

from math import sqrt




def 					_lowercase     (				a_				:					int				)				->	bool:




					'''simple docstring'''







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

					__magic_name__							=    True

					# 0 and 1 are none primes.
					if number <= 1:
										__magic_name__							=    False

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

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

					return status




def 					_lowercase     (				a_				:					Any				)				->	str:




					'''simple docstring'''







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

					# beginList: contains all natural numbers from 2 up to N
					__magic_name__							=    list(range(2					,n + 1				)				)

					__magic_name__							=    []  # this list will be returns.

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

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

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

					return ans




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	Optional[int]:




					'''simple docstring'''







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

					__magic_name__							=    []

					# 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(a_				):
															ans.append(a_				)

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

					return ans




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	Any:




					'''simple docstring'''







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

					__magic_name__							=    []  # this list will be returns of the function.

					# potential prime number factors.

					__magic_name__							=    2

					__magic_name__							=    number

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

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

					else:
										ans.append(a_				)

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

					return ans




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	str:




					'''simple docstring'''







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

					__magic_name__							=    0

					# prime factorization of 'number'
					__magic_name__							=    prime_factorization(a_				)

					__magic_name__							=    max(a_				)

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

					return ans




def 					_lowercase     (				a_				:					str				)				->	Tuple:




					'''simple docstring'''







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

					__magic_name__							=    0

					# prime factorization of 'number'
					__magic_name__							=    prime_factorization(a_				)

					__magic_name__							=    min(a_				)

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

					return ans




def 					_lowercase     (				a_				:					Tuple				)				->	Tuple:




					'''simple docstring'''







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

					return number % 2 == 0




def 					_lowercase     (				a_				:					Optional[int]				)				->	str:




					'''simple docstring'''







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

					return number % 2 != 0




def 					_lowercase     (				a_				:					int				)				->	Any:




					'''simple docstring'''







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

					__magic_name__							=    []  # this list will returned

					# creates a list of prime numbers between 2 up to 'number'
					__magic_name__							=    get_prime_numbers(a_				)
					__magic_name__							=    len(a_				)

					# run variable for while-loops.
					__magic_name__							=    0
					__magic_name__							=    None

					# exit variable. for break up the loops
					__magic_name__							=    True

					while i < len_pn and loop:
										__magic_name__							=    i + 1

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

															j += 1

										i += 1

					# precondition
					assert (
					    isinstance(a_					,a_				)
					    and (len(a_				) == 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 					_lowercase     (				a_				:					Union[str, Any]					,a_				:					List[str]				)				->	int:




					'''simple docstring'''







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

					__magic_name__							=    0

					while numbera != 0:
										__magic_name__							=    numbera % numbera
										__magic_name__							=    numbera
										__magic_name__							=    rest

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

					return numbera




def 					_lowercase     (				a_				:					Optional[Any]					,a_				:					List[Any]				)				->	str:




					'''simple docstring'''







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

					__magic_name__							=    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'
										__magic_name__							=    prime_factorization(a_				)
										__magic_name__							=    prime_factorization(a_				)

					elif numbera == 1 or numbera == 1:
										__magic_name__							=    []
										__magic_name__							=    []
										__magic_name__							=    max(a_					,a_				)

					__magic_name__							=    0
					__magic_name__							=    0

					__magic_name__							=    []  # 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:
																				__magic_name__							=    prime_fac_a.count(a_				)
																				__magic_name__							=    prime_fac_a.count(a_				)

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

															else:
																				__magic_name__							=    prime_fac_a.count(a_				)

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

															done.append(a_				)

    # iterates through primeFac2
					for n in prime_fac_a:
										if n not in done:
															__magic_name__							=    prime_fac_a.count(a_				)

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

															done.append(a_				)

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

					return ans




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	List[str]:




					'''simple docstring'''







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

					__magic_name__							=    0
					__magic_name__							=    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(a_				):
															ans += 1

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

					return ans




def 					_lowercase     (				a_				:					List[Any]					,a_				:					List[str]				)				->	Dict:




					'''simple docstring'''







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

					__magic_name__							=    p_number_a + 1  # jump to the next number

					__magic_name__							=    []  # this list will be returns.

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

					while number < p_number_a:
										ans.append(a_				)

										number += 1

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

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

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




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	int:




					'''simple docstring'''







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

					__magic_name__							=    []  # will be returned.

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

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

					return ans




def 					_lowercase     (				a_				:					Union[str, Any]				)				->	Union[str, Any]:




					'''simple docstring'''







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

					__magic_name__							=    get_divisors(a_				)

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

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




def 					_lowercase     (				a_				:					Any					,a_				:					Union[str, Any]				)				->	List[Any]:




					'''simple docstring'''







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

					# build the greatest common divisor of numerator and denominator.
					__magic_name__							=    gcd(abs(a_				)					,abs(a_				)				)

					# precondition
					assert (
					    isinstance(a_					,a_				)
					    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 					_lowercase     (				a_				:					List[Any]				)				->	Tuple:




					'''simple docstring'''







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

					__magic_name__							=    1  # this will be return.

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

					return ans




def 					_lowercase     (				a_				:					Optional[int]				)				->	List[str]:




					'''simple docstring'''







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

					__magic_name__							=    0
					__magic_name__							=    1
					__magic_name__							=    1  # this will be return

					for _ in range(n - 1				):
										__magic_name__							=    ans
										ans += fiba
										__magic_name__							=    tmp

					return ans







import unittest

from transformers import AutoConfig, AutoTokenizer, BertConfig, TensorType, is_flax_available
from transformers.testing_utils import DUMMY_UNKNOWN_IDENTIFIER, require_flax, slow


if is_flax_available():
						import jax

						from transformers.models.auto.modeling_flax_auto import FlaxAutoModel
						from transformers.models.bert.modeling_flax_bert import FlaxBertModel
						from transformers.models.roberta.modeling_flax_roberta import FlaxRobertaModel

@require_flax
class 				__UpperCamelCase				(					unittest.TestCase			):







	@slow
	def 	_SCREAMING_SNAKE_CASE							(   self: Any      ):

						'''simple docstring'''





						for model_name in ["bert-base-cased", "bert-large-uncased"]:
											with self.subTest(__UpperCamelCase      ):
																__magic_name__							=    AutoConfig.from_pretrained(__UpperCamelCase      )
																self.assertIsNotNone(__UpperCamelCase      )
																self.assertIsInstance(__UpperCamelCase  , __UpperCamelCase      )

																__magic_name__							=    FlaxAutoModel.from_pretrained(__UpperCamelCase      )
																self.assertIsNotNone(__UpperCamelCase      )
																self.assertIsInstance(__UpperCamelCase  , __UpperCamelCase      )







	@slow
	def 	_SCREAMING_SNAKE_CASE							(   self: Tuple      ):

						'''simple docstring'''





						for model_name in ["roberta-base", "roberta-large"]:
											with self.subTest(__UpperCamelCase      ):
																__magic_name__							=    AutoConfig.from_pretrained(__UpperCamelCase      )
																self.assertIsNotNone(__UpperCamelCase      )
																self.assertIsInstance(__UpperCamelCase  , __UpperCamelCase      )

																__magic_name__							=    FlaxAutoModel.from_pretrained(__UpperCamelCase      )
																self.assertIsNotNone(__UpperCamelCase      )
																self.assertIsInstance(__UpperCamelCase  , __UpperCamelCase      )







	@slow
	def 	_SCREAMING_SNAKE_CASE							(   self: Dict      ):

						'''simple docstring'''





						for model_name in ["bert-base-cased", "bert-large-uncased"]:
											__magic_name__							=    AutoTokenizer.from_pretrained(__UpperCamelCase      )
											__magic_name__							=    FlaxBertModel.from_pretrained(__UpperCamelCase      )
											__magic_name__							=    tokenizer('Do you support jax jitted function?'  , return_tensors=TensorType.JAX      )

											@jax.jit
											def eval(**__UpperCamelCase: Optional[Any]      ):
																return model(**__UpperCamelCase      )

											eval(**__UpperCamelCase      ).block_until_ready()







	@slow
	def 	_SCREAMING_SNAKE_CASE							(   self: int      ):

						'''simple docstring'''





						for model_name in ["roberta-base", "roberta-large"]:
											__magic_name__							=    AutoTokenizer.from_pretrained(__UpperCamelCase      )
											__magic_name__							=    FlaxRobertaModel.from_pretrained(__UpperCamelCase      )
											__magic_name__							=    tokenizer('Do you support jax jitted function?'  , return_tensors=TensorType.JAX      )

											@jax.jit
											def eval(**__UpperCamelCase: Any      ):
																return model(**__UpperCamelCase      )

											eval(**__UpperCamelCase      ).block_until_ready()







	def 	_SCREAMING_SNAKE_CASE							(   self: Tuple      ):

						'''simple docstring'''





						with self.assertRaisesRegex(
						    __UpperCamelCase  , 'bert-base is not a local folder and is not a valid model identifier'      ):
											__magic_name__							=    FlaxAutoModel.from_pretrained('bert-base'      )







	def 	_SCREAMING_SNAKE_CASE							(   self: List[Any]      ):

						'''simple docstring'''





						with self.assertRaisesRegex(
						    __UpperCamelCase  , r'aaaaaa is not a valid git identifier \(branch name, tag name or commit id\)'      ):
											__magic_name__							=    FlaxAutoModel.from_pretrained(__UpperCamelCase  , revision='aaaaaa'      )







	def 	_SCREAMING_SNAKE_CASE							(   self: str      ):

						'''simple docstring'''





						with self.assertRaisesRegex(
						    __UpperCamelCase  , 'hf-internal-testing/config-no-model does not appear to have a file named flax_model.msgpack'  , ):
											__magic_name__							=    FlaxAutoModel.from_pretrained('hf-internal-testing/config-no-model'      )







	def 	_SCREAMING_SNAKE_CASE							(   self: int      ):

						'''simple docstring'''





						with self.assertRaisesRegex(__UpperCamelCase  , 'Use `from_pt=True` to load this model'      ):
											__magic_name__							=    FlaxAutoModel.from_pretrained('hf-internal-testing/tiny-bert-pt-only'      )




