





"""simple docstring"""






from math import sqrt





def __A						(   a_ :							Any     )->							bool:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     int				= True

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

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

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

		return status





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




		'''simple docstring'''






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

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

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

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

    # filters actual prime numbers.
		SCREAMING_SNAKE_CASE       :     Optional[Any]				= [x for x in begin_list if x != 0]

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

		return ans





def __A						(   a_ :							Dict     )->							List[str]:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Any				= []

		# 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(UpperCamelCase__     ):
						ans.append(UpperCamelCase__     )

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

		return ans





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




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Any				= []  # this list will be returns of the function.

		# potential prime number factors.

		SCREAMING_SNAKE_CASE       :     int				= 2

		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= number

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

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

		else:
				ans.append(UpperCamelCase__     )

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

		return ans





def __A						(   a_ :							Tuple     )->							Optional[int]:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Any				= 0

		# prime factorization of 'number'
		SCREAMING_SNAKE_CASE       :     Tuple				= prime_factorization(UpperCamelCase__     )

		SCREAMING_SNAKE_CASE       :     List[str]				= max(UpperCamelCase__     )

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

		return ans





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




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Optional[int]				= 0

		# prime factorization of 'number'
		SCREAMING_SNAKE_CASE       :     int				= prime_factorization(UpperCamelCase__     )

		SCREAMING_SNAKE_CASE       :     Any				= min(UpperCamelCase__     )

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

		return ans





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




		'''simple docstring'''






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

		return number % 2 == 0





def __A						(   a_ :							Any     )->							str:




		'''simple docstring'''






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

		return number % 2 != 0





def __A						(   a_ :							List[Any]     )->							int:




		'''simple docstring'''






		assert (
		    isinstance(UpperCamelCase__		,		UpperCamelCase__     ) and (number > 2) and is_even(UpperCamelCase__     )
		), "'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       :     List[str]				= get_prime_numbers(UpperCamelCase__     )
		SCREAMING_SNAKE_CASE       :     int				= len(UpperCamelCase__     )

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

		# exit variable. for break up the loops
		SCREAMING_SNAKE_CASE       :     Optional[int]				= True

		while i < len_pn and loop:
				SCREAMING_SNAKE_CASE       :     Optional[Any]				= i + 1

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

						j += 1

				i += 1

		# precondition
		assert (
		    isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    and (len(UpperCamelCase__     ) == 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						(   a_ :							List[str]		,		a_ :							Optional[int]     )->							Tuple:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Any				= 0

		while numbera != 0:
				SCREAMING_SNAKE_CASE       :     Dict				= numbera % numbera
				SCREAMING_SNAKE_CASE       :     Optional[Any]				= numbera
				SCREAMING_SNAKE_CASE       :     int				= rest

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

		return numbera





def __A						(   a_ :							Any		,		a_ :							Tuple     )->							Any:




		'''simple docstring'''






		assert (
		    isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    and isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    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       :     Union[str, Any]				= prime_factorization(UpperCamelCase__     )
				SCREAMING_SNAKE_CASE       :     Optional[int]				= prime_factorization(UpperCamelCase__     )

		elif numbera == 1 or numbera == 1:
				SCREAMING_SNAKE_CASE       :     int				= []
				SCREAMING_SNAKE_CASE       :     Tuple				= []
				SCREAMING_SNAKE_CASE       :     List[Any]				= max(UpperCamelCase__		,		UpperCamelCase__     )

		SCREAMING_SNAKE_CASE       :     int				= 0
		SCREAMING_SNAKE_CASE       :     Optional[int]				= 0

		SCREAMING_SNAKE_CASE       :     Union[str, 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       :     Tuple				= prime_fac_a.count(UpperCamelCase__     )
								SCREAMING_SNAKE_CASE       :     int				= prime_fac_a.count(UpperCamelCase__     )

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

						else:
								SCREAMING_SNAKE_CASE       :     int				= prime_fac_a.count(UpperCamelCase__     )

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

						done.append(UpperCamelCase__     )

    # iterates through primeFac2
		for n in prime_fac_a:
				if n not in done:
						SCREAMING_SNAKE_CASE       :     Union[str, Any]				= prime_fac_a.count(UpperCamelCase__     )

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

						done.append(UpperCamelCase__     )

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

		return ans





def __A						(   a_ :							Optional[int]     )->							Dict:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     List[Any]				= 0
		SCREAMING_SNAKE_CASE       :     Dict				= 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(UpperCamelCase__     ):
						ans += 1

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

		return ans





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




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     List[str]				= p_number_a + 1  # jump to the next number

		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= []  # this list will be returns.

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

		while number < p_number_a:
				ans.append(UpperCamelCase__     )

				number += 1

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

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

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





def __A						(   a_ :							List[str]     )->							Dict:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     int				= []  # will be returned.

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

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

		return ans





def __A						(   a_ :							str     )->							Any:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     Union[str, Any]				= get_divisors(UpperCamelCase__     )

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

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





def __A						(   a_ :							List[str]		,		a_ :							Dict     )->							int:




		'''simple docstring'''






		assert (
		    isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    and isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    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       :     Union[str, Any]				= gcd(abs(UpperCamelCase__     )		,		abs(UpperCamelCase__     )     )

		# precondition
		assert (
		    isinstance(UpperCamelCase__		,		UpperCamelCase__     )
		    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						(   a_ :							Dict     )->							int:




		'''simple docstring'''






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

		SCREAMING_SNAKE_CASE       :     str				= 1  # this will be return.

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

		return ans





def __A						(   a_ :							str     )->							str:




		'''simple docstring'''






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

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

		for _ in range(n - 1     ):
				SCREAMING_SNAKE_CASE       :     Tuple				= ans
				ans += fiba
				SCREAMING_SNAKE_CASE       :     List[Any]				= tmp

		return ans







"""simple docstring"""






import json
import os
from typing import Optional, Tuple

from ...tokenization_utils import PreTrainedTokenizer
from ...utils import logging


lowerCamelCase__ :       List[str]						     =			logging.get_logger(__name__)

lowerCamelCase__ :       Optional[int]						     =			{"vocab_file": "vocab.json"}

lowerCamelCase__ :       Dict						     =			{
    "vocab_file": {
        "mgp-str": "https://huggingface.co/alibaba-damo/mgp-str-base/blob/main/vocab.json",
    }
}

lowerCamelCase__ :       Optional[Any]						     =			{"mgp-str": 27}




class 				lowercase__(				_UpperCAmelCase   ):
	'''simple docstring'''

	UpperCamelCase				=  VOCAB_FILES_NAMES
	UpperCamelCase				=  PRETRAINED_VOCAB_FILES_MAP
	UpperCamelCase				=  PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES





	def __init__(						self    :int		, lowerCamelCase_    :Optional[int]		, lowerCamelCase_    :Optional[int]="[GO]"		, lowerCamelCase_    :int="[GO]"		, lowerCamelCase_    :str="[s]"		, lowerCamelCase_    :Dict="[GO]"		, **lowerCamelCase_    :List[str]					)							->			Tuple:







			'''simple docstring'''




			super().__init__(
			    unk_token=lowerCamelCase_		, bos_token=lowerCamelCase_		, eos_token=lowerCamelCase_		, pad_token=lowerCamelCase_		, **lowerCamelCase_		, )

			with open(lowerCamelCase_		, encoding='''utf-8'''					) as vocab_handle:
					SCREAMING_SNAKE_CASE       :     int				= json.load(lowerCamelCase_					)
			SCREAMING_SNAKE_CASE       :     Union[str, Any]				= {v: k for k, v in self.vocab.items()}





	@property
	def   __lowerCAmelCase (						self    :int					)							->			Dict:







			'''simple docstring'''




			return len(self.vocab					)





	def   __lowerCAmelCase (						self    :List[str]					)							->			Dict:







			'''simple docstring'''




			return dict(self.vocab		, **self.added_tokens_encoder					)





	def   __lowerCAmelCase (						self    :List[str]		, lowerCamelCase_    :Optional[Any]					)							->			List[str]:







			'''simple docstring'''




			SCREAMING_SNAKE_CASE       :     Union[str, Any]				= []
			for s in text:
					char_tokens.extend(lowerCamelCase_					)
			return char_tokens





	def   __lowerCAmelCase (						self    :Dict		, lowerCamelCase_    :Tuple					)							->			Optional[int]:







			'''simple docstring'''




			return self.vocab.get(lowerCamelCase_		, self.vocab.get(self.unk_token					)					)





	def   __lowerCAmelCase (						self    :List[str]		, lowerCamelCase_    :Dict					)							->			Optional[int]:







			'''simple docstring'''




			return self.decoder.get(lowerCamelCase_					)







	def   __lowerCAmelCase (						self    :Optional[int]		, lowerCamelCase_    :str		, lowerCamelCase_    :Optional[str] = None					)							->			Tuple[str]:







			'''simple docstring'''




			if not os.path.isdir(lowerCamelCase_					):
					logger.error('''Vocabulary path ({}) should be a directory'''.format(lowerCamelCase_					)					)
					return
			SCREAMING_SNAKE_CASE       :     List[Any]				= os.path.join(
			    lowerCamelCase_		, (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file''']					)

			with open(lowerCamelCase_		, '''w'''		, encoding='''utf-8'''					) as f:
					f.write(json.dumps(self.vocab		, indent=2		, sort_keys=lowerCamelCase_		, ensure_ascii=lowerCamelCase_					) + '''\n'''					)

			return (vocab_file,)





