKE_CASE_   :	List[str]													=   TFDebertaVaForQuestionAnswering(config=UpperCamelCase__       )
						SCREAMING_SNAKE_CASE_   :	Dict													=   {
						    'input_ids': input_ids,
						    'attention_mask': input_mask,
						    'token_type_ids': token_type_ids,
						}

						SCREAMING_SNAKE_CASE_   :	List[str]													=   model(UpperCamelCase__       )
						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   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Dict													=   self.prepare_config_and_inputs()
						(
						    SCREAMING_SNAKE_CASE_       
						)   :	Tuple													=   config_and_inputs
						SCREAMING_SNAKE_CASE_   :	int													=   {'input_ids': input_ids, 'token_type_ids': token_type_ids, 'attention_mask': input_mask}
						return config, inputs_dict






@require_tf
class 							__a							(  __A ,	__A ,	unittest.TestCase						):





		'''simple docstring'''



		UpperCAmelCase__      :				Optional[int]				    =						(
		    (
		        TFDebertaVaModel,
		        TFDebertaVaForMaskedLM,
		        TFDebertaVaForQuestionAnswering,
		        TFDebertaVaForSequenceClassification,
		        TFDebertaVaForTokenClassification,
		    )
		    if is_tf_available()
		    else ()
		)
		UpperCAmelCase__      :				Optional[Any]				    =						(
		    {
		        """feature-extraction""": TFDebertaVaModel,
		        """fill-mask""": TFDebertaVaForMaskedLM,
		        """question-answering""": TFDebertaVaForQuestionAnswering,
		        """text-classification""": TFDebertaVaForSequenceClassification,
		        """token-classification""": TFDebertaVaForTokenClassification,
		        """zero-shot""": TFDebertaVaForSequenceClassification,
		    }
		    if is_tf_available()
		    else {}
		)

		UpperCAmelCase__      :				Optional[int]				    =						False
		UpperCAmelCase__      :				str				    =						False


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Dict													=   TFDebertaVaModelTester(self       )
						SCREAMING_SNAKE_CASE_   :	List[str]													=   ConfigTester(self ,    config_class=UpperCamelCase__ ,    hidden_size=37       )


		def   __snake_case			(						self       ):
						self.config_tester.run_common_tests()


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Tuple													=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_model(*UpperCamelCase__       )


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_masked_lm(*UpperCamelCase__       )


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	str													=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_question_answering(*UpperCamelCase__       )


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	int													=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_sequence_classification(*UpperCamelCase__       )


		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Optional[int]													=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_token_classification(*UpperCamelCase__       )






		@slow
		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	Tuple													=   TFDebertaVaModel.from_pretrained('kamalkraj/deberta-v2-xlarge'       )
						self.assertIsNotNone(UpperCamelCase__       )






@require_tf
class 							__a							(  unittest.TestCase						):





		'''simple docstring'''



		@unittest.skip(reason='Model not available yet'       )
		def   __snake_case			(						self       ):
						pass






		@slow
		def   __snake_case			(						self       ):
						SCREAMING_SNAKE_CASE_   :	int													=   TFDebertaVaModel.from_pretrained('kamalkraj/deberta-v2-xlarge'       )
						SCREAMING_SNAKE_CASE_   :	int													=   tf.constant([[0, 31414, 232, 328, 740, 1140, 12695, 69, 46078, 1588, 2]]       )
						SCREAMING_SNAKE_CASE_   :	List[Any]													=   tf.constant([[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]       )
						SCREAMING_SNAKE_CASE_   :	List[str]													=   model(UpperCamelCase__ ,    attention_mask=UpperCamelCase__       )[0]

						SCREAMING_SNAKE_CASE_   :	List[str]													=   tf.constant(
						    [[[0.23_56, 0.19_48, 0.03_69], [-0.10_63, 0.35_86, -0.51_52], [-0.63_99, -0.02_59, -0.25_25]]]       )
						tf.debugging.assert_near(output[:, 1:4, 1:4] ,    UpperCamelCase__ ,    atol=1E-4       )







from math import sqrt



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    number >= 0
				), "'number' must been an int and positive"

				SCREAMING_SNAKE_CASE_   :	Dict													=   True

				# 0 and 1 are none primes.
				if number <= 1:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   False

				for divisor in range(2    ,    int(round(sqrt(lowerCAmelCase__      )      )      ) + 1      ):
								# if 'number' divisible by 'divisor' then sets 'status'
								# of false and break up the loop.
								if number % divisor == 0:
												SCREAMING_SNAKE_CASE_   :	Dict													=   False
												break

    # precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'status' must been from type bool"

				return status



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n > 2), "'N' must been an int and > 2"

				# beginList: contains all natural numbers from 2 up to N
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   list(range(2    ,    n + 1      )      )

				SCREAMING_SNAKE_CASE_   :	Any													=   []  # this list will be returns.

				# actual sieve of erathostenes
				for i in range(len(lowerCAmelCase__      )      ):
								for j in range(i + 1    ,    len(lowerCAmelCase__      )      ):
												if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
																SCREAMING_SNAKE_CASE_   :	str													=   0

    # filters actual prime numbers.
				SCREAMING_SNAKE_CASE_   :	int													=   [x for x in begin_list if x != 0]

				# precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'ans' must been from type list"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		List[str]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n > 2), "'N' must been an int and > 2"

				SCREAMING_SNAKE_CASE_   :	int													=   []

				# iterates over all numbers between 2 up to N+1
				# if a number is prime then appends to list 'ans'
				for number in range(2    ,    n + 1      ):
								if is_prime(lowerCAmelCase__      ):
												ans.append(lowerCAmelCase__      )

    # precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'ans' must been from type list"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Union[str, Any]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and number >= 0, "'number' must been an int and >= 0"

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   []  # this list will be returns of the function.

				# potential prime number factors.

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   2

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   number

				if number == 0 or number == 1:
								ans.append(lowerCAmelCase__      )

				# if 'number' not prime then builds the prime factorization of 'number'
				elif not is_prime(lowerCAmelCase__      ):
								while quotient != 1:
												if is_prime(lowerCAmelCase__      ) and (quotient % factor == 0):
																ans.append(lowerCAmelCase__      )
																quotient /= factor
												else:
																factor += 1

				else:
								ans.append(lowerCAmelCase__      )

				# precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'ans' must been from type list"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Any      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				SCREAMING_SNAKE_CASE_   :	int													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Dict													=   max(lowerCAmelCase__      )

				# precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'ans' must been from type int"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   min(lowerCAmelCase__      )

				# precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'ans' must been from type int"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[int]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'number' must been an int"
				assert isinstance(number % 2 == 0    ,    lowerCAmelCase__      ), "compare bust been from type bool"

				return number % 2 == 0



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[int]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ), "'number' must been an int"
				assert isinstance(number % 2 != 0    ,    lowerCAmelCase__      ), "compare bust been from type bool"

				return number % 2 != 0



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (number > 2) and is_even(lowerCAmelCase__      )
				), "'number' must been an int, even and > 2"

				SCREAMING_SNAKE_CASE_   :	Any													=   []  # this list will returned

				# creates a list of prime numbers between 2 up to 'number'
				SCREAMING_SNAKE_CASE_   :	int													=   get_prime_numbers(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   len(lowerCAmelCase__      )

				# run variable for while-loops.
				SCREAMING_SNAKE_CASE_   :	Any													=   0
				SCREAMING_SNAKE_CASE_   :	List[str]													=   None

				# exit variable. for break up the loops
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   True

				while i < len_pn and loop:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																SCREAMING_SNAKE_CASE_   :	List[str]													=   False
																ans.append(prime_numbers[i]      )
																ans.append(prime_numbers[j]      )

												j += 1

								i += 1

				# precondition
				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (len(lowerCAmelCase__      ) == 2)
				    and (ans[0] + ans[1] == number)
				    and is_prime(ans[0]      )
				    and is_prime(ans[1]      )
				), "'ans' must contains two primes. And sum of elements must been eq 'number'"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		str    ,    lowerCAmelCase__				:		List[Any]      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				SCREAMING_SNAKE_CASE_   :	int													=   0

				while numbera != 0:
								SCREAMING_SNAKE_CASE_   :	List[str]													=   numbera % numbera
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   numbera
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   rest

				# precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    numbera >= 0
				), "'number' must been from type int and positive"

				return numbera



def 					_lowerCamelCase(			lowerCAmelCase__				:		int    ,    lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (numbera >= 1)
				    and (numbera >= 1)
				), "'number1' and 'number2' must been positive integer."

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   1  # actual answer that will be return.

				# for kgV (x,1)
				if numbera > 1 and numbera > 1:
								# builds the prime factorization of 'number1' and 'number2'
								SCREAMING_SNAKE_CASE_   :	Tuple													=   prime_factorization(lowerCAmelCase__      )
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   prime_factorization(lowerCAmelCase__      )

				elif numbera == 1 or numbera == 1:
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	int													=   max(lowerCAmelCase__    ,    lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   0
				SCREAMING_SNAKE_CASE_   :	Any													=   0

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []  # captured numbers int both 'primeFac1' and 'primeFac2'

				# iterates through primeFac1
				for n in prime_fac_a:
								if n not in done:
												if n in prime_fac_a:
																SCREAMING_SNAKE_CASE_   :	int													=   prime_fac_a.count(lowerCAmelCase__      )
																SCREAMING_SNAKE_CASE_   :	Tuple													=   prime_fac_a.count(lowerCAmelCase__      )

																for _ in range(max(lowerCAmelCase__    ,    lowerCAmelCase__      )      ):
																				ans *= n

												else:
																SCREAMING_SNAKE_CASE_   :	List[Any]													=   prime_fac_a.count(lowerCAmelCase__      )

																for _ in range(lowerCAmelCase__      ):
																				ans *= n

												done.append(lowerCAmelCase__      )

    # iterates through primeFac2
				for n in prime_fac_a:
								if n not in done:
												SCREAMING_SNAKE_CASE_   :	int													=   prime_fac_a.count(lowerCAmelCase__      )

												for _ in range(lowerCAmelCase__      ):
																ans *= n

												done.append(lowerCAmelCase__      )

    # precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    ans >= 0
				), "'ans' must been from type int and positive"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Any      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n >= 0), "'number' must been a positive int"

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   2  # this variable holds the answer

				while index < n:
								index += 1

								ans += 1  # counts to the next number

								# if ans not prime then
								# runs to the next prime number.
								while not is_prime(lowerCAmelCase__      ):
												ans += 1

    # precondition
				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and is_prime(
				    lowerCAmelCase__      ), "'ans' must been a prime number and from type int"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		List[str]    ,    lowerCAmelCase__				:		Optional[int]      ):





				'''simple docstring'''







				assert (
				    is_prime(lowerCAmelCase__      ) and is_prime(lowerCAmelCase__      ) and (p_number_a < p_number_a)
				), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

				SCREAMING_SNAKE_CASE_   :	str													=   p_number_a + 1  # jump to the next number

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   []  # this list will be returns.

				# if number is not prime then
				# fetch the next prime number.
				while not is_prime(lowerCAmelCase__      ):
								number += 1

				while number < p_number_a:
								ans.append(lowerCAmelCase__      )

								number += 1

								# fetch the next prime number.
								while not is_prime(lowerCAmelCase__      ):
												number += 1

    # precondition
				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and ans[0] != p_number_a
				    and ans[len(lowerCAmelCase__      ) - 1] != p_number_a
				), "'ans' must been a list without the arguments"

				# 'ans' contains not 'pNumber1' and 'pNumber2' !
				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n >= 1), "'n' must been int and >= 1"

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []  # will be returned.

				for divisor in range(1    ,    n + 1      ):
								if n % divisor == 0:
												ans.append(lowerCAmelCase__      )

    # precondition
				assert ans[0] == 1 and ans[len(lowerCAmelCase__      ) - 1] == n, "Error in function getDivisiors(...)"

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (
				    number > 1
				), "'number' must been an int and >= 1"

				SCREAMING_SNAKE_CASE_   :	int													=   get_divisors(lowerCAmelCase__      )

				# precondition
				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (divisors[0] == 1)
				    and (divisors[len(lowerCAmelCase__      ) - 1] == number)
				), "Error in help-function getDivisiors(...)"

				# summed all divisors up to 'number' (exclusive), hence [:-1]
				return sum(divisors[:-1]      ) == number



def 					_lowerCamelCase(			lowerCAmelCase__				:		Dict    ,    lowerCAmelCase__				:		str      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (denominator != 0)
				), "The arguments must been from type int and 'denominator' != 0"

				# build the greatest common divisor of numerator and denominator.
				SCREAMING_SNAKE_CASE_   :	str													=   gcd(abs(lowerCAmelCase__      )    ,    abs(lowerCAmelCase__      )      )

				# precondition
				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and (numerator % gcd_of_fraction == 0)
				    and (denominator % gcd_of_fraction == 0)
				), "Error in function gcd(...,...)"

				return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)



def 					_lowerCamelCase(			lowerCAmelCase__				:		Tuple      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n >= 0), "'n' must been a int and >= 0"

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   1  # this will be return.

				for factor in range(1    ,    n + 1      ):
								ans *= factor

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Tuple      ):





				'''simple docstring'''







				assert isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (n >= 0), "'n' must been an int and >= 0"

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   0
				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   1
				SCREAMING_SNAKE_CASE_   :	int													=   1  # this will be return

				for _ in range(n - 1      ):
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   ans
								ans += fiba
								SCREAMING_SNAKE_CASE_   :	List[str]													=   tmp

				return ans