





import os
from typing import Optional

import fsspec
from fsspec.archive import AbstractArchiveFileSystem
from fsspec.utils import DEFAULT_BLOCK_SIZE
class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       Optional[Any]       =	""""""
		__a       :       str       =	(
		    None  # protocol passed in prefix to the url. ex: "gzip", for gzip://file.txt::http://foo.bar/file.txt.gz
		)
		__a       :       str       =	None  # compression type in fsspec. ex: "gzip"
		__a       :       str       =	None  # extension of the filename to strip. ex: "".gz" to get file.txt from file.txt.gz






		def __init__(							self,   snake_case__ = "",   snake_case__ = None,   snake_case__ = None,   **snake_case__  )       -> Dict:






									"""simple docstring"""
									super().__init__(self,   **snake_case__  )
									# always open as "rb" since fsspec can then use the TextIOWrapper to make it work for "r" mode
									lowercase_	:   Union[str, Any]  				=     fsspec.open(
									    snake_case__,   mode="""rb""",   protocol=snake_case__,   compression=self.compression,   client_kwargs={
									        """requote_redirect_url""": False,  # see https://github.com/huggingface/datasets/pull/5459
									        """trust_env""": True,  # Enable reading proxy env variables.
									        **(target_options or {}).pop("""client_kwargs""",   {}  ),  # To avoid issues if it was already passed.
									    },   **(target_options or {}),   )
									lowercase_	:   Tuple  				=     os.path.basename(self.file.path.split("""::"""  )[0]  )
									lowercase_	:   Optional[int]  				=     (
									    self.compressed_name[: self.compressed_name.rindex("""."""  )]
									    if """.""" in self.compressed_name
									    else self.compressed_name
									)
									lowercase_	:   str  				=     None






		@classmethod
		def 						snake_case__				(							cls,   snake_case__  )       -> str:






									"""simple docstring"""
									# compressed file paths are always relative to the archive root
									return super()._strip_protocol(snake_case__  ).lstrip("""/"""  )






		def 						snake_case__				(							self  )       -> str:






									"""simple docstring"""
									if self.dir_cache is None:
																lowercase_	:   Optional[Any]  				=     {**self.file.fs.info(self.file.path  ), """name""": self.uncompressed_name}
																lowercase_	:   Any  				=     {f["""name"""]: f}






		def 						snake_case__				(							self,   snake_case__  )       -> Union[str, Any]:






									"""simple docstring"""
									return self.file.open().read()






		def 						snake_case__				(							self,   snake_case__,   snake_case__ = "rb",   snake_case__=None,   snake_case__=True,   snake_case__=None,   **snake_case__,   )       -> Optional[Any]:






									"""simple docstring"""
									lowercase_	:   Optional[Any]  				=     self._strip_protocol(snake_case__  )
									if mode != "rb":
																raise ValueError(f"""Tried to read with mode {mode} on file {self.file.path} opened with mode 'rb'"""  )
									return self.file.open()




class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       Tuple       =	"""bz2"""
		__a       :       List[Any]       =	"""bz2"""
		__a       :       Any       =	""".bz2"""




class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       Optional[int]       =	"""gzip"""
		__a       :       Optional[int]       =	"""gzip"""
		__a       :       Tuple       =	""".gz"""




class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       Optional[int]       =	"""lz4"""
		__a       :       Tuple       =	"""lz4"""
		__a       :       Optional[int]       =	""".lz4"""




class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       int       =	"""xz"""
		__a       :       Optional[int]       =	"""xz"""
		__a       :       Union[str, Any]       =	""".xz"""




class     UpperCamelCase__					(     lowerCamelCase__				):






		'''simple docstring'''






		__a       :       Optional[Any]       =	"""zstd"""
		__a       :       Tuple       =	"""zstd"""
		__a       :       Union[str, Any]       =	""".zst"""






		def __init__(							self,   snake_case__,   snake_case__ = "rb",   snake_case__ = None,   snake_case__ = None,   snake_case__ = DEFAULT_BLOCK_SIZE,   **snake_case__,   )       -> List[str]:






									"""simple docstring"""
									super().__init__(
									    fo=snake_case__,   mode=snake_case__,   target_protocol=snake_case__,   target_options=snake_case__,   block_size=snake_case__,   **snake_case__,   )
									# We need to wrap the zstd decompressor to avoid this error in fsspec==2021.7.0 and zstandard==0.15.2:
									#
									# File "/Users/user/.virtualenvs/hf-datasets/lib/python3.7/site-packages/fsspec/core.py", line 145, in open
									#     out.close = close
									# AttributeError: 'zstd.ZstdDecompressionReader' object attribute 'close' is read-only
									#
									# see https://github.com/intake/filesystem_spec/issues/725
									lowercase_	:   Optional[int]  				=     self.file.__enter__
									class     UpperCamelCase__					:






											'''simple docstring'''






											def __init__(							self,   snake_case__  )       -> str:






																		"""simple docstring"""
																		lowercase_	:   Optional[Any]  				=     file_






											def __enter__(							self  )       -> Any:






																		"""simple docstring"""
																		self._file.__enter__()
																		return self






											def __exit__(							self,   *snake_case__,   **snake_case__  )       -> Optional[Any]:






																		"""simple docstring"""
																		self._file.__exit__(*snake_case__,   **snake_case__  )






											def __iter__(							self  )       -> int:






																		"""simple docstring"""
																		return iter(self._file  )






											def 						snake_case__				(							self  )       -> str:






																		"""simple docstring"""
																		return next(self._file  )






											def __getattr__(							self,   snake_case__  )       -> List[str]:






																		"""simple docstring"""
																		return getattr(self._file,   snake_case__  )

									def fixed_enter(*snake_case__,   **snake_case__  ):
																return WrappedFile(_enter(*snake_case__,   **snake_case__  )  )

									lowercase_	:   List[str]  				=     fixed_enter






from __future__ import annotations

from math import gcd





def  __magic_name__  (				lowercase				,       lowercase = 2				,       lowercase = 1				,       lowercase = 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(lowercase				,       lowercase				,       lowercase				) -> int:
														return (pow(lowercase				,       2				) + step) % modulus

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

														while True:
																					# At each iteration, the tortoise moves one step and the hare moves two.
																					lowercase_	:   List[str]  				=     rand_fn(lowercase				,       lowercase				,       lowercase				)
																					lowercase_	:   str  				=     rand_fn(lowercase				,       lowercase				,       lowercase				)
																					lowercase_	:   Any  				=     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``.
																					lowercase_	:   Tuple  				=     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.
														lowercase_	:   int  				=     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_							=				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_							=				parser.parse_args()

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