


import unittest

from transformers import AlbertTokenizer, AlbertTokenizerFast
from transformers.testing_utils import get_tests_dir, require_sentencepiece, require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin


_UpperCAmelCase			:  List[Any]     =get_tests_dir("""fixtures/spiece.model""")







@require_sentencepiece
@require_tokenizers
class 				snake_case__(							UpperCAmelCase__,						unittest.TestCase							):







						'''simple docstring'''




						SCREAMING_SNAKE_CASE__      :  Optional[int]					=							AlbertTokenizer
						SCREAMING_SNAKE_CASE__      :  List[str]					=							AlbertTokenizerFast
						SCREAMING_SNAKE_CASE__      :  Dict					=							True
						SCREAMING_SNAKE_CASE__      :  Dict					=							True
						SCREAMING_SNAKE_CASE__      :  List[str]					=							True




						def 						lowercase_ (				self							)					->    Dict:
										super().setUp()

										# We have a SentencePiece fixture for testing
										lowerCAmelCase_ :      Union[str, Any]    				=				AlbertTokenizer(__lowercase							)
										tokenizer.save_pretrained(self.tmpdirname							)




						def 						lowercase_ (				self   ,						__lowercase							)					->    Tuple:
										lowerCAmelCase_ :      Union[str, Any]    				=				'''this is a test'''
										lowerCAmelCase_ :      Tuple    				=				'''this is a test'''
										return input_text, output_text




						def 						lowercase_ (				self							)					->    List[Any]:
										lowerCAmelCase_ :      Dict    				=				'''<pad>'''
										lowerCAmelCase_ :      Union[str, Any]    				=				0

										self.assertEqual(self.get_tokenizer()._convert_token_to_id(__lowercase							)   ,						__lowercase							)
										self.assertEqual(self.get_tokenizer()._convert_id_to_token(__lowercase							)   ,						__lowercase							)




						def 						lowercase_ (				self							)					->    Optional[int]:
										lowerCAmelCase_ :      Optional[Any]    				=				list(self.get_tokenizer().get_vocab().keys()							)

										self.assertEqual(vocab_keys[0]   ,						'''<pad>'''							)
										self.assertEqual(vocab_keys[1]   ,						'''<unk>'''							)
										self.assertEqual(vocab_keys[-1]   ,						'''▁eloquent'''							)
										self.assertEqual(len(__lowercase							)   ,						3_0_0_0_0							)




						def 						lowercase_ (				self							)					->    Tuple:
										self.assertEqual(self.get_tokenizer().vocab_size   ,						3_0_0_0_0							)




						def 						lowercase_ (				self							)					->    Optional[Any]:
										if not self.test_rust_tokenizer:
														return

										lowerCAmelCase_ :      int    				=				self.get_tokenizer()
										lowerCAmelCase_ :      Optional[Any]    				=				self.get_rust_tokenizer()

										lowerCAmelCase_ :      int    				=				'''I was born in 92000, and this is falsé.'''

										lowerCAmelCase_ :      int    				=				tokenizer.tokenize(__lowercase							)
										lowerCAmelCase_ :      str    				=				rust_tokenizer.tokenize(__lowercase							)
										self.assertListEqual(__lowercase   ,						__lowercase							)

										lowerCAmelCase_ :      str    				=				tokenizer.encode(__lowercase   ,						add_special_tokens=__lowercase							)
										lowerCAmelCase_ :      Union[str, Any]    				=				rust_tokenizer.encode(__lowercase   ,						add_special_tokens=__lowercase							)
										self.assertListEqual(__lowercase   ,						__lowercase							)

										lowerCAmelCase_ :      List[str]    				=				self.get_rust_tokenizer()
										lowerCAmelCase_ :      str    				=				tokenizer.encode(__lowercase							)
										lowerCAmelCase_ :      Optional[int]    				=				rust_tokenizer.encode(__lowercase							)
										self.assertListEqual(__lowercase   ,						__lowercase							)




						def 						lowercase_ (				self							)					->    Optional[int]:
										lowerCAmelCase_ :      List[str]    				=				AlbertTokenizer(__lowercase   ,						keep_accents=__lowercase							)

										lowerCAmelCase_ :      Any    				=				tokenizer.tokenize('''This is a test'''							)
										self.assertListEqual(__lowercase   ,						['''▁this''', '''▁is''', '''▁a''', '''▁test''']							)

										self.assertListEqual(tokenizer.convert_tokens_to_ids(__lowercase							)   ,						[4_8, 2_5, 2_1, 1_2_8_9]							)

										lowerCAmelCase_ :      List[str]    				=				tokenizer.tokenize('''I was born in 92000, and this is falsé.'''							)
										self.assertListEqual(
										    __lowercase   ,						['''▁i''', '''▁was''', '''▁born''', '''▁in''', '''▁9''', '''2000''', ''',''', '''▁and''', '''▁this''', '''▁is''', '''▁fal''', '''s''', '''é''', '''.''']							)
										lowerCAmelCase_ :      Any    				=				tokenizer.convert_tokens_to_ids(__lowercase							)
										self.assertListEqual(__lowercase   ,						[3_1, 2_3, 3_8_6, 1_9, 5_6_1, 3_0_5_0, 1_5, 1_7, 4_8, 2_5, 8_2_5_6, 1_8, 1, 9]							)

										lowerCAmelCase_ :      Optional[int]    				=				tokenizer.convert_ids_to_tokens(__lowercase							)
										self.assertListEqual(
										    __lowercase   ,						['''▁i''', '''▁was''', '''▁born''', '''▁in''', '''▁9''', '''2000''', ''',''', '''▁and''', '''▁this''', '''▁is''', '''▁fal''', '''s''', '''<unk>''', '''.''']   ,						)




						def 						lowercase_ (				self							)					->    List[str]:
										lowerCAmelCase_ :      Dict    				=				AlbertTokenizer(__lowercase							)

										lowerCAmelCase_ :      Optional[int]    				=				tokenizer.encode('''sequence builders'''							)
										lowerCAmelCase_ :      List[Any]    				=				tokenizer.encode('''multi-sequence build'''							)

										lowerCAmelCase_ :      Optional[int]    				=				tokenizer.build_inputs_with_special_tokens(__lowercase							)
										lowerCAmelCase_ :      str    				=				tokenizer.build_inputs_with_special_tokens(__lowercase   ,						__lowercase							)

										assert encoded_sentence == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id]
										assert encoded_pair == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id] + text_a + [
										    tokenizer.sep_token_id
										]




						@slow
						def 						lowercase_ (				self							)					->    str:
										# fmt: off
										lowerCAmelCase_ :      Optional[Any]    				=				{'''attention_mask''': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], '''input_ids''': [[2, 2_1_9_7_0, 1_3, 5, 6_0_9_2, 1_6_7, 2_8, 7_1_0_3, 2_1_5_3, 6_7_3, 8, 7_0_2_8, 1_2_0_5_1, 1_8, 1_7, 7_1_0_3, 2_1_5_3, 6_7_3, 8, 3_5_1_5, 1_8_6_8_4, 8, 4_4_6_1, 6, 1_9_2_7, 2_9_7, 8, 1_2_0_6_0, 2_6_0_7, 1_8, 1_3, 5, 4_4_6_1, 1_5, 1_0_5_3_8, 3_8, 8, 1_3_5, 1_5, 8_2_2, 5_8, 1_5, 9_9_3, 1_0_3_6_3, 1_5, 1_4_6_0, 8_0_0_5, 4_4_6_1, 1_5, 9_9_3, 2_5_5, 2_3_2_8, 9, 9, 9, 6, 2_6, 1_1_1_2, 8_1_6, 3_2_6_0, 1_3, 5, 1_0_3, 2_3_7_7, 6, 1_7, 1_1_1_2, 8_1_6, 2_7_8_2, 1_3, 5, 1_0_3, 1_0_6_4_1, 6, 2_9, 8_4, 2_5_1_2, 2_4_3_0, 7_8_2, 1_8_6_8_4, 2_7_6_1, 1_9, 8_0_8, 2_4_3_0, 2_5_5_6, 1_7, 8_5_5, 1_4_8_0, 9_4_7_7, 4_0_9_1, 1_2_8, 1_1_7_1_2, 1_5, 7_1_0_3, 2_1_5_3, 6_7_3, 1_7, 2_4_8_8_3, 9_9_9_0, 9, 3], [2, 1_1_5_0_2, 2_5, 1_0_0_6, 2_0, 7_8_2, 8, 1_1_8_0_9, 8_5_5, 1_7_3_2, 1_9_3_9_3, 1_8_6_6_7, 3_7, 3_6_7, 2_1_0_1_8, 6_9, 1_8_5_4, 3_4, 1_1_8_6_0, 1_9_1_2_4, 2_7, 1_5_6, 2_2_5, 1_7, 1_9_3, 4_1_4_1, 1_9, 6_5, 9_1_2_4, 9, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1_4, 2_2_3_1, 8_8_6, 2_3_8_5, 1_7_6_5_9, 8_4, 1_4, 1_6_7_9_2, 1_9_5_2, 9, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], '''token_type_ids''': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}  # noqa: E501
										# fmt: on

										self.tokenizer_integration_test_util(
										    expected_encoding=__lowercase   ,						model_name='''albert-base-v2'''   ,						revision='''6b6560eaf5ff2e250b00c50f380c5389a9c2d82e'''   ,						)



from math import sqrt



def 			lowerCAmelCase (		lowerCAmelCase_ )-> bool:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' must been an int and positive"

				lowerCAmelCase_ :      str    				=				True

				# 0 and 1 are none primes.
				if number <= 1:
								lowerCAmelCase_ :      List[Any]    				=				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:
												lowerCAmelCase_ :      Any    				=				False
												break

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

				return status



def 			lowerCAmelCase (		lowerCAmelCase_ )-> List[str]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n > 2), "'N' must been an int and > 2"

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

				lowerCAmelCase_ :      List[Any]    				=				[]  # 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):
																lowerCAmelCase_ :      Tuple    				=				0

    # filters actual prime numbers.
				lowerCAmelCase_ :      List[str]    				=				[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_ )-> int:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n > 2), "'N' must been an int and > 2"

				lowerCAmelCase_ :      List[str]    				=				[]

				# 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[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and number >= 0, "'number' must been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				[]  # this list will be returns of the function.

				# potential prime number factors.

				lowerCAmelCase_ :      Any    				=				2

				lowerCAmelCase_ :      List[str]    				=				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]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				0

				# prime factorization of 'number'
				lowerCAmelCase_ :      Optional[int]    				=				prime_factorization(lowerCAmelCase_ )

				lowerCAmelCase_ :      Dict    				=				max(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> str:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowerCAmelCase_ :      Union[str, Any]    				=				0

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

				lowerCAmelCase_ :      Union[str, Any]    				=				min(lowerCAmelCase_ )

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

				return ans



def 			lowerCAmelCase (		lowerCAmelCase_ )-> Dict:
				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_ )-> List[str]:
				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_ )-> List[Any]:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (number > 2) and is_even(lowerCAmelCase_ )
				), "'number' must been an int, even and > 2"

				lowerCAmelCase_ :      Union[str, Any]    				=				[]  # this list will returned

				# creates a list of prime numbers between 2 up to 'number'
				lowerCAmelCase_ :      List[Any]    				=				get_prime_numbers(lowerCAmelCase_ )
				lowerCAmelCase_ :      Any    				=				len(lowerCAmelCase_ )

				# run variable for while-loops.
				lowerCAmelCase_ :      List[Any]    				=				0
				lowerCAmelCase_ :      List[Any]    				=				None

				# exit variable. for break up the loops
				lowerCAmelCase_ :      int    				=				True

				while i < len_pn and loop:
								lowerCAmelCase_ :      Tuple    				=				i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																lowerCAmelCase_ :      Union[str, Any]    				=				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_ ,   lowerCAmelCase_ )-> Optional[int]:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				lowerCAmelCase_ :      List[str]    				=				0

				while numbera != 0:
								lowerCAmelCase_ :      int    				=				numbera % numbera
								lowerCAmelCase_ :      Union[str, Any]    				=				numbera
								lowerCAmelCase_ :      Tuple    				=				rest

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

				return numbera



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ )-> Any:
				assert (
				    isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ )
				    and (numbera >= 1)
				    and (numbera >= 1)
				), "'number1' and 'number2' must been positive integer."

				lowerCAmelCase_ :      Dict    				=				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'
								lowerCAmelCase_ :      Tuple    				=				prime_factorization(lowerCAmelCase_ )
								lowerCAmelCase_ :      str    				=				prime_factorization(lowerCAmelCase_ )

				elif numbera == 1 or numbera == 1:
								lowerCAmelCase_ :      List[Any]    				=				[]
								lowerCAmelCase_ :      List[Any]    				=				[]
								lowerCAmelCase_ :      str    				=				max(lowerCAmelCase_ ,   lowerCAmelCase_ )

				lowerCAmelCase_ :      str    				=				0
				lowerCAmelCase_ :      List[str]    				=				0

				lowerCAmelCase_ :      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:
																lowerCAmelCase_ :      str    				=				prime_fac_a.count(lowerCAmelCase_ )
																lowerCAmelCase_ :      List[str]    				=				prime_fac_a.count(lowerCAmelCase_ )

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

												else:
																lowerCAmelCase_ :      Dict    				=				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:
												lowerCAmelCase_ :      Optional[int]    				=				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_ )-> Dict:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'number' must been a positive int"

				lowerCAmelCase_ :      Optional[int]    				=				0
				lowerCAmelCase_ :      Optional[int]    				=				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_ ,   lowerCAmelCase_ )-> Dict:
				assert (
				    is_prime(lowerCAmelCase_ ) and is_prime(lowerCAmelCase_ ) and (p_number_a < p_number_a)
				), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

				lowerCAmelCase_ :      str    				=				p_number_a + 1  # jump to the next number

				lowerCAmelCase_ :      Dict    				=				[]  # 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[str]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 1), "'n' must been int and >= 1"

				lowerCAmelCase_ :      List[str]    				=				[]  # 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_ )-> List[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (
				    number > 1
				), "'number' must been an int and >= 1"

				lowerCAmelCase_ :      Tuple    				=				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_ ,   lowerCAmelCase_ )-> Any:
				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.
				lowerCAmelCase_ :      List[str]    				=				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_ )-> List[Any]:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'n' must been a int and >= 0"

				lowerCAmelCase_ :      Tuple    				=				1  # this will be return.

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

				return ans




def 			lowerCAmelCase (		lowerCAmelCase_ )-> Tuple:
				assert isinstance(lowerCAmelCase_ ,   lowerCAmelCase_ ) and (n >= 0), "'n' must been an int and >= 0"

				lowerCAmelCase_ :      Tuple    				=				0
				lowerCAmelCase_ :      Optional[Any]    				=				1
				lowerCAmelCase_ :      Tuple    				=				1  # this will be return

				for _ in range(n - 1 ):
								lowerCAmelCase_ :      Any    				=				ans
								ans += fiba
								lowerCAmelCase_ :      Dict    				=				tmp

				return ans