



'''simple docstring'''

from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
							import PIL


__lowerCAmelCase		     =  logging.get_logger(__name__)



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_    )     -> str:
		_a	: Optional[int]								=				b.T
		_a	: Tuple								=				np.sum(np.square(lowerCAmelCase_    )		,     axis=1    )
		_a	: Any								=				np.sum(np.square(lowerCAmelCase_    )		,     axis=0    )
		_a	: List[str]								=				np.matmul(lowerCAmelCase_		,     lowerCAmelCase_    )
		_a	: Tuple								=				aa[:, None] - 2 * ab + ba[None, :]
		return d



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_    )     -> Union[str, Any]:
		_a	: List[str]								=				x.reshape(-1		,     3    )
		_a	: Union[str, Any]								=				squared_euclidean_distance(lowerCAmelCase_		,     lowerCAmelCase_    )
		return np.argmin(lowerCAmelCase_		,     axis=1    )

class       __magic_name__		(       _UpperCamelCase  ):
							lowerCAmelCase			:       str  							=   ['pixel_values']







							def __init__(				self   :			Optional[Any]      ,_UpperCAmelCase   :			Optional[Union[List[List[int]], np.ndarray]] = None      ,_UpperCAmelCase   :			bool = True      ,_UpperCAmelCase   :			Dict[str, int] = None      ,_UpperCAmelCase   :			PILImageResampling = PILImageResampling.BILINEAR      ,_UpperCAmelCase   :			bool = True      ,_UpperCAmelCase   :			bool = True      ,**_UpperCAmelCase   :			Optional[int]      ,):
									super().__init__(**_UpperCAmelCase						)
									_a	: Union[str, Any]								=				size if size is not None else {'height': 256, 'width': 256}
									_a	: Dict								=				get_size_dict(_UpperCAmelCase						)
									_a	: Any								=				np.array(_UpperCAmelCase						) if clusters is not None else None
									_a	: List[str]								=				do_resize
									_a	: List[Any]								=				size
									_a	: str								=				resample
									_a	: str								=				do_normalize
									_a	: Tuple								=				do_color_quantize







							def 				__lowercase     (				self   :			int      ,_UpperCAmelCase   :			np.ndarray      ,_UpperCAmelCase   :			Dict[str, int]      ,_UpperCAmelCase   :			PILImageResampling = PILImageResampling.BILINEAR      ,_UpperCAmelCase   :			Optional[Union[str, ChannelDimension]] = None      ,**_UpperCAmelCase   :			Tuple      ,):
									_a	: Union[str, Any]								=				get_size_dict(_UpperCAmelCase						)
									if "height" not in size or "width" not in size:
											raise ValueError(F"""Size dictionary must contain both height and width keys. Got {size.keys()}"""						)
									return resize(
									    _UpperCAmelCase      ,size=(size['height'], size['width'])      ,resample=_UpperCAmelCase      ,data_format=_UpperCAmelCase      ,**_UpperCAmelCase						)







							def 				__lowercase     (				self   :			Dict      ,_UpperCAmelCase   :			np.ndarray      ,_UpperCAmelCase   :			Optional[Union[str, ChannelDimension]] = None      ,):
									_a	: str								=				rescale(image=_UpperCAmelCase      ,scale=1 / 1_27.5      ,data_format=_UpperCAmelCase						)
									_a	: Dict								=				image - 1
									return image







							def 				__lowercase     (				self   :			Union[str, Any]      ,_UpperCAmelCase   :			ImageInput      ,_UpperCAmelCase   :			bool = None      ,_UpperCAmelCase   :			Dict[str, int] = None      ,_UpperCAmelCase   :			PILImageResampling = None      ,_UpperCAmelCase   :			bool = None      ,_UpperCAmelCase   :			Optional[bool] = None      ,_UpperCAmelCase   :			Optional[Union[List[List[int]], np.ndarray]] = None      ,_UpperCAmelCase   :			Optional[Union[str, TensorType]] = None      ,_UpperCAmelCase   :			Optional[Union[str, ChannelDimension]] = ChannelDimension.FIRST      ,**_UpperCAmelCase   :			List[str]      ,):
									_a	: Tuple								=				do_resize if do_resize is not None else self.do_resize
									_a	: Any								=				size if size is not None else self.size
									_a	: Dict								=				get_size_dict(_UpperCAmelCase						)
									_a	: Dict								=				resample if resample is not None else self.resample
									_a	: Optional[int]								=				do_normalize if do_normalize is not None else self.do_normalize
									_a	: Optional[int]								=				do_color_quantize if do_color_quantize is not None else self.do_color_quantize
									_a	: Optional[int]								=				clusters if clusters is not None else self.clusters
									_a	: Optional[int]								=				np.array(_UpperCAmelCase						)

									_a	: Any								=				make_list_of_images(_UpperCAmelCase						)

									if not valid_images(_UpperCAmelCase						):
											raise ValueError(
											    'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
											    'torch.Tensor, tf.Tensor or jax.ndarray.'						)

									if do_resize and size is None or resample is None:
											raise ValueError('Size and resample must be specified if do_resize is True.'						)

									if do_color_quantize and clusters is None:
											raise ValueError('Clusters must be specified if do_color_quantize is True.'						)

									# All transformations expect numpy arrays.
									_a	: int								=				[to_numpy_array(_UpperCAmelCase						) for image in images]

									if do_resize:
											_a	: str								=				[self.resize(image=_UpperCAmelCase      ,size=_UpperCAmelCase      ,resample=_UpperCAmelCase						) for image in images]

									if do_normalize:
											_a	: Tuple								=				[self.normalize(image=_UpperCAmelCase						) for image in images]

									if do_color_quantize:
											_a	: Any								=				[to_channel_dimension_format(_UpperCAmelCase      ,ChannelDimension.LAST						) for image in images]
											# color quantize from (batch_size, height, width, 3) to (batch_size, height, width)
											_a	: List[str]								=				np.array(_UpperCAmelCase						)
											_a	: Dict								=				color_quantize(_UpperCAmelCase      ,_UpperCAmelCase						).reshape(images.shape[:-1]						)

											# flatten to (batch_size, height*width)
											_a	: Any								=				images.shape[0]
											_a	: Tuple								=				images.reshape(_UpperCAmelCase      ,-1						)

											# We need to convert back to a list of images to keep consistent behaviour across processors.
											_a	: int								=				list(_UpperCAmelCase						)
									else:
											_a	: Tuple								=				[to_channel_dimension_format(_UpperCAmelCase      ,_UpperCAmelCase						) for image in images]

									_a	: Any								=				{'input_ids': images}
									return BatchFeature(data=_UpperCAmelCase      ,tensor_type=_UpperCAmelCase						)









'''simple docstring'''

from __future__ import annotations

from math import gcd



def 	__lowerCamelCase	( 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.
				_a	: Optional[int]								=				seed
				_a	: str								=				seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						_a	: str								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Dict								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Tuple								=				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	: Optional[Any]								=				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	: Union[str, 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		     =  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}""")




