





'''simple docstring'''







from math import sqrt






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

				_a								= True

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

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

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

				return status






def  _lowerCamelCase				( lowercase						:      Tuple						)	->	Dict:
				assert isinstance(lowercase    ,							lowercase						) and (n > 2), "'N' must been an int and > 2"

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

				_a								= []  # this list will be returns.

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

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

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

				return ans






def  _lowerCamelCase				( lowercase						:      int						)	->	int:
				assert isinstance(lowercase    ,							lowercase						) and (n > 2), "'N' must been an int and > 2"

				_a								= []

				# 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(lowercase						):
												ans.append(lowercase						)

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

				return ans






def  _lowerCamelCase				( lowercase						:      Tuple						)	->	List[Any]:
				assert isinstance(lowercase    ,							lowercase						) and number >= 0, "'number' must been an int and >= 0"

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

				# potential prime number factors.

				_a								= 2

				_a								= number

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

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

				else:
								ans.append(lowercase						)

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

				return ans






def  _lowerCamelCase				( lowercase						:      List[Any]						)	->	List[Any]:
				assert isinstance(lowercase    ,							lowercase						) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				_a								= 0

				# prime factorization of 'number'
				_a								= prime_factorization(lowercase						)

				_a								= max(lowercase						)

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

				return ans






def  _lowerCamelCase				( lowercase						:      Dict						)	->	List[Any]:
				assert isinstance(lowercase    ,							lowercase						) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				_a								= 0

				# prime factorization of 'number'
				_a								= prime_factorization(lowercase						)

				_a								= min(lowercase						)

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

				return ans






def  _lowerCamelCase				( lowercase						:      List[Any]						)	->	Dict:
				assert isinstance(lowercase    ,							lowercase						), "'number' must been an int"
				assert isinstance(number % 2 == 0    ,							lowercase						), "compare bust been from type bool"

				return number % 2 == 0






def  _lowerCamelCase				( lowercase						:      Optional[int]						)	->	Tuple:
				assert isinstance(lowercase    ,							lowercase						), "'number' must been an int"
				assert isinstance(number % 2 != 0    ,							lowercase						), "compare bust been from type bool"

				return number % 2 != 0






def  _lowerCamelCase				( lowercase						:      List[str]						)	->	Optional[int]:
				assert (
				    isinstance(lowercase    ,							lowercase						) and (number > 2) and is_even(lowercase						)
				), "'number' must been an int, even and > 2"

				_a								= []  # this list will returned

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

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

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

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

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

												j += 1

								i += 1

				# precondition
				assert (
				    isinstance(lowercase    ,							lowercase						)
				    and (len(lowercase						) == 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				( lowercase						:      str    ,							lowercase						:      int						)	->	int:
				assert (
				    isinstance(lowercase    ,							lowercase						)
				    and isinstance(lowercase    ,							lowercase						)
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				_a								= 0

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

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

				return numbera






def  _lowerCamelCase				( lowercase						:      str    ,							lowercase						:      str						)	->	List[str]:
				assert (
				    isinstance(lowercase    ,							lowercase						)
				    and isinstance(lowercase    ,							lowercase						)
				    and (numbera >= 1)
				    and (numbera >= 1)
				), "'number1' and 'number2' must been positive integer."

				_a								= 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'
								_a								= prime_factorization(lowercase						)
								_a								= prime_factorization(lowercase						)

				elif numbera == 1 or numbera == 1:
								_a								= []
								_a								= []
								_a								= max(lowercase    ,							lowercase						)

				_a								= 0
				_a								= 0

				_a								= []  # 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:
																_a								= prime_fac_a.count(lowercase						)
																_a								= prime_fac_a.count(lowercase						)

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

												else:
																_a								= prime_fac_a.count(lowercase						)

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

												done.append(lowercase						)

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

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

												done.append(lowercase						)

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

				return ans






def  _lowerCamelCase				( lowercase						:      int						)	->	Optional[int]:
				assert isinstance(lowercase    ,							lowercase						) and (n >= 0), "'number' must been a positive int"

				_a								= 0
				_a								= 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(lowercase						):
												ans += 1

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

				return ans






def  _lowerCamelCase				( lowercase						:      Tuple    ,							lowercase						:      Tuple						)	->	str:
				assert (
				    is_prime(lowercase						) and is_prime(lowercase						) and (p_number_a < p_number_a)
				), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

				_a								= p_number_a + 1  # jump to the next number

				_a								= []  # this list will be returns.

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

				while number < p_number_a:
								ans.append(lowercase						)

								number += 1

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

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

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






def  _lowerCamelCase				( lowercase						:      List[str]						)	->	Dict:
				assert isinstance(lowercase    ,							lowercase						) and (n >= 1), "'n' must been int and >= 1"

				_a								= []  # will be returned.

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

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

				return ans






def  _lowerCamelCase				( lowercase						:      int						)	->	Optional[Any]:
				assert isinstance(lowercase    ,							lowercase						) and (
				    number > 1
				), "'number' must been an int and >= 1"

				_a								= get_divisors(lowercase						)

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

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






def  _lowerCamelCase				( lowercase						:      Optional[int]    ,							lowercase						:      List[str]						)	->	int:
				assert (
				    isinstance(lowercase    ,							lowercase						)
				    and isinstance(lowercase    ,							lowercase						)
				    and (denominator != 0)
				), "The arguments must been from type int and 'denominator' != 0"

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

				# precondition
				assert (
				    isinstance(lowercase    ,							lowercase						)
				    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				( lowercase						:      int						)	->	Any:
				assert isinstance(lowercase    ,							lowercase						) and (n >= 0), "'n' must been a int and >= 0"

				_a								= 1  # this will be return.

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

				return ans






def  _lowerCamelCase				( lowercase						:      int						)	->	int:
				assert isinstance(lowercase    ,							lowercase						) and (n >= 0), "'n' must been an int and >= 0"

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

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

				return ans







'''simple docstring'''







import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
class 				__SCREAMING_SNAKE_CASE  (lowerCamelCase_      ):






				"""simple docstring"""







				__a            =['image_processor', 'tokenizer']
				__a            ='LayoutLMv3ImageProcessor'
				__a            =('LayoutLMv3Tokenizer', 'LayoutLMv3TokenizerFast')




				def __init__(  self     :					Tuple					,				__a     :					int=None					,				__a     :					Union[str, Any]=None					,				**__a     :					Optional[Any]					):
								_a								= None
								if "feature_extractor" in kwargs:
												warnings.warn(
												    "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
												    " instead."					,				__a					,				)
												_a								= kwargs.pop("feature_extractor"					)

								_a								= image_processor if image_processor is not None else feature_extractor
								if image_processor is None:
												raise ValueError("You need to specify an `image_processor`."					)
								if tokenizer is None:
												raise ValueError("You need to specify a `tokenizer`."					)

								super().__init__(__a					,				__a					)




				def __call__(  self     :					Any					,				__a     :					List[str]					,				__a     :					Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None					,				__a     :					Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None					,				__a     :					Union[List[List[int]], List[List[List[int]]]] = None					,				__a     :					Optional[Union[List[int], List[List[int]]]] = None					,				__a     :					bool = True					,				__a     :					Union[bool, str, PaddingStrategy] = False					,				__a     :					Union[bool, str, TruncationStrategy] = None					,				__a     :					Optional[int] = None					,				__a     :					int = 0					,				__a     :					Optional[int] = None					,				__a     :					Optional[bool] = None					,				__a     :					Optional[bool] = None					,				__a     :					bool = False					,				__a     :					bool = False					,				__a     :					bool = False					,				__a     :					bool = False					,				__a     :					bool = True					,				__a     :					Optional[Union[str, TensorType]] = None					,				**__a     :					Dict					,				):
								# verify input
								if self.image_processor.apply_ocr and (boxes is not None):
												raise ValueError(
												    "You cannot provide bounding boxes if you initialized the image processor with apply_ocr set to True."					)

								if self.image_processor.apply_ocr and (word_labels is not None):
												raise ValueError(
												    "You cannot provide word labels if you initialized the image processor with apply_ocr set to True."					)

								# first, apply the image processor
								_a								= self.image_processor(images=__a					,				return_tensors=__a					)

								# second, apply the tokenizer
								if text is not None and self.image_processor.apply_ocr and text_pair is None:
												if isinstance(__a					,				__a					):
																_a								= [text]  # add batch dimension (as the image processor always adds a batch dimension)
												_a								= features["words"]

								_a								= self.tokenizer(
								    text=text if text is not None else features["words"]					,				text_pair=text_pair if text_pair is not None else None					,				boxes=boxes if boxes is not None else features["boxes"]					,				word_labels=__a					,				add_special_tokens=__a					,				padding=__a					,				truncation=__a					,				max_length=__a					,				stride=__a					,				pad_to_multiple_of=__a					,				return_token_type_ids=__a					,				return_attention_mask=__a					,				return_overflowing_tokens=__a					,				return_special_tokens_mask=__a					,				return_offsets_mapping=__a					,				return_length=__a					,				verbose=__a					,				return_tensors=__a					,				**__a					,				)

								# add pixel values
								_a								= features.pop("pixel_values"					)
								if return_overflowing_tokens is True:
												_a								= self.get_overflowing_images(__a					,				encoded_inputs["overflow_to_sample_mapping"]					)
								_a								= images

								return encoded_inputs




				def   UpperCamelCase__   (  self     :					Optional[int]					,				__a     :					str					,				__a     :					List[Any]					):
								# in case there's an overflow, ensure each `input_ids` sample is mapped to its corresponding image
								_a								= []
								for sample_idx in overflow_to_sample_mapping:
												images_with_overflow.append(images[sample_idx]					)

								if len(__a					) != len(__a					):
												raise ValueError(
												    "Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"
												    f' {len(__a					)} and {len(__a					)}'					)

								return images_with_overflow




				def   UpperCamelCase__   (  self     :					int					,				*__a     :					str					,				**__a     :					Tuple					):
								return self.tokenizer.batch_decode(*__a					,				**__a					)




				def   UpperCamelCase__   (  self     :					str					,				*__a     :					List[Any]					,				**__a     :					List[str]					):
								return self.tokenizer.decode(*__a					,				**__a					)




				@property
				def   UpperCamelCase__   (  self     :					Tuple					):
								return ["input_ids", "bbox", "attention_mask", "pixel_values"]




				@property
				def   UpperCamelCase__   (  self     :					int					):
								warnings.warn(
								    "`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."					,				__a					,				)
								return self.image_processor_class




				@property
				def   UpperCamelCase__   (  self     :					List[str]					):
								warnings.warn(
								    "`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."					,				__a					,				)
								return self.image_processor
