






from __future__ import annotations

from math import gcd
def      a_ (      _A      ,   _A = 2      ,   _A = 1      ,   _A = 3      ,   )			->			str:







						"""simple docstring"""
						# 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(_A      ,   _A      ,   _A  ) -> int:
												return (pow(lowercase__      ,   2  ) + step) % modulus

						for _ in range(lowercase__  ):
												# 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(lowercase__      ,   lowercase__      ,   lowercase__  )
																		snake_case__									=     rand_fn(lowercase__      ,   lowercase__      ,   lowercase__  )
																		snake_case__									=     rand_fn(lowercase__      ,   lowercase__      ,   lowercase__  )

																		# 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      ,   lowercase__  )

																		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

							__UpperCamelCase					:		Optional[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""",
							)
							__UpperCamelCase					:		List[str]	  =						parser.parse_args()

							__UpperCamelCase					:		Tuple	  =						pollard_rho(args.num, attempts=args.attempts)
							if divisor is None:
														print(f'''{args.num} is probably prime''')
							else:
														__UpperCamelCase					:		int	  =						args.num // divisor
														print(f'''{args.num} = {divisor} * {quotient}''')












import doctest
import logging
import os
import unittest
from pathlib import Path
from typing import List, Union

import transformers
from transformers.testing_utils import require_tf, require_torch, slow


__UpperCamelCase					:		Optional[Any]	  =						logging.getLogger()


@unittest.skip("Temporarily disable the doc tests."	)
@require_torch
@require_tf
@slow
class   __SCREAMING_SNAKE_CASE(	unittest.TestCase	):
							def lowerCAmelCase_ (     self:      Dict       ,	UpperCamelCase:      Path       ,	UpperCamelCase:      Union[str, None] = None       ,	UpperCamelCase:      Union[List[str], None] = None       ,	UpperCamelCase:      Union[str, List[str], None] = None       ,	UpperCamelCase:      bool = True       ,	)		->		int:
											snake_case__									=     [file for file in os.listdir(UpperCamelCase						) if os.path.isfile(os.path.join(UpperCamelCase       ,	UpperCamelCase						)						)]

											if identifier is not None:
															snake_case__									=     [file for file in files if identifier in file]

											if n_identifier is not None:
															if isinstance(UpperCamelCase       ,	UpperCamelCase						):
																			for n_ in n_identifier:
																							snake_case__									=     [file for file in files if n_ not in file]
															else:
																			snake_case__									=     [file for file in files if n_identifier not in file]

											snake_case__									=     ignore_files or []
											ignore_files.append('__init__.py'						)
											snake_case__									=     [file for file in files if file not in ignore_files]

											for file in files:
															# Open all files
															print('Testing'       ,	UpperCamelCase						)

															if only_modules:
																			snake_case__									=     file.split('.'						)[0]
																			try:
																							snake_case__									=     getattr(UpperCamelCase       ,	UpperCamelCase						)
																							snake_case__									=     doctest.DocTestSuite(UpperCamelCase						)
																							snake_case__									=     unittest.TextTestRunner().run(UpperCamelCase						)
																							self.assertIs(len(result.failures						)       ,	0						)
																			except AttributeError:
																							logger.info(F'''{module_identifier} is not a module.'''						)
															else:
																			snake_case__									=     doctest.testfile(str('..' / directory / file						)       ,	optionflags=doctest.ELLIPSIS						)
																			self.assertIs(result.failed       ,	0						)
							def lowerCAmelCase_ (     self:      Tuple						)		->		int:
											snake_case__									=     Path('src/transformers'						)
											snake_case__									=     'modeling'
											snake_case__									=     [
											    'modeling_ctrl.py',
											    'modeling_tf_ctrl.py',
											]
											self.analyze_directory(UpperCamelCase       ,	identifier=UpperCamelCase       ,	ignore_files=UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Optional[int]						)		->		str:
											snake_case__									=     Path('src/transformers'						)
											snake_case__									=     'tokenization'
											self.analyze_directory(UpperCamelCase       ,	identifier=UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Optional[Any]						)		->		int:
											snake_case__									=     Path('src/transformers'						)
											snake_case__									=     'configuration'
											self.analyze_directory(UpperCamelCase       ,	identifier=UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Dict						)		->		List[Any]:
											snake_case__									=     Path('src/transformers'						)
											snake_case__									=     ['configuration', 'modeling', 'tokenization']
											self.analyze_directory(UpperCamelCase       ,	n_identifier=UpperCamelCase						)


							def lowerCAmelCase_ (     self:      Tuple						)		->		Union[str, Any]:
											snake_case__									=     Path('docs/source'						)
											snake_case__									=     ['favicon.ico']
											self.analyze_directory(UpperCamelCase       ,	ignore_files=UpperCamelCase       ,	only_modules=UpperCamelCase						)




