

from __future__ import annotations

from math import gcd







def 					SCREAMING_SNAKE_CASE    (			snake_case_ :							List[str]					,  snake_case_ :							Optional[Any] = 2					,  snake_case_ :							str = 1					,  snake_case_ :							Dict = 3					,  ):





	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(snake_case_ :							Optional[Any]					,  snake_case_ :							Any					,  snake_case_ :							str       ) -> int:
		return (pow(__snake_case					,  2       ) + step) % modulus

	for _ in range(__snake_case       ):
		# These track the position within the cycle detection logic.
		snake_case__			:				List[Any]       =  seed
		snake_case__			:				Any       =  seed

		while True:
			# At each iteration, the tortoise moves one step and the hare moves two.
			snake_case__			:				str       =  rand_fn(__snake_case					,  __snake_case					,  __snake_case       )
			snake_case__			:				int       =  rand_fn(__snake_case					,  __snake_case					,  __snake_case       )
			snake_case__			:				Optional[int]       =  rand_fn(__snake_case					,  __snake_case					,  __snake_case       )

			# 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__			:				Union[str, Any]       =  gcd(hare - tortoise					,  __snake_case       )

			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__			:				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 :      List[str]										=				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[int]										=				parser.parse_args()

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











import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType



class 							SCREAMING_SNAKE_CASE__						(    UpperCamelCase_						):





					"""simple docstring"""






					a_     =		["image_processor", "tokenizer"]
					a_     =		"ViltImageProcessor"
					a_     =		("BertTokenizer", "BertTokenizerFast")



					def __init__( self					:  Optional[int]							,		__A					:  Optional[int]=None							,		__A					:  Optional[Any]=None							,		**__A					:  int	):
						snake_case__			:				Union[str, Any]       =  None
						if "feature_extractor" in kwargs:
							warnings.warn(
							    "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
							    " instead."							,		__A							,		)
							snake_case__			:				Tuple       =  kwargs.pop("feature_extractor"	)

						snake_case__			:				Any       =  image_processor if image_processor is not None else feature_extractor
						if image_processor is None:
							raise ValueError("You need to specify an `image_processor`."	)
						if tokenizer is None:
							raise ValueError("You need to specify a `tokenizer`."	)

						super().__init__(__A							,		__A	)
						snake_case__			:				Tuple       =  self.image_processor



					def __call__( self					:  List[Any]							,		__A					:  int							,		__A					:  Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None							,		__A					:  bool = True							,		__A					:  Union[bool, str, PaddingStrategy] = False							,		__A					:  Union[bool, str, TruncationStrategy] = None							,		__A					:  Optional[int] = None							,		__A					:  int = 0							,		__A					:  Optional[int] = None							,		__A					:  Optional[bool] = None							,		__A					:  Optional[bool] = None							,		__A					:  bool = False							,		__A					:  bool = False							,		__A					:  bool = False							,		__A					:  bool = False							,		__A					:  bool = True							,		__A					:  Optional[Union[str, TensorType]] = None							,		**__A					:  List[Any]							,		):
						snake_case__			:				Optional[int]       =  self.tokenizer(
						    text=__A							,		add_special_tokens=__A							,		padding=__A							,		truncation=__A							,		max_length=__A							,		stride=__A							,		pad_to_multiple_of=__A							,		return_token_type_ids=__A							,		return_attention_mask=__A							,		return_overflowing_tokens=__A							,		return_special_tokens_mask=__A							,		return_offsets_mapping=__A							,		return_length=__A							,		verbose=__A							,		return_tensors=__A							,		**__A							,		)
						# add pixel_values + pixel_mask
						snake_case__			:				Optional[Any]       =  self.image_processor(__A							,		return_tensors=__A	)
						encoding.update(__A	)

						return encoding



					def 	_lowercase					( self					:  Optional[Any]							,		*__A					:  List[str]							,		**__A					:  Optional[int]	):
						return self.tokenizer.batch_decode(*__A							,		**__A	)



					def 	_lowercase					( self					:  Dict							,		*__A					:  str							,		**__A					:  str	):
						return self.tokenizer.decode(*__A							,		**__A	)



					@property
					def 	_lowercase					( self					:  str	):
						snake_case__			:				Optional[Any]       =  self.tokenizer.model_input_names
						snake_case__			:				Any       =  self.image_processor.model_input_names
						return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names	)	)



					@property
					def 	_lowercase					( self					:  List[Any]	):
						warnings.warn(
						    "`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."							,		__A							,		)
						return self.image_processor_class






					@property
					def 	_lowercase					( self					:  str	):
						warnings.warn(
						    "`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."							,		__A							,		)
						return self.image_processor



