






"""simple docstring"""





from __future__ import annotations

from math import gcd



def   a    (     __UpperCAmelCase      :    int      ,   __UpperCAmelCase      :    int = 2      ,   __UpperCAmelCase      :    int = 1      ,   __UpperCAmelCase      :    int = 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(__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.
												__magic_name__:	List[str]							=       seed
												__magic_name__:	int							=       seed

												while True:
																		# At each iteration, the tortoise moves one step and the hare moves two.
																		__magic_name__:	List[Any]							=       rand_fn(__UpperCAmelCase      ,   __UpperCAmelCase      ,   __UpperCAmelCase  )
																		__magic_name__:	Dict							=       rand_fn(__UpperCAmelCase      ,   __UpperCAmelCase      ,   __UpperCAmelCase  )
																		__magic_name__:	Tuple							=       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``.
																		__magic_name__:	Tuple							=       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.
												__magic_name__:	Dict							=       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}''')











"""simple docstring"""





import json
import os
import unittest

from transformers import OpenAIGPTTokenizer, OpenAIGPTTokenizerFast
from transformers.models.openai.tokenization_openai import VOCAB_FILES_NAMES
from transformers.testing_utils import require_ftfy, require_spacy, require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin



@require_tokenizers
class       __A		(   SCREAMING_SNAKE_CASE_     ,unittest.TestCase			):
					UpperCAmelCase__								=				OpenAIGPTTokenizer
					UpperCAmelCase__								=				OpenAIGPTTokenizerFast
					UpperCAmelCase__								=				True
					UpperCAmelCase__								=				False

					def   lowerCamelCase__   (			self  :      Dict					)			->							Optional[Any]:
											super().setUp()

											# Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
											__magic_name__:	str							=       [
											    """l""",
											    """o""",
											    """w""",
											    """e""",
											    """r""",
											    """s""",
											    """t""",
											    """i""",
											    """d""",
											    """n""",
											    """w</w>""",
											    """r</w>""",
											    """t</w>""",
											    """lo""",
											    """low""",
											    """er</w>""",
											    """low</w>""",
											    """lowest</w>""",
											    """newer</w>""",
											    """wider</w>""",
											    """<unk>""",
											]
											__magic_name__:	Any							=       dict(zip(__snake_case     ,		range(len(__snake_case					)					)					)					)
											__magic_name__:	List[str]							=       ["""#version: 0.2""", """l o""", """lo w""", """e r</w>""", """"""]

											__magic_name__:	Optional[Any]							=       os.path.join(self.tmpdirname     ,		VOCAB_FILES_NAMES["""vocab_file"""]					)
											__magic_name__:	Any							=       os.path.join(self.tmpdirname     ,		VOCAB_FILES_NAMES["""merges_file"""]					)
											with open(self.vocab_file     ,		"""w"""					) as fp:
																	fp.write(json.dumps(__snake_case					)					)
											with open(self.merges_file     ,		"""w"""					) as fp:
																	fp.write("""\n""".join(__snake_case					)					)

					def   lowerCamelCase__   (			self  :      List[Any]     ,		__snake_case  :      Optional[Any]					)			->							Optional[int]:
											return "lower newer", "lower newer"

					def   lowerCamelCase__   (			self  :      List[Any]					)			->							Union[str, Any]:
											__magic_name__:	Optional[Any]							=       OpenAIGPTTokenizer(self.vocab_file     ,		self.merges_file					)

											__magic_name__:	Union[str, Any]							=       """lower"""
											__magic_name__:	Optional[int]							=       ["""low""", """er</w>"""]
											__magic_name__:	List[Any]							=       tokenizer.tokenize(__snake_case					)
											self.assertListEqual(__snake_case     ,		__snake_case					)

											__magic_name__:	Optional[int]							=       tokens + ["""<unk>"""]
											__magic_name__:	List[str]							=       [1_4, 1_5, 2_0]
											self.assertListEqual(tokenizer.convert_tokens_to_ids(__snake_case					)     ,		__snake_case					)

					def   lowerCamelCase__   (			self  :      Optional[Any]     ,		__snake_case  :      Any=1_5					)			->							Tuple:
											for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
																	with self.subTest(F'{tokenizer.__class__.__name__} ({pretrained_name})'					):
																							__magic_name__:	str							=       self.rust_tokenizer_class.from_pretrained(__snake_case     ,		**__snake_case					)

																							# Simple input
																							__magic_name__:	Dict							=       """This is a simple input"""
																							__magic_name__:	Any							=       ["""This is a simple input 1""", """This is a simple input 2"""]
																							__magic_name__:	int							=       ("""This is a simple input""", """This is a pair""")
																							__magic_name__:	int							=       [
																							    ("""This is a simple input 1""", """This is a simple input 2"""),
																							    ("""This is a simple pair 1""", """This is a simple pair 2"""),
																							]

																							# Simple input tests
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Simple input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Simple input
																							self.assertRaises(
																							    __snake_case     ,		tokenizer_r.batch_encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""     ,		)

																							# Pair input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Pair input
																							self.assertRaises(__snake_case     ,		tokenizer_r.encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""					)

																							# Pair input
																							self.assertRaises(
																							    __snake_case     ,		tokenizer_r.batch_encode_plus     ,		__snake_case     ,		max_length=__snake_case     ,		padding="""max_length"""     ,		)






					def   lowerCamelCase__   (			self  :      Dict					)			->							Any:
											pass



@require_ftfy
@require_spacy
@require_tokenizers
class       __A		(   SCREAMING_SNAKE_CASE_			):
					pass



