





from __future__ import annotations

from math import gcd




def  __UpperCAmelCase(   lowercase_			,     lowercase_ = 2			,     lowercase_ = 1			,     lowercase_ = 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(lowercase_			,     lowercase_			,     lowercase_   ) -> int:
              return (pow(lowercase_			,     2   ) + step) % modulus

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

              while True:
                     # At each iteration, the tortoise moves one step and the hare moves two.
                     _lowerCamelCase				:  Dict						=		rand_fn(lowercase_			,     lowercase_			,     lowercase_   )
                     _lowerCamelCase				:  int						=		rand_fn(lowercase_			,     lowercase_			,     lowercase_   )
                     _lowerCamelCase				:  Union[str, Any]						=		rand_fn(lowercase_			,     lowercase_			,     lowercase_   )

                     # 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``.
                     _lowerCamelCase				:  Optional[int]						=		gcd(hare - tortoise			,     lowercase_   )

                     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.
              _lowerCamelCase				:  int						=		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      							=   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      							=   parser.parse_args()

       _lowerCamelCase      							=   pollard_rho(args.num, attempts=args.attempts)
       if divisor is None:
              print(F'''{args.num} is probably prime''')
       else:
              _lowerCamelCase      							=   args.num // divisor
              print(F'''{args.num} = {divisor} * {quotient}''')








import unittest

import numpy as np
import requests

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
       import torch

       from transformers.pytorch_utils import is_torch_greater_or_equal_than_1_11
else:
       _lowerCamelCase      							=   False

if is_vision_available():
       from PIL import Image

       from transformers import PixaStructImageProcessor







class       __A							(   unittest.TestCase	):




      """simple docstring"""







      def __init__(		self   ,				a__   ,				a__=7   ,				a__=3   ,				a__=18   ,				a__=30   ,				a__=400   ,				a__=None   ,				a__=True   ,				a__=True   ,				a__=None   ,				):



             """simple docstring"""





             _lowerCamelCase				:  str						=		size if size is not None else {'''height''': 20, '''width''': 20}
             _lowerCamelCase				:  int						=		parent
             _lowerCamelCase				:  Tuple						=		batch_size
             _lowerCamelCase				:  Union[str, Any]						=		num_channels
             _lowerCamelCase				:  Tuple						=		image_size
             _lowerCamelCase				:  Dict						=		min_resolution
             _lowerCamelCase				:  int						=		max_resolution
             _lowerCamelCase				:  Dict						=		size
             _lowerCamelCase				:  Dict						=		do_normalize
             _lowerCamelCase				:  List[Any]						=		do_convert_rgb
             _lowerCamelCase				:  Optional[int]						=		[512, 1024, 2048, 4096]
             _lowerCamelCase				:  Optional[int]						=		patch_size if patch_size is not None else {'''height''': 16, '''width''': 16}


      def 					__snake_case      (		self):



             """simple docstring"""





             return {"do_normalize": self.do_normalize, "do_convert_rgb": self.do_convert_rgb}



      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Dict						=		'''https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/australia.jpg'''
             _lowerCamelCase				:  Union[str, Any]						=		Image.open(requests.get(a__   ,				stream=a__).raw).convert('''RGB''')
             return raw_image







@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11			,reason="""`Pix2StructImageProcessor` requires `torch>=1.11.0`."""			,)
@require_torch
@require_vision
class       __A							(   lowerCamelCase__			,unittest.TestCase	):




      """simple docstring"""







      UpperCAmelCase__							=   PixaStructImageProcessor if is_vision_available() else None


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  int						=		PixaStructImageProcessingTester(self)


      @property
      def 					__snake_case      (		self):



             """simple docstring"""





             return self.image_processor_tester.prepare_image_processor_dict()


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  int						=		self.image_processing_class(**self.image_processor_dict)
             self.assertTrue(hasattr(a__   ,				'''do_normalize'''))
             self.assertTrue(hasattr(a__   ,				'''do_convert_rgb'''))


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Any						=		self.image_processor_tester.prepare_dummy_image()

             _lowerCamelCase				:  List[Any]						=		self.image_processing_class(**self.image_processor_dict)
             _lowerCamelCase				:  Optional[int]						=		2048

             _lowerCamelCase				:  Any						=		image_processor(a__   ,				return_tensors='''pt'''   ,				max_patches=a__)
             self.assertTrue(torch.allclose(inputs.flattened_patches.mean()   ,				torch.tensor(0.0606)   ,				atol=1e-3   ,				rtol=1e-3))


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Dict						=		self.image_processing_class(**self.image_processor_dict)
             # create random PIL images
             _lowerCamelCase				:  Any						=		prepare_image_inputs(self.image_processor_tester   ,				equal_resolution=a__)
             for image in image_inputs:
                    self.assertIsInstance(a__   ,				Image.Image)

             # Test not batched input
             _lowerCamelCase				:  Optional[Any]						=		(
                 (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
                 * self.image_processor_tester.num_channels
             ) + 2

             for max_patch in self.image_processor_tester.max_patches:
                    # Test not batched input
                    _lowerCamelCase				:  Optional[int]						=		image_processor(
                        image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(1, max_patch, expected_hidden_dim)   ,				)

                    # Test batched
                    _lowerCamelCase				:  Dict						=		image_processor(
                        a__   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)   ,				)


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Dict						=		self.image_processing_class(**self.image_processor_dict)
             # create random PIL images
             _lowerCamelCase				:  Optional[int]						=		prepare_image_inputs(self.image_processor_tester   ,				equal_resolution=a__)
             for image in image_inputs:
                    self.assertIsInstance(a__   ,				Image.Image)

             # Test not batched input
             _lowerCamelCase				:  List[str]						=		(
                 (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
                 * self.image_processor_tester.num_channels
             ) + 2

             _lowerCamelCase				:  Dict						=		True

             for max_patch in self.image_processor_tester.max_patches:
                    # Test not batched input
                    with self.assertRaises(a__):
                           _lowerCamelCase				:  List[Any]						=		image_processor(
                               image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches

                    _lowerCamelCase				:  List[Any]						=		'''Hello'''

                    _lowerCamelCase				:  int						=		image_processor(
                        image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__   ,				header_text=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(1, max_patch, expected_hidden_dim)   ,				)

                    # Test batched
                    _lowerCamelCase				:  Dict						=		image_processor(
                        a__   ,				return_tensors='''pt'''   ,				max_patches=a__   ,				header_text=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)   ,				)


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  List[Any]						=		self.image_processing_class(**self.image_processor_dict)
             # create random numpy tensors
             _lowerCamelCase				:  Tuple						=		prepare_image_inputs(self.image_processor_tester   ,				equal_resolution=a__   ,				numpify=a__)
             for image in image_inputs:
                    self.assertIsInstance(a__   ,				np.ndarray)

             _lowerCamelCase				:  Any						=		(
                 (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
                 * self.image_processor_tester.num_channels
             ) + 2

             for max_patch in self.image_processor_tester.max_patches:
                    # Test not batched input
                    _lowerCamelCase				:  List[str]						=		image_processor(
                        image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(1, max_patch, expected_hidden_dim)   ,				)

                    # Test batched
                    _lowerCamelCase				:  Tuple						=		image_processor(
                        a__   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)   ,				)



      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Optional[int]						=		self.image_processing_class(**self.image_processor_dict)
             # create random PyTorch tensors
             _lowerCamelCase				:  str						=		prepare_image_inputs(self.image_processor_tester   ,				equal_resolution=a__   ,				torchify=a__)
             for image in image_inputs:
                    self.assertIsInstance(a__   ,				torch.Tensor)

             # Test not batched input
             _lowerCamelCase				:  Tuple						=		(
                 (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
                 * self.image_processor_tester.num_channels
             ) + 2

             for max_patch in self.image_processor_tester.max_patches:
                    # Test not batched input
                    _lowerCamelCase				:  Optional[int]						=		image_processor(
                        image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(1, max_patch, expected_hidden_dim)   ,				)

                    # Test batched
                    _lowerCamelCase				:  List[str]						=		image_processor(
                        a__   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)   ,				)







@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11			,reason="""`Pix2StructImageProcessor` requires `torch>=1.11.0`."""			,)
@require_torch
@require_vision
class       __A							(   lowerCamelCase__			,unittest.TestCase	):




      """simple docstring"""







      UpperCAmelCase__							=   PixaStructImageProcessor if is_vision_available() else None


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  Optional[Any]						=		PixaStructImageProcessingTester(self   ,				num_channels=4)
             _lowerCamelCase				:  Union[str, Any]						=		3


      @property
      def 					__snake_case      (		self):



             """simple docstring"""





             return self.image_processor_tester.prepare_image_processor_dict()


      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  str						=		self.image_processing_class(**self.image_processor_dict)
             self.assertTrue(hasattr(a__   ,				'''do_normalize'''))
             self.assertTrue(hasattr(a__   ,				'''do_convert_rgb'''))



      def 					__snake_case      (		self):



             """simple docstring"""





             _lowerCamelCase				:  List[str]						=		self.image_processing_class(**self.image_processor_dict)
             # create random PIL images
             _lowerCamelCase				:  Any						=		prepare_image_inputs(self.image_processor_tester   ,				equal_resolution=a__)
             for image in image_inputs:
                    self.assertIsInstance(a__   ,				Image.Image)

             # Test not batched input
             _lowerCamelCase				:  List[Any]						=		(
                 (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
                 * (self.image_processor_tester.num_channels - 1)
             ) + 2

             for max_patch in self.image_processor_tester.max_patches:
                    # Test not batched input
                    _lowerCamelCase				:  Union[str, Any]						=		image_processor(
                        image_inputs[0]   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(1, max_patch, expected_hidden_dim)   ,				)

                    # Test batched
                    _lowerCamelCase				:  Union[str, Any]						=		image_processor(
                        a__   ,				return_tensors='''pt'''   ,				max_patches=a__).flattened_patches
                    self.assertEqual(
                        encoded_images.shape   ,				(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)   ,				)

