import math
from typing import Dict, Iterable, List, Optional, Tuple, Union

import numpy as np

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


if is_torch_available():
					import torch

if is_vision_available():
					import PIL


_lowerCAmelCase       =		logging.get_logger(__name__)
def 					_snake_case	(  __snake_case  ,     __snake_case  ,     __snake_case  ,     __snake_case						):
					def constraint_to_multiple_of(__snake_case  ,     __snake_case  ,     __snake_case=0  ,     __snake_case=None						):
										_UpperCamelCase			     =     round(val / multiple						) * multiple

										if max_val is not None and x > max_val:
															_UpperCamelCase			     =     math.floor(val / multiple						) * multiple

										if x < min_val:
															_UpperCamelCase			     =     math.ceil(val / multiple						) * multiple

										return x

					_UpperCamelCase			     =     (output_size, output_size) if isinstance(__snake_case  ,     __snake_case						) else output_size

					_UpperCamelCase     ,    _UpperCamelCase			     =     get_image_size(__snake_case						)
					_UpperCamelCase     ,    _UpperCamelCase			     =     output_size

					# determine new height and width
					_UpperCamelCase			     =     output_height / input_height
					_UpperCamelCase			     =     output_width / input_width

					if keep_aspect_ratio:
										# scale as little as possible
										if abs(1 - scale_width						) < abs(1 - scale_height						):
															# fit width
															_UpperCamelCase			     =     scale_width
										else:
															# fit height
															_UpperCamelCase			     =     scale_height

					_UpperCamelCase			     =     constraint_to_multiple_of(scale_height * input_height  ,     multiple=__snake_case						)
					_UpperCamelCase			     =     constraint_to_multiple_of(scale_width * input_width  ,     multiple=__snake_case						)

					return (new_height, new_width)







class     lowerCAmelCase_     (       __lowercase ):
							UpperCAmelCase				   =     ["pixel_values"]







							def __init__(   self      :     List[Any] ,			_A      :     bool = True ,			_A      :     Dict[str, int] = None ,			_A      :     PILImageResampling = PILImageResampling.BILINEAR ,			_A      :     bool = False ,			_A      :     int = 1 ,			_A      :     bool = True ,			_A      :     Union[int, float] = 1 / 255 ,			_A      :     bool = True ,			_A      :     Optional[Union[float, List[float]]] = None ,			_A      :     Optional[Union[float, List[float]]] = None ,			**_A      :     List[str] ,			):
												super().__init__(**_A		)
												_UpperCamelCase			     =     size if size is not None else {'''height''': 384, '''width''': 384}
												_UpperCamelCase			     =     get_size_dict(_A		)
												_UpperCamelCase			     =     do_resize
												_UpperCamelCase			     =     size
												_UpperCamelCase			     =     keep_aspect_ratio
												_UpperCamelCase			     =     ensure_multiple_of
												_UpperCamelCase			     =     resample
												_UpperCamelCase			     =     do_rescale
												_UpperCamelCase			     =     rescale_factor
												_UpperCamelCase			     =     do_normalize
												_UpperCamelCase			     =     image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
												_UpperCamelCase			     =     image_std if image_std is not None else IMAGENET_STANDARD_STD







							def  UpperCamelCase_						(   self      :     List[str] ,			_A      :     np.ndarray ,			_A      :     Dict[str, int] ,			_A      :     bool = False ,			_A      :     int = 1 ,			_A      :     PILImageResampling = PILImageResampling.BICUBIC ,			_A      :     Optional[Union[str, ChannelDimension]] = None ,			**_A      :     Any ,			):
												_UpperCamelCase			     =     get_size_dict(_A		)
												if "height" not in size or "width" not in size:
																	raise ValueError(F"""The size dictionary must contain the keys 'height' and 'width'. Got {size.keys()}"""		)
												_UpperCamelCase			     =     get_resize_output_image_size(
												    _A ,			output_size=(size['''height'''], size['''width''']) ,			keep_aspect_ratio=_A ,			multiple=_A ,			)
												return resize(_A ,			size=_A ,			resample=_A ,			data_format=_A ,			**_A		)







							def  UpperCamelCase_						(   self      :     str ,			_A      :     np.ndarray ,			_A      :     Union[int, float] ,			_A      :     Optional[Union[str, ChannelDimension]] = None ,			**_A      :     Any ,			):
												return rescale(_A ,			scale=_A ,			data_format=_A ,			**_A		)







							def  UpperCamelCase_						(   self      :     int ,			_A      :     np.ndarray ,			_A      :     Union[float, List[float]] ,			_A      :     Union[float, List[float]] ,			_A      :     Optional[Union[str, ChannelDimension]] = None ,			**_A      :     Any ,			):
												return normalize(_A ,			mean=_A ,			std=_A ,			data_format=_A ,			**_A		)







							def  UpperCamelCase_						(   self      :     Optional[int] ,			_A      :     ImageInput ,			_A      :     bool = None ,			_A      :     int = None ,			_A      :     bool = None ,			_A      :     int = None ,			_A      :     PILImageResampling = None ,			_A      :     bool = None ,			_A      :     float = None ,			_A      :     bool = None ,			_A      :     Optional[Union[float, List[float]]] = None ,			_A      :     Optional[Union[float, List[float]]] = None ,			_A      :     Optional[Union[str, TensorType]] = None ,			_A      :     ChannelDimension = ChannelDimension.FIRST ,			**_A      :     str ,			):
												_UpperCamelCase			     =     do_resize if do_resize is not None else self.do_resize
												_UpperCamelCase			     =     size if size is not None else self.size
												_UpperCamelCase			     =     get_size_dict(_A		)
												_UpperCamelCase			     =     keep_aspect_ratio if keep_aspect_ratio is not None else self.keep_aspect_ratio
												_UpperCamelCase			     =     ensure_multiple_of if ensure_multiple_of is not None else self.ensure_multiple_of
												_UpperCamelCase			     =     resample if resample is not None else self.resample
												_UpperCamelCase			     =     do_rescale if do_rescale is not None else self.do_rescale
												_UpperCamelCase			     =     rescale_factor if rescale_factor is not None else self.rescale_factor
												_UpperCamelCase			     =     do_normalize if do_normalize is not None else self.do_normalize
												_UpperCamelCase			     =     image_mean if image_mean is not None else self.image_mean
												_UpperCamelCase			     =     image_std if image_std is not None else self.image_std

												_UpperCamelCase			     =     make_list_of_images(_A		)

												if not valid_images(_A		):
																	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_rescale and rescale_factor is None:
																	raise ValueError('''Rescale factor must be specified if do_rescale is True.'''		)

												if do_normalize and (image_mean is None or image_std is None):
																	raise ValueError('''Image mean and std must be specified if do_normalize is True.'''		)

												# All transformations expect numpy arrays.
												_UpperCamelCase			     =     [to_numpy_array(_A		) for image in images]

												if do_resize:
																	_UpperCamelCase			     =     [self.resize(image=_A ,			size=_A ,			resample=_A		) for image in images]

												if do_rescale:
																	_UpperCamelCase			     =     [self.rescale(image=_A ,			scale=_A		) for image in images]

												if do_normalize:
																	_UpperCamelCase			     =     [self.normalize(image=_A ,			mean=_A ,			std=_A		) for image in images]

												_UpperCamelCase			     =     [to_channel_dimension_format(_A ,			_A		) for image in images]

												_UpperCamelCase			     =     {'''pixel_values''': images}
												return BatchFeature(data=_A ,			tensor_type=_A		)







							def  UpperCamelCase_						(   self      :     Any ,			_A      :     Any ,			_A      :     List[Tuple] = None		):
												_UpperCamelCase			     =     outputs.logits

												# Resize logits and compute semantic segmentation maps
												if target_sizes is not None:
																	if len(_A		) != len(_A		):
																						raise ValueError(
																						    '''Make sure that you pass in as many target sizes as the batch dimension of the logits'''		)

																	if is_torch_tensor(_A		):
																						_UpperCamelCase			     =     target_sizes.numpy()

																	_UpperCamelCase			     =     []

																	for idx in range(len(_A		)		):
																						_UpperCamelCase			     =     torch.nn.functional.interpolate(
																						    logits[idx].unsqueeze(dim=0		) ,			size=target_sizes[idx] ,			mode='''bilinear''' ,			align_corners=_A		)
																						_UpperCamelCase			     =     resized_logits[0].argmax(dim=0		)
																						semantic_segmentation.append(_A		)
												else:
																	_UpperCamelCase			     =     logits.argmax(dim=1		)
																	_UpperCamelCase			     =     [semantic_segmentation[i] for i in range(semantic_segmentation.shape[0]		)]

												return semantic_segmentation




from __future__ import annotations

from math import gcd



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int = 2		,    lowerCAmelCase_				:int = 1		,    lowerCAmelCase_				:int = 3		,    )->int | None:
   '''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(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.
      snake_case_            =       seed
      snake_case_            =       seed

      while True:
         # At each iteration, the tortoise moves one step and the hare moves two.
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       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``.
         snake_case_            =       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.
      snake_case_            =       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

   SCREAMING_SNAKE_CASE						:Union[str, Any]			=  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''',
   )
   SCREAMING_SNAKE_CASE						:List[str]			=  parser.parse_args()

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




