

from math import sqrt





def      A__					(			__A  :						int			)					->bool:
      assert isinstance(__A     ,				__A			) 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(__A			)			)			) + 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(__A     ,				__A			), "'status' must been from type bool"

      return status





def      A__					(			__A  :						List[str]			)					->Optional[int]:
      assert isinstance(__A     ,				__A			) 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(__A			)			):
            for j in range(i + 1     ,				len(__A			)			):
                  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(__A     ,				__A			), "'ans' must been from type list"

      return ans





def      A__					(			__A  :						List[Any]			)					->Optional[Any]:
      assert isinstance(__A     ,				__A			) 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(__A			):
                  ans.append(__A			)

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

      return ans





def      A__					(			__A  :						Dict			)					->List[Any]:
      assert isinstance(__A     ,				__A			) 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(__A			)

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

      else:
            ans.append(__A			)

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

      return ans





def      A__					(			__A  :						Tuple			)					->Union[str, Any]:
      assert isinstance(__A     ,				__A			) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      __A    =0

      # prime factorization of 'number'
      __A    =prime_factorization(__A			)

      __A    =max(__A			)

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

      return ans





def      A__					(			__A  :						List[str]			)					->Optional[Any]:
      assert isinstance(__A     ,				__A			) and (
          number >= 0
      ), "'number' bust been an int and >= 0"

      __A    =0

      # prime factorization of 'number'
      __A    =prime_factorization(__A			)

      __A    =min(__A			)

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

      return ans





def      A__					(			__A  :						Dict			)					->Tuple:
      assert isinstance(__A     ,				__A			), "'number' must been an int"
      assert isinstance(number % 2 == 0     ,				__A			), "compare bust been from type bool"

      return number % 2 == 0





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

      return number % 2 != 0





def      A__					(			__A  :						Optional[Any]			)					->List[str]:
      assert (
          isinstance(__A     ,				__A			) and (number > 2) and is_even(__A			)
      ), "'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(__A			)
      __A    =len(__A			)

      # 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(__A     ,				__A			)
          and (len(__A			) == 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  :						Optional[int]     ,				__A  :						Dict			)					->Tuple:
      assert (
          isinstance(__A     ,				__A			)
          and isinstance(__A     ,				__A			)
          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(__A     ,				__A			) and (
          numbera >= 0
      ), "'number' must been from type int and positive"

      return numbera





def      A__					(			__A  :						List[Any]     ,				__A  :						str			)					->Dict:
      assert (
          isinstance(__A     ,				__A			)
          and isinstance(__A     ,				__A			)
          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(__A			)
            __A    =prime_factorization(__A			)

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

      __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(__A			)
                        __A    =prime_fac_a.count(__A			)

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

                  else:
                        __A    =prime_fac_a.count(__A			)

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

                  done.append(__A			)

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

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

                  done.append(__A			)

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

      return ans





def      A__					(			__A  :						Any			)					->str:
      assert isinstance(__A     ,				__A			) 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(__A			):
                  ans += 1

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

      return ans





def      A__					(			__A  :						Tuple     ,				__A  :						List[str]			)					->str:
      assert (
          is_prime(__A			) and is_prime(__A			) 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(__A			):
            number += 1

      while number < p_number_a:
            ans.append(__A			)

            number += 1

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

    # precondition
      assert (
          isinstance(__A     ,				__A			)
          and ans[0] != p_number_a
          and ans[len(__A			) - 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]			)					->Tuple:
      assert isinstance(__A     ,				__A			) 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(__A			)

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

      return ans





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

      __A    =get_divisors(__A			)

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

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





def      A__					(			__A  :						Any     ,				__A  :						Optional[int]			)					->str:
      assert (
          isinstance(__A     ,				__A			)
          and isinstance(__A     ,				__A			)
          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(__A			)     ,				abs(__A			)			)

      # precondition
      assert (
          isinstance(__A     ,				__A			)
          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  :						Tuple			)					->Union[str, Any]:
      assert isinstance(__A     ,				__A			) 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      A__					(			__A  :						Optional[int]			)					->List[str]:
      assert isinstance(__A     ,				__A			) 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





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        lowerCAmelCase__  (					__magic_name__			):



       '''simple docstring'''







       lowercase_						=    ["""image_processor""", """tokenizer"""]
       lowercase_						=    """LayoutLMv2ImageProcessor"""
       lowercase_						=    ("""LayoutXLMTokenizer""", """LayoutXLMTokenizerFast""")

       def __init__(							self ,   lowercase__=None ,   lowercase__=None ,   **lowercase__     ):







             '''simple docstring'''



             if "feature_extractor" in kwargs:
                   warnings.warn(
                       '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
                       ''' instead.''' ,   lowercase__ ,   )
                   __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__(lowercase__ ,   lowercase__     )

       def __call__(							self ,   lowercase__ ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = True ,   lowercase__ = False ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = 0 ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = None ,   lowercase__ = False ,   lowercase__ = False ,   lowercase__ = False ,   lowercase__ = False ,   lowercase__ = True ,   lowercase__ = None ,   **lowercase__ ,   ):







             '''simple docstring'''



             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.'''     )

             if return_overflowing_tokens is True and return_offsets_mapping is False:
                   raise ValueError('''You cannot return overflowing tokens without returning the offsets mapping.'''     )

             # first, apply the image processor
             __A    =self.image_processor(images=lowercase__ ,   return_tensors=lowercase__     )

             # second, apply the tokenizer
             if text is not None and self.image_processor.apply_ocr and text_pair is None:
                   if isinstance(lowercase__ ,   lowercase__     ):
                         __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=lowercase__ ,   add_special_tokens=lowercase__ ,   padding=lowercase__ ,   truncation=lowercase__ ,   max_length=lowercase__ ,   stride=lowercase__ ,   pad_to_multiple_of=lowercase__ ,   return_token_type_ids=lowercase__ ,   return_attention_mask=lowercase__ ,   return_overflowing_tokens=lowercase__ ,   return_special_tokens_mask=lowercase__ ,   return_offsets_mapping=lowercase__ ,   return_length=lowercase__ ,   verbose=lowercase__ ,   return_tensors=lowercase__ ,   **lowercase__ ,   )

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

             return encoded_inputs

       def     __UpperCamelCase     (							self ,   lowercase__ ,   lowercase__     ):







             '''simple docstring'''



             __A    =[]
             for sample_idx in overflow_to_sample_mapping:
                   images_with_overflow.append(images[sample_idx]     )

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

             return images_with_overflow

       def     __UpperCamelCase     (							self ,   *lowercase__ ,   **lowercase__     ):







             '''simple docstring'''



             return self.tokenizer.batch_decode(*lowercase__ ,   **lowercase__     )

       def     __UpperCamelCase     (							self ,   *lowercase__ ,   **lowercase__     ):







             '''simple docstring'''



             return self.tokenizer.decode(*lowercase__ ,   **lowercase__     )

       @property
       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             return ["input_ids", "bbox", "attention_mask", "image"]

       @property
       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             warnings.warn(
                 '''`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead.''' ,   lowercase__ ,   )
             return self.image_processor_class


       @property
       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             warnings.warn(
                 '''`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead.''' ,   lowercase__ ,   )
             return self.image_processor


