



from __future__ import annotations

from math import gcd






def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      int = 2      ,			UpperCamelCase		:      int = 1      ,			UpperCamelCase		:      int = 3      ,			):



			'''simple docstring'''







			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(UpperCamelCase		:      int      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int ) -> int:
						return (pow(UpperCamelCase      ,			2 ) + step) % modulus

			for _ in range(UpperCamelCase ):
						# These track the position within the cycle detection logic.
						lowerCamelCase__ :      int								=		seed
						lowerCamelCase__ :      str								=		seed

						while True:
									# At each iteration, the tortoise moves one step and the hare moves two.
									lowerCamelCase__ :      List[Any]								=		rand_fn(UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )
									lowerCamelCase__ :      str								=		rand_fn(UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )
									lowerCamelCase__ :      str								=		rand_fn(UpperCamelCase      ,			UpperCamelCase      ,			UpperCamelCase )

									# 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__ :      Any								=		gcd(hare - tortoise      ,			UpperCamelCase )

									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__ :      List[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

				_lowercase     							=						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''',
				)
				_lowercase     							=						parser.parse_args()

				_lowercase     							=						pollard_rho(args.num, attempts=args.attempts)
				if divisor is None:
								print(F'''{args.num} is probably prime''')
				else:
								_lowercase     							=						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:
				_lowercase     							=						False

if is_vision_available():
				from PIL import Image

				from transformers import PixaStructImageProcessor
class 				__A					( unittest.TestCase      ):





			def __init__(self							,    __magic_name__							,    __magic_name__=7							,    __magic_name__=3							,    __magic_name__=18							,    __magic_name__=30							,    __magic_name__=400							,    __magic_name__=None							,    __magic_name__=True							,    __magic_name__=True							,    __magic_name__=None							,    ):
						lowerCamelCase__ :      Optional[Any]								=		size if size is not None else {"""height""": 20, """width""": 20}
						lowerCamelCase__ :      List[str]								=		parent
						lowerCamelCase__ :      str								=		batch_size
						lowerCamelCase__ :      List[str]								=		num_channels
						lowerCamelCase__ :      Optional[int]								=		image_size
						lowerCamelCase__ :      Union[str, Any]								=		min_resolution
						lowerCamelCase__ :      List[Any]								=		max_resolution
						lowerCamelCase__ :      Optional[int]								=		size
						lowerCamelCase__ :      List[str]								=		do_normalize
						lowerCamelCase__ :      str								=		do_convert_rgb
						lowerCamelCase__ :      str								=		[512, 1024, 2048, 4096]
						lowerCamelCase__ :      Any								=		patch_size if patch_size is not None else {"""height""": 16, """width""": 16}





			def        _snake_case    (self				):
						return {"do_normalize": self.do_normalize, "do_convert_rgb": self.do_convert_rgb}





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		"""https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/australia.jpg"""
						lowerCamelCase__ :      int								=		Image.open(requests.get(__magic_name__							,    stream=__magic_name__				).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					( A_					, unittest.TestCase      ):
			UpperCamelCase					:Union[str, Any]     =			PixaStructImageProcessor if is_vision_available() else None





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		PixaStructImageProcessingTester(self				)





			@property
			def        _snake_case    (self				):
						return self.image_processor_tester.prepare_image_processor_dict()





			def        _snake_case    (self				):
						lowerCamelCase__ :      int								=		self.image_processing_class(**self.image_processor_dict				)
						self.assertTrue(hasattr(__magic_name__							,    """do_normalize"""				)				)
						self.assertTrue(hasattr(__magic_name__							,    """do_convert_rgb"""				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		self.image_processor_tester.prepare_dummy_image()

						lowerCamelCase__ :      Tuple								=		self.image_processing_class(**self.image_processor_dict				)
						lowerCamelCase__ :      List[str]								=		2048

						lowerCamelCase__ :      Any								=		image_processor(__magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				)
						self.assertTrue(torch.allclose(inputs.flattened_patches.mean()							,    torch.tensor(0.06_06				)							,    atol=1E-3							,    rtol=1E-3				)				)





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      List[Any]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      Optional[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    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[Any]								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      List[str]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      Optional[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    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
						) + 2

						lowerCamelCase__ :      List[str]								=		True

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									with self.assertRaises(__magic_name__				):
												lowerCamelCase__ :      Tuple								=		image_processor(
												    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches

									lowerCamelCase__ :      Optional[Any]								=		"""Hello"""

									lowerCamelCase__ :      Dict								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__							,    header_text=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Tuple								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__							,    header_text=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      Any								=		self.image_processing_class(**self.image_processor_dict				)
						# create random numpy tensors
						lowerCamelCase__ :      Dict								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__							,    numpify=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    np.ndarray				)

						lowerCamelCase__ :      Optional[int]								=		(
						    (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=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

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





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      Optional[int]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PyTorch tensors
						lowerCamelCase__ :      Dict								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__							,    torchify=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    torch.Tensor				)

						# 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

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      Tuple								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).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					( A_					, unittest.TestCase      ):
			UpperCamelCase					:Optional[int]     =			PixaStructImageProcessor if is_vision_available() else None





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		PixaStructImageProcessingTester(self							,    num_channels=4				)
						lowerCamelCase__ :      Optional[int]								=		3





			@property
			def        _snake_case    (self				):
						return self.image_processor_tester.prepare_image_processor_dict()





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		self.image_processing_class(**self.image_processor_dict				)
						self.assertTrue(hasattr(__magic_name__							,    """do_normalize"""				)				)
						self.assertTrue(hasattr(__magic_name__							,    """do_convert_rgb"""				)				)





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      str								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      List[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    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 - 1)
						) + 2

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      str								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )



