



from math import sqrt






def  lowerCamelCase_	(      lowerCAmelCase__	:	int				)       ->							bool:

							'''simple docstring'''






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

							A      						=    True

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

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

							return status






def  lowerCamelCase_	(      lowerCAmelCase__	:	Tuple				)       ->							str:

							'''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
							A      						=    list(range(2			,	n + 1				)				)

							A      						=    []  # 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):
																												A      						=    0

    # filters actual prime numbers.
							A      						=    [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__	:	str				)       ->							Dict:

							'''simple docstring'''






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

							A      						=    []

							# 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__	:	Optional[int]				)       ->							Dict:

							'''simple docstring'''






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

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

							# potential prime number factors.

							A      						=    2

							A      						=    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__	:	List[Any]				)       ->							Tuple:

							'''simple docstring'''






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

							A      						=    0

							# prime factorization of 'number'
							A      						=    prime_factorization(lowerCAmelCase__				)

							A      						=    max(lowerCAmelCase__				)

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

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	int				)       ->							List[Any]:

							'''simple docstring'''






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

							A      						=    0

							# prime factorization of 'number'
							A      						=    prime_factorization(lowerCAmelCase__				)

							A      						=    min(lowerCAmelCase__				)

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

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]				)       ->							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__	:	Tuple				)       ->							Any:

							'''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]				)       ->							int:

							'''simple docstring'''






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

							A      						=    []  # this list will returned

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

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

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

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

														while j < len_pn and loop:
																					if prime_numbers[i] + prime_numbers[j] == number:
																												A      						=    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__	:	List[Any]			,	lowerCAmelCase__	:	Optional[int]				)       ->							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."

							A      						=    0

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

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

							return numbera






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]			,	lowerCAmelCase__	:	List[Any]				)       ->							Union[str, Any]:

							'''simple docstring'''






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

							A      						=    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'
														A      						=    prime_factorization(lowerCAmelCase__				)
														A      						=    prime_factorization(lowerCAmelCase__				)

							elif numbera == 1 or numbera == 1:
														A      						=    []
														A      						=    []
														A      						=    max(lowerCAmelCase__			,	lowerCAmelCase__				)

							A      						=    0
							A      						=    0

							A      						=    []  # 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:
																												A      						=    prime_fac_a.count(lowerCAmelCase__				)
																												A      						=    prime_fac_a.count(lowerCAmelCase__				)

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

																					else:
																												A      						=    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:
																					A      						=    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__	:	Tuple				)       ->							Any:

							'''simple docstring'''






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

							A      						=    0
							A      						=    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[Any]			,	lowerCAmelCase__	:	str				)       ->							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'"

							A      						=    p_number_a + 1  # jump to the next number

							A      						=    []  # 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__	:	List[Any]				)       ->							List[str]:

							'''simple docstring'''






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

							A      						=    []  # 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__	:	Optional[int]				)       ->							Optional[Any]:

							'''simple docstring'''






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

							A      						=    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__	:	Any			,	lowerCAmelCase__	:	Union[str, Any]				)       ->							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.
							A      						=    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__	:	Dict				)       ->							int:

							'''simple docstring'''






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

							A      						=    1  # this will be return.

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

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[str]				)       ->							Union[str, Any]:

							'''simple docstring'''






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

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

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

							return ans




import json
import os
import unittest

from transformers import BatchEncoding, LEDTokenizer, LEDTokenizerFast
from transformers.models.led.tokenization_led import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers, require_torch
from transformers.utils import cached_property

from ...test_tokenization_common import TokenizerTesterMixin



@require_tokenizers
class        lowerCAmelCase__					(  _lowerCamelCase ,				unittest.TestCase       ):
				A_   :     Dict								=     LEDTokenizer
				A_   :     Union[str, Any]								=     LEDTokenizerFast
				A_   :     Tuple								=     True


				def __UpperCamelCase						(							self      :  str       )		->     str:
											super().setUp()
											A      						=    [
											    'l',
											    'o',
											    'w',
											    'e',
											    'r',
											    's',
											    't',
											    'i',
											    'd',
											    'n',
											    '\u0120',
											    '\u0120l',
											    '\u0120n',
											    '\u0120lo',
											    '\u0120low',
											    'er',
											    '\u0120lowest',
											    '\u0120newer',
											    '\u0120wider',
											    '<unk>',
											]
											A      						=    dict(zip(__UpperCamelCase						, range(len(__UpperCamelCase       )       )       )       )
											A      						=    ['#version: 0.2', '\u0120 l', '\u0120l o', '\u0120lo w', 'e r', '']
											A      						=    {'unk_token': '<unk>'}

											A      						=    os.path.join(self.tmpdirname						, VOCAB_FILES_NAMES['vocab_file']       )
											A      						=    os.path.join(self.tmpdirname						, VOCAB_FILES_NAMES['merges_file']       )
											with open(self.vocab_file						, 'w'						, encoding='utf-8'       ) as fp:
																		fp.write(json.dumps(__UpperCamelCase       ) + '\n'       )
											with open(self.merges_file						, 'w'						, encoding='utf-8'       ) as fp:
																		fp.write('\n'.join(__UpperCamelCase       )       )


				def __UpperCamelCase						(							self      :  str						, **__UpperCamelCase      :  str       )		->     Tuple:
											kwargs.update(self.special_tokens_map       )
											return self.tokenizer_class.from_pretrained(self.tmpdirname						, **__UpperCamelCase       )


				def __UpperCamelCase						(							self      :  List[str]						, **__UpperCamelCase      :  List[Any]       )		->     str:
											kwargs.update(self.special_tokens_map       )
											return self.rust_tokenizer_class.from_pretrained(self.tmpdirname						, **__UpperCamelCase       )


				def __UpperCamelCase						(							self      :  Optional[Any]						, __UpperCamelCase      :  Optional[int]       )		->     Dict:
											return "lower newer", "lower newer"


				@cached_property
				def __UpperCamelCase						(							self      :  Union[str, Any]       )		->     Any:
											return LEDTokenizer.from_pretrained('allenai/led-base-16384'       )


				@cached_property
				def __UpperCamelCase						(							self      :  str       )		->     str:
											return LEDTokenizerFast.from_pretrained('allenai/led-base-16384'       )


				@require_torch
				def __UpperCamelCase						(							self      :  str       )		->     Optional[Any]:
											A      						=    ['A long paragraph for summarization.', 'Another paragraph for summarization.']
											A      						=    [0, 250, 251, 17_818, 13, 39_186, 1_938, 4, 2]

											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    tokenizer(__UpperCamelCase						, max_length=len(__UpperCamelCase       )						, padding=__UpperCamelCase						, return_tensors='pt'       )
																		self.assertIsInstance(__UpperCamelCase						, __UpperCamelCase       )

																		self.assertEqual((2, 9)						, batch.input_ids.shape       )
																		self.assertEqual((2, 9)						, batch.attention_mask.shape       )
																		A      						=    batch.input_ids.tolist()[0]
																		self.assertListEqual(__UpperCamelCase						, __UpperCamelCase       )


				@require_torch
				def __UpperCamelCase						(							self      :  Optional[int]       )		->     str:
											A      						=    ['A long paragraph for summarization.', 'Another paragraph for summarization.']
											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    tokenizer(__UpperCamelCase						, padding=__UpperCamelCase						, return_tensors='pt'       )
																		self.assertIn('input_ids'						, __UpperCamelCase       )
																		self.assertIn('attention_mask'						, __UpperCamelCase       )
																		self.assertNotIn('labels'						, __UpperCamelCase       )
																		self.assertNotIn('decoder_attention_mask'						, __UpperCamelCase       )


				@require_torch
				def __UpperCamelCase						(							self      :  List[Any]       )		->     Union[str, Any]:
											A      						=    [
											    'Summary of the text.',
											    'Another summary.',
											]
											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    tokenizer(text_target=__UpperCamelCase						, max_length=32						, padding='max_length'						, return_tensors='pt'       )
																		self.assertEqual(32						, targets['input_ids'].shape[1]       )


				@require_torch
				def __UpperCamelCase						(							self      :  List[str]       )		->     Any:
											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    tokenizer(
																		    ['I am a small frog' * 1_024, 'I am a small frog']						, padding=__UpperCamelCase						, truncation=__UpperCamelCase						, return_tensors='pt'       )
																		self.assertIsInstance(__UpperCamelCase						, __UpperCamelCase       )
																		self.assertEqual(batch.input_ids.shape						, (2, 5_122)       )


				@require_torch
				def __UpperCamelCase						(							self      :  int       )		->     Optional[Any]:
											A      						=    ['A long paragraph for summarization.']
											A      						=    [
											    'Summary of the text.',
											]
											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    tokenizer(__UpperCamelCase						, return_tensors='pt'       )
																		A      						=    tokenizer(text_target=__UpperCamelCase						, return_tensors='pt'       )
																		A      						=    inputs['input_ids']
																		A      						=    targets['input_ids']
																		self.assertTrue((input_ids[:, 0] == tokenizer.bos_token_id).all().item()       )
																		self.assertTrue((labels[:, 0] == tokenizer.bos_token_id).all().item()       )
																		self.assertTrue((input_ids[:, -1] == tokenizer.eos_token_id).all().item()       )
																		self.assertTrue((labels[:, -1] == tokenizer.eos_token_id).all().item()       )


				@require_torch
				def __UpperCamelCase						(							self      :  Union[str, Any]       )		->     Tuple:
											for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																		A      						=    ['Summary of the text.', 'Another summary.']
																		A      						=    [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, -1]]

																		A      						=    tokenizer(__UpperCamelCase						, padding=__UpperCamelCase       )
																		A      						=    [[0] * len(__UpperCamelCase       ) for x in encoded_output['input_ids']]
																		A      						=    tokenizer.pad(__UpperCamelCase       )
																		self.assertSequenceEqual(outputs['global_attention_mask']						, __UpperCamelCase       )


				def __UpperCamelCase						(							self      :  str       )		->     int:
											pass


				def __UpperCamelCase						(							self      :  Dict       )		->     Any:
											for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
																		with self.subTest(f'''{tokenizer.__class__.__name__} ({pretrained_name})'''       ):
																									A      						=    self.rust_tokenizer_class.from_pretrained(__UpperCamelCase						, **__UpperCamelCase       )
																									A      						=    self.tokenizer_class.from_pretrained(__UpperCamelCase						, **__UpperCamelCase       )
																									A      						=    'A, <mask> AllenNLP sentence.'
																									A      						=    tokenizer_r.encode_plus(__UpperCamelCase						, add_special_tokens=__UpperCamelCase						, return_token_type_ids=__UpperCamelCase       )
																									A      						=    tokenizer_p.encode_plus(__UpperCamelCase						, add_special_tokens=__UpperCamelCase						, return_token_type_ids=__UpperCamelCase       )
																									self.assertEqual(sum(tokens_r['token_type_ids']       )						, sum(tokens_p['token_type_ids']       )       )
																									self.assertEqual(
																									    sum(tokens_r['attention_mask']       ) / len(tokens_r['attention_mask']       )						, sum(tokens_p['attention_mask']       ) / len(tokens_p['attention_mask']       )						, )

																									A      						=    tokenizer_r.convert_ids_to_tokens(tokens_r['input_ids']       )
																									A      						=    tokenizer_p.convert_ids_to_tokens(tokens_p['input_ids']       )
																									self.assertSequenceEqual(tokens_p['input_ids']						, [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]       )
																									self.assertSequenceEqual(tokens_r['input_ids']						, [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]       )

																									self.assertSequenceEqual(
																									    __UpperCamelCase						, ['<s>', 'A', ',', '<mask>', 'ĠAllen', 'N', 'LP', 'Ġsentence', '.', '</s>']       )
																									self.assertSequenceEqual(
																									    __UpperCamelCase						, ['<s>', 'A', ',', '<mask>', 'ĠAllen', 'N', 'LP', 'Ġsentence', '.', '</s>']       )