


from math import sqrt







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

				_SCREAMING_SNAKE_CASE			  =True

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

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

				return status







def 						lowerCamelCase(   a__):
				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			  =list(range(2	,n + 1))

				_SCREAMING_SNAKE_CASE			  =[]  # 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			  =0

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

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

				return ans







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

				_SCREAMING_SNAKE_CASE			  =[]

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

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

				# potential prime number factors.

				_SCREAMING_SNAKE_CASE			  =2

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

				_SCREAMING_SNAKE_CASE			  =0

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

				_SCREAMING_SNAKE_CASE			  =max(lowerCAmelCase__)

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

				return ans







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

				_SCREAMING_SNAKE_CASE			  =0

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

				_SCREAMING_SNAKE_CASE			  =min(lowerCAmelCase__)

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

				return ans







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

				_SCREAMING_SNAKE_CASE			  =[]  # this list will returned

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

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

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

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

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																_SCREAMING_SNAKE_CASE			  =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(   a__	,a__):
				assert (
				    isinstance(lowerCAmelCase__	,lowerCAmelCase__)
				    and isinstance(lowerCAmelCase__	,lowerCAmelCase__)
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				_SCREAMING_SNAKE_CASE			  =0

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

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

				return numbera







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

				_SCREAMING_SNAKE_CASE			  =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			  =prime_factorization(lowerCAmelCase__)
								_SCREAMING_SNAKE_CASE			  =prime_factorization(lowerCAmelCase__)

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

				_SCREAMING_SNAKE_CASE			  =0
				_SCREAMING_SNAKE_CASE			  =0

				_SCREAMING_SNAKE_CASE			  =[]  # 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			  =prime_fac_a.count(lowerCAmelCase__)
																_SCREAMING_SNAKE_CASE			  =prime_fac_a.count(lowerCAmelCase__)

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

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

				_SCREAMING_SNAKE_CASE			  =0
				_SCREAMING_SNAKE_CASE			  =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(   a__	,a__):
				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			  =p_number_a + 1  # jump to the next number

				_SCREAMING_SNAKE_CASE			  =[]  # 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(   a__):
				assert isinstance(lowerCAmelCase__	,lowerCAmelCase__) and (n >= 1), "'n' must been int and >= 1"

				_SCREAMING_SNAKE_CASE			  =[]  # 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(   a__):
				assert isinstance(lowerCAmelCase__	,lowerCAmelCase__) and (
				    number > 1
				), "'number' must been an int and >= 1"

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

				_SCREAMING_SNAKE_CASE			  =1  # this will be return.

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

				return ans







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

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

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

				return ans



import os
import unittest

from transformers import LxmertTokenizer, LxmertTokenizerFast
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin

@require_tokenizers
class 						A__							(		UpperCamelCase__   ,     unittest.TestCase  ):
						UpperCAmelCase             =						LxmertTokenizer
						UpperCAmelCase             =						LxmertTokenizerFast
						UpperCAmelCase             =						True
						UpperCAmelCase             =						True




						def 							__UpperCamelCase				(       self					:      Optional[int]  )							->     Tuple:


										"""simple docstring"""





										super().setUp()

										_SCREAMING_SNAKE_CASE			  =[
										    '''[UNK]''',
										    '''[CLS]''',
										    '''[SEP]''',
										    '''want''',
										    '''##want''',
										    '''##ed''',
										    '''wa''',
										    '''un''',
										    '''runn''',
										    '''##ing''',
										    ''',''',
										    '''low''',
										    '''lowest''',
										]
										_SCREAMING_SNAKE_CASE			  =os.path.join(self.tmpdirname				,    VOCAB_FILES_NAMES['''vocab_file''']  )
										with open(self.vocab_file				,    '''w'''				,    encoding='''utf-8'''  ) as vocab_writer:
														vocab_writer.write(''''''.join([x + '''\n''' for x in vocab_tokens]  )  )




						def 							__UpperCamelCase				(       self					:      List[str]				,    _a					:      Tuple  )							->     Optional[Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE			  ='''UNwant\u00E9d,running'''
										_SCREAMING_SNAKE_CASE			  ='''unwanted, running'''
										return input_text, output_text




						def 							__UpperCamelCase				(       self					:      Tuple  )							->     List[Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE			  =self.tokenizer_class(self.vocab_file  )

										_SCREAMING_SNAKE_CASE			  =tokenizer.tokenize('''UNwant\u00E9d,running'''  )
										self.assertListEqual(_a				,    ['''un''', '''##want''', '''##ed''', ''',''', '''runn''', '''##ing''']  )
										self.assertListEqual(tokenizer.convert_tokens_to_ids(_a  )				,    [7, 4, 5, 10, 8, 9]  )




						def 							__UpperCamelCase				(       self					:      Dict  )							->     List[Any]:


										"""simple docstring"""





										if not self.test_rust_tokenizer:
														return

										_SCREAMING_SNAKE_CASE			  =self.get_tokenizer()
										_SCREAMING_SNAKE_CASE			  =self.get_rust_tokenizer()

										_SCREAMING_SNAKE_CASE			  ='''I was born in 92000, and this is falsé.'''

										_SCREAMING_SNAKE_CASE			  =tokenizer.tokenize(_a  )
										_SCREAMING_SNAKE_CASE			  =rust_tokenizer.tokenize(_a  )
										self.assertListEqual(_a				,    _a  )

										_SCREAMING_SNAKE_CASE			  =tokenizer.encode(_a				,    add_special_tokens=_a  )
										_SCREAMING_SNAKE_CASE			  =rust_tokenizer.encode(_a				,    add_special_tokens=_a  )
										self.assertListEqual(_a				,    _a  )

										_SCREAMING_SNAKE_CASE			  =self.get_rust_tokenizer()
										_SCREAMING_SNAKE_CASE			  =tokenizer.encode(_a  )
										_SCREAMING_SNAKE_CASE			  =rust_tokenizer.encode(_a  )
										self.assertListEqual(_a				,    _a  )