





'''simple docstring'''

from __future__ import annotations

from math import gcd





def 		UpperCamelCase							(				_lowerCamelCase   :   int		,			_lowerCamelCase   :   int = 2		,			_lowerCamelCase   :   int = 1		,			_lowerCamelCase   :   int = 3		,			):
    # 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   :   int		,			_lowerCamelCase   :   int		,			_lowerCamelCase   :   int			) -> int:
        return (pow(_lowerCamelCase		,			2			) + step) % modulus

    for _ in range(_lowerCamelCase			):
        # These track the position within the cycle detection logic.
        A__							=     seed
        A__							=     seed

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            A__							=     rand_fn(_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)
            A__							=     rand_fn(_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)
            A__							=     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``.
            A__							=     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.
        A__							=     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				:      int						      =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				:      Optional[Any]						      =parser.parse_args()

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










'''simple docstring'''

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   UpperCAmelCase      :
   @staticmethod
   def 	UpperCAmelCase_				(							*lowercase_ :Optional[Any]		,			**lowercase_ :List[Any]				)->				Optional[int]:
       pass





  def 		UpperCamelCase							(				_lowerCamelCase   :   List[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				:      int						      =(
    "https://huggingface.co/spaces/impira/docquery/resolve/2f6c96314dc84dfda62d40de9da55f2f5165d403/invoice.png"
)






@is_pipeline_test
@require_torch
@require_vision
class   UpperCAmelCase      (			unittest.TestCase							):
 __lowercase  						=							MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING
 @require_pytesseract
 @require_vision
 def 	UpperCAmelCase_				(							self :int		,			lowercase_ :Optional[Any]		,			lowercase_ :Optional[Any]		,			lowercase_ :Dict				)->				int:
     A__							=     pipeline(
         "document-question-answering"		,			model=lowercase_		,			tokenizer=lowercase_		,			image_processor=lowercase_				)

     A__							=     INVOICE_URL
     A__							=     list(zip(*apply_tesseract(load_image(lowercase_				)		,			lowercase_		,			""				)				)				)
     A__							=     "What is the placebo?"
     A__							=     [
         {
             "image": load_image(lowercase_				),
             "question": question,
         },
         {
             "image": image,
             "question": question,
         },
         {
             "image": image,
             "question": question,
             "word_boxes": word_boxes,
         },
     ]
     return dqa_pipeline, examples
 def 	UpperCAmelCase_				(							self :str		,			lowercase_ :List[Any]		,			lowercase_ :List[str]				)->				List[str]:
     A__							=     dqa_pipeline(lowercase_		,			top_k=2				)
     self.assertEqual(
         lowercase_		,			[
             [
                 {"score": ANY(lowercase_				), "answer": ANY(lowercase_				), "start": ANY(lowercase_				), "end": ANY(lowercase_				)},
                 {"score": ANY(lowercase_				), "answer": ANY(lowercase_				), "start": ANY(lowercase_				), "end": ANY(lowercase_				)},
             ]
         ]
         * 3		,			)
 @require_torch
 @require_detectrona
 @require_pytesseract
 def 	UpperCAmelCase_				(							self :Dict				)->				Optional[Any]:
     A__							=     pipeline("document-question-answering"		,			model="hf-internal-testing/tiny-random-layoutlmv2"				)
     A__							=     INVOICE_URL
     A__							=     "How many cats are there?"

     A__							=     [
         {"score": 0.0_0_0_1, "answer": "oy 2312/2019", "start": 38, "end": 39},
         {"score": 0.0_0_0_1, "answer": "oy 2312/2019 DUE", "start": 38, "end": 40},
     ]
     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(nested_simplify(lowercase_		,			decimals=4				)		,			lowercase_				)

     A__							=     dqa_pipeline({"image": image, "question": question}		,			top_k=2				)
     self.assertEqual(nested_simplify(lowercase_		,			decimals=4				)		,			lowercase_				)

     # This image does not detect ANY text in it, meaning layoutlmv2 should fail.
     # Empty answer probably
     A__							=     "./tests/fixtures/tests_samples/COCO/000000039769.png"
     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(lowercase_		,			[]				)

     # We can optionnally pass directly the words and bounding boxes
     A__							=     "./tests/fixtures/tests_samples/COCO/000000039769.png"
     A__							=     []
     A__							=     []
     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			words=lowercase_		,			boxes=lowercase_		,			top_k=2				)
     self.assertEqual(lowercase_		,			[]				)
 @slow
 @require_torch
 @require_detectrona
 @require_pytesseract
 def 	UpperCAmelCase_				(							self :Optional[Any]				)->				Tuple:
     A__							=     pipeline(
         "document-question-answering"		,			model="tiennvcs/layoutlmv2-base-uncased-finetuned-docvqa"		,			revision="9977165"		,			)
     A__							=     INVOICE_URL
     A__							=     "What is the invoice number?"

     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_4_4, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.0_0_0_9, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)

     A__							=     dqa_pipeline({"image": image, "question": question}		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_4_4, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.0_0_0_9, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)

     A__							=     dqa_pipeline(
         [{"image": image, "question": question}, {"image": image, "question": question}]		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             [
                 {"score": 0.9_9_4_4, "answer": "us-001", "start": 16, "end": 16},
                 {"score": 0.0_0_0_9, "answer": "us-001", "start": 16, "end": 16},
             ],
         ]
         * 2		,			)
 @slow
 @require_torch
 @require_detectrona
 @require_pytesseract
 def 	UpperCAmelCase_				(							self :Tuple				)->				Optional[Any]:
     A__							=     pipeline(
         "document-question-answering"		,			model="tiennvcs/layoutlmv2-base-uncased-finetuned-docvqa"		,			revision="9977165"		,			max_seq_len=50		,			)
     A__							=     INVOICE_URL
     A__							=     "What is the invoice number?"

     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_7_4, "answer": "1110212019", "start": 23, "end": 23},
             {"score": 0.9_9_4_8, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)

     A__							=     dqa_pipeline({"image": image, "question": question}		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_7_4, "answer": "1110212019", "start": 23, "end": 23},
             {"score": 0.9_9_4_8, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)

     A__							=     dqa_pipeline(
         [{"image": image, "question": question}, {"image": image, "question": question}]		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             [
                 {"score": 0.9_9_7_4, "answer": "1110212019", "start": 23, "end": 23},
                 {"score": 0.9_9_4_8, "answer": "us-001", "start": 16, "end": 16},
             ]
         ]
         * 2		,			)
 @slow
 @require_torch
 @require_pytesseract
 @require_vision
 def 	UpperCAmelCase_				(							self :List[Any]				)->				Any:
     A__							=     AutoTokenizer.from_pretrained(
         "impira/layoutlm-document-qa"		,			revision="3dc6de3"		,			add_prefix_space=lowercase_				)
     A__							=     pipeline(
         "document-question-answering"		,			model="impira/layoutlm-document-qa"		,			tokenizer=lowercase_		,			revision="3dc6de3"		,			)
     A__							=     INVOICE_URL
     A__							=     "What is the invoice number?"

     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.4_2_5_1, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.0_8_1_9, "answer": "1110212019", "start": 23, "end": 23},
         ]		,			)

     A__							=     dqa_pipeline({"image": image, "question": question}		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.4_2_5_1, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.0_8_1_9, "answer": "1110212019", "start": 23, "end": 23},
         ]		,			)

     A__							=     dqa_pipeline(
         [{"image": image, "question": question}, {"image": image, "question": question}]		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             [
                 {"score": 0.4_2_5_1, "answer": "us-001", "start": 16, "end": 16},
                 {"score": 0.0_8_1_9, "answer": "1110212019", "start": 23, "end": 23},
             ]
         ]
         * 2		,			)

     A__							=     list(zip(*apply_tesseract(load_image(lowercase_				)		,			lowercase_		,			""				)				)				)

     # This model should also work if `image` is set to None
     A__							=     dqa_pipeline({"image": None, "word_boxes": word_boxes, "question": question}		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.4_2_5_1, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.0_8_1_9, "answer": "1110212019", "start": 23, "end": 23},
         ]		,			)
 @slow
 @require_torch
 @require_pytesseract
 @require_vision
 def 	UpperCAmelCase_				(							self :Optional[int]				)->				Union[str, Any]:
     A__							=     AutoTokenizer.from_pretrained(
         "impira/layoutlm-document-qa"		,			revision="3dc6de3"		,			add_prefix_space=lowercase_				)
     A__							=     pipeline(
         "document-question-answering"		,			model="impira/layoutlm-document-qa"		,			tokenizer=lowercase_		,			revision="3dc6de3"		,			max_seq_len=50		,			)
     A__							=     INVOICE_URL
     A__							=     "What is the invoice number?"

     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_9_9, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.9_9_9_8, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)

     A__							=     dqa_pipeline(
         [{"image": image, "question": question}, {"image": image, "question": question}]		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             [
                 {"score": 0.9_9_9_9, "answer": "us-001", "start": 16, "end": 16},
                 {"score": 0.9_9_9_8, "answer": "us-001", "start": 16, "end": 16},
             ]
         ]
         * 2		,			)

     A__							=     list(zip(*apply_tesseract(load_image(lowercase_				)		,			lowercase_		,			""				)				)				)

     # This model should also work if `image` is set to None
     A__							=     dqa_pipeline({"image": None, "word_boxes": word_boxes, "question": question}		,			top_k=2				)
     self.assertEqual(
         nested_simplify(lowercase_		,			decimals=4				)		,			[
             {"score": 0.9_9_9_9, "answer": "us-001", "start": 16, "end": 16},
             {"score": 0.9_9_9_8, "answer": "us-001", "start": 16, "end": 16},
         ]		,			)
 @slow
 @require_torch
 def 	UpperCAmelCase_				(							self :Optional[int]				)->				Tuple:
     A__							=     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"		,			)

     A__							=     INVOICE_URL
     A__							=     "What is the invoice number?"
     A__							=     dqa_pipeline(image=lowercase_		,			question=lowercase_		,			top_k=2				)
     self.assertEqual(nested_simplify(lowercase_		,			decimals=4				)		,			[{"answer": "us-001"}]				)



 @require_tf
 @unittest.skip("Document question answering not implemented in TF"				)
 def 	UpperCAmelCase_				(							self :Optional[Any]				)->				List[str]:
     pass



