






import argparse
import pathlib

import fairseq
import torch
from fairseq.models.roberta import RobertaModel as FairseqRobertaModel
from fairseq.modules import TransformerSentenceEncoderLayer
from packaging import version

from transformers import XLMRobertaConfig, XLMRobertaXLForMaskedLM, XLMRobertaXLForSequenceClassification
from transformers.models.bert.modeling_bert import (
    BertIntermediate,
    BertLayer,
    BertOutput,
    BertSelfAttention,
    BertSelfOutput,
)
from transformers.models.roberta.modeling_roberta import RobertaAttention
from transformers.utils import logging


if version.parse(fairseq.__version__) < version.parse('1.0.0a'):
				raise Exception('requires fairseq >= 1.0.0a')

logging.set_verbosity_info()
A        =   logging.get_logger(__name__)

A        =   "Hello world! cécé herlolip"



def 					_lowerCamelCase(			lowerCAmelCase__				:		Any    ,    lowerCAmelCase__				:		Tuple    ,    lowerCAmelCase__				:		Tuple      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   FairseqRobertaModel.from_pretrained(lowerCAmelCase__      )
				roberta.eval()  # disable dropout
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   roberta.model.encoder.sentence_encoder
				SCREAMING_SNAKE_CASE_   :	str													=   XLMRobertaConfig(
				    vocab_size=roberta_sent_encoder.embed_tokens.num_embeddings    ,    hidden_size=roberta.cfg.model.encoder_embed_dim    ,    num_hidden_layers=roberta.cfg.model.encoder_layers    ,    num_attention_heads=roberta.cfg.model.encoder_attention_heads    ,    intermediate_size=roberta.cfg.model.encoder_ffn_embed_dim    ,    max_position_embeddings=514    ,    type_vocab_size=1    ,    layer_norm_eps=1E-5    ,    )
				if classification_head:
								SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.model.classification_heads['mnli'].out_proj.weight.shape[0]

				print('Our RoBERTa config:'    ,    lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Any													=   XLMRobertaXLForSequenceClassification(lowerCAmelCase__      ) if classification_head else XLMRobertaXLForMaskedLM(lowerCAmelCase__      )
				model.eval()

				# Now let's copy all the weights.
				# Embeddings
				SCREAMING_SNAKE_CASE_   :	Dict													=   roberta_sent_encoder.embed_tokens.weight
				SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_sent_encoder.embed_positions.weight
				SCREAMING_SNAKE_CASE_   :	Dict													=   torch.zeros_like(
				    model.roberta.embeddings.token_type_embeddings.weight      )  # just zero them out b/c RoBERTa doesn't use them.

				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   roberta_sent_encoder.layer_norm.weight
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   roberta_sent_encoder.layer_norm.bias

				for i in range(config.num_hidden_layers      ):
								# Encoder: start of layer
								SCREAMING_SNAKE_CASE_   :	Any													=   model.roberta.encoder.layer[i]
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_sent_encoder.layers[i]

								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   layer.attention
								SCREAMING_SNAKE_CASE_   :	int													=   roberta_layer.self_attn_layer_norm.weight
								SCREAMING_SNAKE_CASE_   :	int													=   roberta_layer.self_attn_layer_norm.bias

								# self attention
								SCREAMING_SNAKE_CASE_   :	int													=   layer.attention.self
								assert (
								    roberta_layer.self_attn.k_proj.weight.data.shape
								    == roberta_layer.self_attn.q_proj.weight.data.shape
								    == roberta_layer.self_attn.v_proj.weight.data.shape
								    == torch.Size((config.hidden_size, config.hidden_size)      )
								)

								SCREAMING_SNAKE_CASE_   :	List[str]													=   roberta_layer.self_attn.q_proj.weight
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   roberta_layer.self_attn.q_proj.bias
								SCREAMING_SNAKE_CASE_   :	Any													=   roberta_layer.self_attn.k_proj.weight
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_layer.self_attn.k_proj.bias
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   roberta_layer.self_attn.v_proj.weight
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_layer.self_attn.v_proj.bias

								# self-attention output
								SCREAMING_SNAKE_CASE_   :	int													=   layer.attention.output
								assert self_output.dense.weight.shape == roberta_layer.self_attn.out_proj.weight.shape
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_layer.self_attn.out_proj.weight
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   roberta_layer.self_attn.out_proj.bias

								# this one is final layer norm
								SCREAMING_SNAKE_CASE_   :	Tuple													=   roberta_layer.final_layer_norm.weight
								SCREAMING_SNAKE_CASE_   :	Tuple													=   roberta_layer.final_layer_norm.bias

								# intermediate
								SCREAMING_SNAKE_CASE_   :	List[str]													=   layer.intermediate
								assert intermediate.dense.weight.shape == roberta_layer.fca.weight.shape
								SCREAMING_SNAKE_CASE_   :	int													=   roberta_layer.fca.weight
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta_layer.fca.bias

								# output
								SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   layer.output
								assert bert_output.dense.weight.shape == roberta_layer.fca.weight.shape
								SCREAMING_SNAKE_CASE_   :	Any													=   roberta_layer.fca.weight
								SCREAMING_SNAKE_CASE_   :	int													=   roberta_layer.fca.bias
								# end of layer

				if classification_head:
								SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.model.classification_heads['mnli'].dense.weight
								SCREAMING_SNAKE_CASE_   :	int													=   roberta.model.classification_heads['mnli'].dense.bias
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   roberta.model.classification_heads['mnli'].out_proj.weight
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta.model.classification_heads['mnli'].out_proj.bias
				else:
								# LM Head
								SCREAMING_SNAKE_CASE_   :	int													=   roberta.model.encoder.lm_head.dense.weight
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   roberta.model.encoder.lm_head.dense.bias
								SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   roberta.model.encoder.lm_head.layer_norm.weight
								SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.model.encoder.lm_head.layer_norm.bias
								SCREAMING_SNAKE_CASE_   :	Tuple													=   roberta.model.encoder.lm_head.weight
								SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.model.encoder.lm_head.bias

				# Let's check that we get the same results.
				SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.encode(lowerCAmelCase__      ).unsqueeze(0      )  # batch of size 1

				SCREAMING_SNAKE_CASE_   :	Dict													=   model(lowerCAmelCase__      )[0]
				if classification_head:
								SCREAMING_SNAKE_CASE_   :	Dict													=   roberta.model.classification_heads['mnli'](roberta.extract_features(lowerCAmelCase__      )      )
				else:
								SCREAMING_SNAKE_CASE_   :	str													=   roberta.model(lowerCAmelCase__      )[0]
				print(our_output.shape    ,    their_output.shape      )
				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   torch.max(torch.abs(our_output - their_output      )      ).item()
				print(F'''max_absolute_diff = {max_absolute_diff}'''      )  # ~ 1e-7
				SCREAMING_SNAKE_CASE_   :	str													=   torch.allclose(lowerCAmelCase__    ,    lowerCAmelCase__    ,    atol=1E-3      )
				print('Do both models output the same tensors?'    ,    '🔥' if success else '💩'      )
				if not success:
								raise Exception('Something went wRoNg'      )

				pathlib.Path(lowerCAmelCase__      ).mkdir(parents=lowerCAmelCase__    ,    exist_ok=lowerCAmelCase__      )
				print(F'''Saving model to {pytorch_dump_folder_path}'''      )
				model.save_pretrained(lowerCAmelCase__      )


if __name__ == "__main__":
				A        =   argparse.ArgumentParser()
				# Required parameters
				parser.add_argument(
				    '--roberta_checkpoint_path', default=None, type=str, required=True, help='Path the official PyTorch dump.'
				)
				parser.add_argument(
				    '--pytorch_dump_folder_path', default=None, type=str, required=True, help='Path to the output PyTorch model.'
				)
				parser.add_argument(
				    '--classification_head', action='store_true', help='Whether to convert a final classification head.'
				)
				A        =   parser.parse_args()
				convert_xlm_roberta_xl_checkpoint_to_pytorch(
				    args.roberta_checkpoint_path, args.pytorch_dump_folder_path, args.classification_head
				)







from math import sqrt



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Dict													=   True

				# 0 and 1 are none primes.
				if number <= 1:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   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_   :	Dict													=   False
												break

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

				return status



def 					_lowerCamelCase(			lowerCAmelCase__				:		int      ):





				'''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
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   list(range(2    ,    n + 1      )      )

				SCREAMING_SNAKE_CASE_   :	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):
																SCREAMING_SNAKE_CASE_   :	str													=   0

    # filters actual prime numbers.
				SCREAMING_SNAKE_CASE_   :	int													=   [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__				:		List[str]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   []

				# 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__				:		Union[str, Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   []  # this list will be returns of the function.

				# potential prime number factors.

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   2

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   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__				:		Any      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Dict													=   max(lowerCAmelCase__      )

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0

				# prime factorization of 'number'
				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   prime_factorization(lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   min(lowerCAmelCase__      )

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		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__				:		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__				:		Optional[Any]      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      ) and (number > 2) and is_even(lowerCAmelCase__      )
				), "'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_   :	int													=   get_prime_numbers(lowerCAmelCase__      )
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   len(lowerCAmelCase__      )

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

				# exit variable. for break up the loops
				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   True

				while i < len_pn and loop:
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																SCREAMING_SNAKE_CASE_   :	List[str]													=   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__				:		str    ,    lowerCAmelCase__				:		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."

				SCREAMING_SNAKE_CASE_   :	int													=   0

				while numbera != 0:
								SCREAMING_SNAKE_CASE_   :	List[str]													=   numbera % numbera
								SCREAMING_SNAKE_CASE_   :	Optional[int]													=   numbera
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   rest

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

				return numbera



def 					_lowerCamelCase(			lowerCAmelCase__				:		int    ,    lowerCAmelCase__				:		Optional[Any]      ):





				'''simple docstring'''







				assert (
				    isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    and isinstance(lowerCAmelCase__    ,    lowerCAmelCase__      )
				    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_   :	Tuple													=   prime_factorization(lowerCAmelCase__      )
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   prime_factorization(lowerCAmelCase__      )

				elif numbera == 1 or numbera == 1:
								SCREAMING_SNAKE_CASE_   :	List[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []
								SCREAMING_SNAKE_CASE_   :	int													=   max(lowerCAmelCase__    ,    lowerCAmelCase__      )

				SCREAMING_SNAKE_CASE_   :	Union[str, Any]													=   0
				SCREAMING_SNAKE_CASE_   :	Any													=   0

				SCREAMING_SNAKE_CASE_   :	Optional[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_   :	int													=   prime_fac_a.count(lowerCAmelCase__      )
																SCREAMING_SNAKE_CASE_   :	Tuple													=   prime_fac_a.count(lowerCAmelCase__      )

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

												else:
																SCREAMING_SNAKE_CASE_   :	List[Any]													=   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_   :	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__				:		Any      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[int]													=   0
				SCREAMING_SNAKE_CASE_   :	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__				:		List[str]    ,    lowerCAmelCase__				:		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'"

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

				SCREAMING_SNAKE_CASE_   :	List[Any]													=   []  # 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__				:		Optional[Any]      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   []  # 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__				:		int      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	int													=   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__				:		Dict    ,    lowerCAmelCase__				:		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.
				SCREAMING_SNAKE_CASE_   :	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__				:		Tuple      ):





				'''simple docstring'''







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

				SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   1  # this will be return.

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

				return ans



def 					_lowerCamelCase(			lowerCAmelCase__				:		Tuple      ):





				'''simple docstring'''







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

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

				for _ in range(n - 1      ):
								SCREAMING_SNAKE_CASE_   :	Optional[Any]													=   ans
								ans += fiba
								SCREAMING_SNAKE_CASE_   :	List[str]													=   tmp

				return ans