
from __future__ import annotations

from math import gcd


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase = 2	,					__lowerCAmelCase = 1	,					__lowerCAmelCase = 3	,					) ->						int | None:
    # A value less than 2 can cause an infinite loop in the algorithm.
    if num < 2:
        raise ValueError('''The input value cannot be less than 2'''	)

    # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
    # algorithm struggles to find factors that are divisible by two.
    # As a workaround, we specifically check for two and even inputs.
    #   See: https://math.stackexchange.com/a/2856214/165820
    if num > 2 and num % 2 == 0:
        return 2

    # Pollard's Rho algorithm requires a function that returns pseudorandom
    # values between 0 <= X < ``num``.  It doesn't need to be random in the
    # sense that the output value is cryptographically secure or difficult
    # to calculate, it only needs to be random in the sense that all output
    # values should be equally likely to appear.
    # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
    # However, the success of Pollard's algorithm isn't guaranteed and is
    # determined in part by the initial seed and the chosen random function.
    # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
    # where ``C`` is a value that we can modify between each attempt.
    def rand_fn(__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	) -> int:
        return (pow(__lowerCAmelCase	,					2	) + step) % modulus

    for _ in range(__lowerCAmelCase	):
        # These track the position within the cycle detection logic.
        __lowercase		:			Any	    =       seed
        __lowercase		:			str	    =       seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            __lowercase		:			Dict	    =       rand_fn(__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	)
            __lowercase		:			int	    =       rand_fn(__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	)
            __lowercase		:			Optional[Any]	    =       rand_fn(__lowerCAmelCase	,					__lowerCAmelCase	,					__lowerCAmelCase	)

            # At some point both the tortoise and the hare will enter a cycle whose
            # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
            # the tortoise and hare will end up on the same value modulo ``p``.
            # We can detect when this happens because the position difference between
            # the tortoise and the hare will share a common divisor with ``num``.
            __lowercase		:			Tuple	    =       gcd(hare - tortoise	,					__lowerCAmelCase	)

            if divisor == 1:
                # No common divisor yet, just keep searching.
                continue
            else:
                # We found a common divisor!
                if divisor == num:
                    # Unfortunately, the divisor is ``num`` itself and is useless.
                    break
                else:
                    # The divisor is a nontrivial factor of ``num``!
                    return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
        __lowercase		:			Optional[Any]	    =       hare

        # The new step value for the random function can just be incremented.
        # At first the results will be similar to what the old function would
        # have produced, but the value will quickly diverge after a bit.
        step += 1

    # We haven't found a divisor within the requested number of attempts.
    # We were unlucky or ``num`` itself is actually prime.
    return None


if __name__ == "__main__":
 import argparse

 __lowerCAmelCase					:			Tuple			      =		argparse.ArgumentParser()
 parser.add_argument(
     "num",
     type=int,
     help="The value to find a divisor of",
 )
 parser.add_argument(
     "--attempts",
     type=int,
     default=3,
     help="The number of attempts before giving up",
 )
 __lowerCAmelCase					:			Dict			      =		parser.parse_args()

 __lowerCAmelCase					:			Any			      =		pollard_rho(args.num, attempts=args.attempts)
 if divisor is None:
  print(F'{args.num} is probably prime')
 else:
  __lowerCAmelCase					:			Union[str, Any]			      =		args.num // divisor
  print(F'{args.num} = {divisor} * {quotient}')




import unittest

from transformers import MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING, AutoTokenizer, is_vision_available
from transformers.pipelines import pipeline
from transformers.pipelines.document_question_answering import apply_tesseract
from transformers.testing_utils import (
    is_pipeline_test,
    nested_simplify,
    require_detectrona,
    require_pytesseract,
    require_tf,
    require_torch,
    require_vision,
    slow,
)

from .test_pipelines_common import ANY


if is_vision_available():
 from PIL import Image

 from transformers.image_utils import load_image
else:


 class 						__lowerCAmelCase	:



       """simple docstring"""







       @staticmethod
       def 		snake_case_			(      *_snake_case		:       Union[str, Any]				,       **_snake_case		:       str				):
           pass






 def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						Union[str, Any]:
     return None


# This is a pinned image from a specific revision of a document question answering space, hosted by HuggingFace,
# so we can expect it to be available.
__lowerCAmelCase					:			Dict			      =		(
    "https://huggingface.co/spaces/impira/docquery/resolve/2f6c96314dc84dfda62d40de9da55f2f5165d403/invoice.png"
)


@is_pipeline_test
@require_torch
@require_vision
class 						__lowerCAmelCase	(	unittest.TestCase      ):



      """simple docstring"""







      A__	:			int        =    MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING




      @require_pytesseract
      @require_vision
      def 		snake_case_			(      self		:       List[Any]				,       _snake_case		:       Any				,       _snake_case		:       Dict				,       _snake_case		:       Any				):
          __lowercase		:			List[str]	    =       pipeline(
              '''document-question-answering'''				,       model=_snake_case				,       tokenizer=_snake_case				,       image_processor=_snake_case				)

          __lowercase		:			int	    =       INVOICE_URL
          __lowercase		:			Optional[int]	    =       list(zip(*apply_tesseract(load_image(_snake_case				)				,       _snake_case				,       ''''''				)				)				)
          __lowercase		:			List[str]	    =       '''What is the placebo?'''
          __lowercase		:			Tuple	    =       [
              {
                  '''image''': load_image(_snake_case				),
                  '''question''': question,
              },
              {
                  '''image''': image,
                  '''question''': question,
              },
              {
                  '''image''': image,
                  '''question''': question,
                  '''word_boxes''': word_boxes,
              },
          ]
          return dqa_pipeline, examples




      def 		snake_case_			(      self		:       List[str]				,       _snake_case		:       int				,       _snake_case		:       List[Any]				):
          __lowercase		:			Optional[Any]	    =       dqa_pipeline(_snake_case				,       top_k=2				)
          self.assertEqual(
              _snake_case				,       [
                  [
                      {'''score''': ANY(_snake_case				), '''answer''': ANY(_snake_case				), '''start''': ANY(_snake_case				), '''end''': ANY(_snake_case				)},
                      {'''score''': ANY(_snake_case				), '''answer''': ANY(_snake_case				), '''start''': ANY(_snake_case				), '''end''': ANY(_snake_case				)},
                  ]
              ]
              * 3				,       )




      @require_torch
      @require_detectrona
      @require_pytesseract
      def 		snake_case_			(      self		:       Optional[int]				):
          __lowercase		:			List[str]	    =       pipeline('''document-question-answering'''				,       model='''hf-internal-testing/tiny-random-layoutlmv2'''				)
          __lowercase		:			Any	    =       INVOICE_URL
          __lowercase		:			str	    =       '''How many cats are there?'''

          __lowercase		:			Optional[int]	    =       [
              {'''score''': 0.00_01, '''answer''': '''oy 2312/2019''', '''start''': 38, '''end''': 39},
              {'''score''': 0.00_01, '''answer''': '''oy 2312/2019 DUE''', '''start''': 38, '''end''': 40},
          ]
          __lowercase		:			Optional[Any]	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(nested_simplify(_snake_case				,       decimals=4				)				,       _snake_case				)

          __lowercase		:			Optional[Any]	    =       dqa_pipeline({'''image''': image, '''question''': question}				,       top_k=2				)
          self.assertEqual(nested_simplify(_snake_case				,       decimals=4				)				,       _snake_case				)

          # This image does not detect ANY text in it, meaning layoutlmv2 should fail.
          # Empty answer probably
          __lowercase		:			Optional[int]	    =       '''./tests/fixtures/tests_samples/COCO/000000039769.png'''
          __lowercase		:			str	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(_snake_case				,       []				)

          # We can optionnally pass directly the words and bounding boxes
          __lowercase		:			List[Any]	    =       '''./tests/fixtures/tests_samples/COCO/000000039769.png'''
          __lowercase		:			Dict	    =       []
          __lowercase		:			List[str]	    =       []
          __lowercase		:			Tuple	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       words=_snake_case				,       boxes=_snake_case				,       top_k=2				)
          self.assertEqual(_snake_case				,       []				)




      @slow
      @require_torch
      @require_detectrona
      @require_pytesseract
      def 		snake_case_			(      self		:       int				):
          __lowercase		:			List[Any]	    =       pipeline(
              '''document-question-answering'''				,       model='''tiennvcs/layoutlmv2-base-uncased-finetuned-docvqa'''				,       revision='''9977165'''				,       )
          __lowercase		:			List[str]	    =       INVOICE_URL
          __lowercase		:			Optional[Any]	    =       '''What is the invoice number?'''

          __lowercase		:			int	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_44, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.00_09, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )

          __lowercase		:			Union[str, Any]	    =       dqa_pipeline({'''image''': image, '''question''': question}				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_44, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.00_09, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )

          __lowercase		:			List[str]	    =       dqa_pipeline(
              [{'''image''': image, '''question''': question}, {'''image''': image, '''question''': question}]				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  [
                      {'''score''': 0.99_44, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                      {'''score''': 0.00_09, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  ],
              ]
              * 2				,       )




      @slow
      @require_torch
      @require_detectrona
      @require_pytesseract
      def 		snake_case_			(      self		:       int				):
          __lowercase		:			Optional[Any]	    =       pipeline(
              '''document-question-answering'''				,       model='''tiennvcs/layoutlmv2-base-uncased-finetuned-docvqa'''				,       revision='''9977165'''				,       max_seq_len=50				,       )
          __lowercase		:			Union[str, Any]	    =       INVOICE_URL
          __lowercase		:			Any	    =       '''What is the invoice number?'''

          __lowercase		:			Any	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_74, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
                  {'''score''': 0.99_48, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )

          __lowercase		:			Dict	    =       dqa_pipeline({'''image''': image, '''question''': question}				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_74, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
                  {'''score''': 0.99_48, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )

          __lowercase		:			List[Any]	    =       dqa_pipeline(
              [{'''image''': image, '''question''': question}, {'''image''': image, '''question''': question}]				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  [
                      {'''score''': 0.99_74, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
                      {'''score''': 0.99_48, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  ]
              ]
              * 2				,       )




      @slow
      @require_torch
      @require_pytesseract
      @require_vision
      def 		snake_case_			(      self		:       str				):
          __lowercase		:			List[Any]	    =       AutoTokenizer.from_pretrained(
              '''impira/layoutlm-document-qa'''				,       revision='''3dc6de3'''				,       add_prefix_space=_snake_case				)
          __lowercase		:			Union[str, Any]	    =       pipeline(
              '''document-question-answering'''				,       model='''impira/layoutlm-document-qa'''				,       tokenizer=_snake_case				,       revision='''3dc6de3'''				,       )
          __lowercase		:			Tuple	    =       INVOICE_URL
          __lowercase		:			Any	    =       '''What is the invoice number?'''

          __lowercase		:			Optional[Any]	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.42_51, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.08_19, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
              ]				,       )

          __lowercase		:			List[Any]	    =       dqa_pipeline({'''image''': image, '''question''': question}				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.42_51, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.08_19, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
              ]				,       )

          __lowercase		:			int	    =       dqa_pipeline(
              [{'''image''': image, '''question''': question}, {'''image''': image, '''question''': question}]				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  [
                      {'''score''': 0.42_51, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                      {'''score''': 0.08_19, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
                  ]
              ]
              * 2				,       )

          __lowercase		:			Union[str, Any]	    =       list(zip(*apply_tesseract(load_image(_snake_case				)				,       _snake_case				,       ''''''				)				)				)

          # This model should also work if `image` is set to None
          __lowercase		:			Union[str, Any]	    =       dqa_pipeline({'''image''': None, '''word_boxes''': word_boxes, '''question''': question}				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.42_51, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.08_19, '''answer''': '''1110212019''', '''start''': 23, '''end''': 23},
              ]				,       )




      @slow
      @require_torch
      @require_pytesseract
      @require_vision
      def 		snake_case_			(      self		:       List[str]				):
          __lowercase		:			Optional[int]	    =       AutoTokenizer.from_pretrained(
              '''impira/layoutlm-document-qa'''				,       revision='''3dc6de3'''				,       add_prefix_space=_snake_case				)
          __lowercase		:			List[str]	    =       pipeline(
              '''document-question-answering'''				,       model='''impira/layoutlm-document-qa'''				,       tokenizer=_snake_case				,       revision='''3dc6de3'''				,       max_seq_len=50				,       )
          __lowercase		:			Tuple	    =       INVOICE_URL
          __lowercase		:			Optional[int]	    =       '''What is the invoice number?'''

          __lowercase		:			Any	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_99, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.99_98, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )

          __lowercase		:			Any	    =       dqa_pipeline(
              [{'''image''': image, '''question''': question}, {'''image''': image, '''question''': question}]				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  [
                      {'''score''': 0.99_99, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                      {'''score''': 0.99_98, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  ]
              ]
              * 2				,       )

          __lowercase		:			int	    =       list(zip(*apply_tesseract(load_image(_snake_case				)				,       _snake_case				,       ''''''				)				)				)

          # This model should also work if `image` is set to None
          __lowercase		:			Tuple	    =       dqa_pipeline({'''image''': None, '''word_boxes''': word_boxes, '''question''': question}				,       top_k=2				)
          self.assertEqual(
              nested_simplify(_snake_case				,       decimals=4				)				,       [
                  {'''score''': 0.99_99, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
                  {'''score''': 0.99_98, '''answer''': '''us-001''', '''start''': 16, '''end''': 16},
              ]				,       )




      @slow
      @require_torch
      def 		snake_case_			(      self		:       List[Any]				):
          __lowercase		:			int	    =       pipeline(
              '''document-question-answering'''				,       model='''naver-clova-ix/donut-base-finetuned-docvqa'''				,       tokenizer=AutoTokenizer.from_pretrained('''naver-clova-ix/donut-base-finetuned-docvqa'''				)				,       feature_extractor='''naver-clova-ix/donut-base-finetuned-docvqa'''				,       )

          __lowercase		:			List[Any]	    =       INVOICE_URL
          __lowercase		:			List[Any]	    =       '''What is the invoice number?'''
          __lowercase		:			int	    =       dqa_pipeline(image=_snake_case				,       question=_snake_case				,       top_k=2				)
          self.assertEqual(nested_simplify(_snake_case				,       decimals=4				)				,       [{'''answer''': '''us-001'''}]				)




      @require_tf
      @unittest.skip('''Document question answering not implemented in TF'''				)
      def 		snake_case_			(      self		:       int				):
          pass


