



from math import sqrt





def 							A			(  _UpperCAmelCase       :     Optional[int]					)       ->				bool:







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

			_UpperCAmelCase	 =     True

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

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

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

			return status





def 							A			(  _UpperCAmelCase       :     Optional[Any]					)       ->				Dict:







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

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

			_UpperCAmelCase	 =     []  # this list will be returns.

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

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

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

			return ans





def 							A			(  _UpperCAmelCase       :     Optional[Any]					)       ->				List[str]:







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

			_UpperCAmelCase	 =     []

			# 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(__snake_case					):
									ans.append(__snake_case					)

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

			return ans





def 							A			(  _UpperCAmelCase       :     Union[str, Any]					)       ->				Optional[int]:







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

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

			# potential prime number factors.

			_UpperCAmelCase	 =     2

			_UpperCAmelCase	 =     number

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

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

			else:
						ans.append(__snake_case					)

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

			return ans





def 							A			(  _UpperCAmelCase       :     int					)       ->				Optional[Any]:







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

			_UpperCAmelCase	 =     0

			# prime factorization of 'number'
			_UpperCAmelCase	 =     prime_factorization(__snake_case					)

			_UpperCAmelCase	 =     max(__snake_case					)

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

			return ans





def 							A			(  _UpperCAmelCase       :     str					)       ->				int:







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

			_UpperCAmelCase	 =     0

			# prime factorization of 'number'
			_UpperCAmelCase	 =     prime_factorization(__snake_case					)

			_UpperCAmelCase	 =     min(__snake_case					)

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

			return ans





def 							A			(  _UpperCAmelCase       :     Union[str, Any]					)       ->				Union[str, Any]:







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

			return number % 2 == 0





def 							A			(  _UpperCAmelCase       :     Optional[int]					)       ->				Union[str, Any]:







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

			return number % 2 != 0





def 							A			(  _UpperCAmelCase       :     int					)       ->				str:







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

			_UpperCAmelCase	 =     []  # this list will returned

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

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

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

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

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

									j += 1

						i += 1

			# precondition
			assert (
			    isinstance(__snake_case							,     __snake_case					)
			    and (len(__snake_case					) == 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 							A			(  _UpperCAmelCase       :     int							,     _UpperCAmelCase       :     List[str]					)       ->				str:







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

			_UpperCAmelCase	 =     0

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

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

			return numbera





def 							A			(  _UpperCAmelCase       :     List[Any]							,     _UpperCAmelCase       :     Dict					)       ->				List[str]:







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

			_UpperCAmelCase	 =     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'
						_UpperCAmelCase	 =     prime_factorization(__snake_case					)
						_UpperCAmelCase	 =     prime_factorization(__snake_case					)

			elif numbera == 1 or numbera == 1:
						_UpperCAmelCase	 =     []
						_UpperCAmelCase	 =     []
						_UpperCAmelCase	 =     max(__snake_case							,     __snake_case					)

			_UpperCAmelCase	 =     0
			_UpperCAmelCase	 =     0

			_UpperCAmelCase	 =     []  # 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:
												_UpperCAmelCase	 =     prime_fac_a.count(__snake_case					)
												_UpperCAmelCase	 =     prime_fac_a.count(__snake_case					)

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

									else:
												_UpperCAmelCase	 =     prime_fac_a.count(__snake_case					)

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

									done.append(__snake_case					)

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

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

									done.append(__snake_case					)

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

			return ans





def 							A			(  _UpperCAmelCase       :     Any					)       ->				Tuple:







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

			_UpperCAmelCase	 =     0
			_UpperCAmelCase	 =     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(__snake_case					):
									ans += 1

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

			return ans





def 							A			(  _UpperCAmelCase       :     List[str]							,     _UpperCAmelCase       :     Any					)       ->				Tuple:







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

			_UpperCAmelCase	 =     p_number_a + 1  # jump to the next number

			_UpperCAmelCase	 =     []  # this list will be returns.

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

			while number < p_number_a:
						ans.append(__snake_case					)

						number += 1

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

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

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





def 							A			(  _UpperCAmelCase       :     int					)       ->				List[Any]:







			'''simple docstring'''
			assert isinstance(__snake_case							,     __snake_case					) and (n >= 1), "'n' must been int and >= 1"

			_UpperCAmelCase	 =     []  # will be returned.

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

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

			return ans





def 							A			(  _UpperCAmelCase       :     Any					)       ->				str:







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

			_UpperCAmelCase	 =     get_divisors(__snake_case					)

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

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





def 							A			(  _UpperCAmelCase       :     Union[str, Any]							,     _UpperCAmelCase       :     Optional[Any]					)       ->				Optional[Any]:







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

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

			# precondition
			assert (
			    isinstance(__snake_case							,     __snake_case					)
			    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 							A			(  _UpperCAmelCase       :     int					)       ->				Optional[Any]:







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

			_UpperCAmelCase	 =     1  # this will be return.

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

			return ans





def 							A			(  _UpperCAmelCase       :     Any					)       ->				Union[str, Any]:







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

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

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

			return ans





import os
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils import AddedToken
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
							from .tokenization_xlnet import XLNetTokenizer
else:
							UpperCAmelCase__     = None


UpperCAmelCase__     = logging.get_logger(__name__)

UpperCAmelCase__     = {"vocab_file": "spiece.model", "tokenizer_file": "tokenizer.json"}

UpperCAmelCase__     = {
    "vocab_file": {
        "xlnet-base-cased": "https://huggingface.co/xlnet-base-cased/resolve/main/spiece.model",
        "xlnet-large-cased": "https://huggingface.co/xlnet-large-cased/resolve/main/spiece.model",
    },
    "tokenizer_file": {
        "xlnet-base-cased": "https://huggingface.co/xlnet-base-cased/resolve/main/tokenizer.json",
        "xlnet-large-cased": "https://huggingface.co/xlnet-large-cased/resolve/main/tokenizer.json",
    },
}

UpperCAmelCase__     = {
    "xlnet-base-cased": None,
    "xlnet-large-cased": None,
}

UpperCAmelCase__     = "▁"

# Segments (not really needed)
UpperCAmelCase__     = 0
UpperCAmelCase__     = 1
UpperCAmelCase__     = 2
UpperCAmelCase__     = 3
UpperCAmelCase__     = 4







class     __lowerCAmelCase					(    A		):
			UpperCamelCase           =  VOCAB_FILES_NAMES
			UpperCamelCase           =  PRETRAINED_VOCAB_FILES_MAP
			UpperCamelCase           =  PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			UpperCamelCase           =  '''left'''
			UpperCamelCase           =  XLNetTokenizer



			def __init__(		self     :						Any				,	A     :						Union[str, Any]=None				,	A     :						str=None				,	A     :						Tuple=False				,	A     :						Tuple=True				,	A     :						Any=False				,	A     :						List[str]="<s>"				,	A     :						List[str]="</s>"				,	A     :						Optional[int]="<unk>"				,	A     :						Tuple="<sep>"				,	A     :						str="<pad>"				,	A     :						Dict="<cls>"				,	A     :						Dict="<mask>"				,	A     :						Optional[Any]=["<eop>", "<eod>"]				,	**A     :						Optional[Any]				,	)     ->					str:



						"""simple docstring"""






						_UpperCAmelCase	 =     AddedToken(A				,	lstrip=A				,	rstrip=A) if isinstance(A				,	A) else mask_token

						super().__init__(
						    vocab_file=A				,	tokenizer_file=A				,	do_lower_case=A				,	remove_space=A				,	keep_accents=A				,	bos_token=A				,	eos_token=A				,	unk_token=A				,	sep_token=A				,	pad_token=A				,	cls_token=A				,	mask_token=A				,	additional_special_tokens=A				,	**A				,	)

						_UpperCAmelCase	 =     3
						_UpperCAmelCase	 =     do_lower_case
						_UpperCAmelCase	 =     remove_space
						_UpperCAmelCase	 =     keep_accents
						_UpperCAmelCase	 =     vocab_file
						_UpperCAmelCase	 =     False if not self.vocab_file else True



			def 					_lowerCamelCase (		self     :						Tuple				,	A     :						List[int]				,	A     :						Optional[List[int]] = None)     ->					List[int]:



						"""simple docstring"""






						_UpperCAmelCase	 =     [self.sep_token_id]
						_UpperCAmelCase	 =     [self.cls_token_id]
						if token_ids_a is None:
									return token_ids_a + sep + cls
						return token_ids_a + sep + token_ids_a + sep + cls



			def 					_lowerCamelCase (		self     :						Tuple				,	A     :						List[int]				,	A     :						Optional[List[int]] = None)     ->					List[int]:



						"""simple docstring"""






						_UpperCAmelCase	 =     [self.sep_token_id]
						_UpperCAmelCase	 =     [2]

						if token_ids_a is None:
									return len(token_ids_a + sep) * [0] + cls_segment_id
						return len(token_ids_a + sep) * [0] + len(token_ids_a + sep) * [1] + cls_segment_id



			def 					_lowerCamelCase (		self     :						List[str]				,	A     :						str				,	A     :						Optional[str] = None)     ->					Tuple[str]:



						"""simple docstring"""






						if not self.can_save_slow_tokenizer:
									raise ValueError(
									    'Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '
									    'tokenizer.')

						if not os.path.isdir(A):
									logger.error(F"Vocabulary path ({save_directory}) should be a directory")
									return
						_UpperCAmelCase	 =     os.path.join(
						    A				,	(filename_prefix + '-' if filename_prefix else '') + VOCAB_FILES_NAMES['vocab_file'])

						if os.path.abspath(self.vocab_file) != os.path.abspath(A):
									copyfile(self.vocab_file				,	A)

						return (out_vocab_file,)
