





'''simple docstring'''






from __future__ import annotations

from fractions import Fraction







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase ) ->				bool:



			"""simple docstring"""


			return (
			    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
			)







def 					_a						(       _lowerCamelCase ) ->				list[str]:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     []
			__snake_case					:      Dict							      =     11
			__snake_case					:      List[Any]							      =     int("""1""" + """0""" * digit_len )
			for num in range(_lowerCamelCase    ,	_lowerCamelCase ):
						while den <= 99:
									if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
												if is_digit_cancelling(_lowerCamelCase    ,	_lowerCamelCase ):
															solutions.append(F'''{num}/{den}''' )
									den += 1
						num += 1
						__snake_case					:      str							      =     10
			return solutions







def 					_a						(       _lowerCamelCase = 2 ) ->				int:



			"""simple docstring"""


			__snake_case					:      List[Any]							      =     1.0
			for fraction in fraction_list(_lowerCamelCase ):
						__snake_case					:      List[Any]							      =     Fraction(_lowerCamelCase )
						result *= frac.denominator / frac.numerator
			return int(_lowerCamelCase )


if __name__ == "__main__":
	print(solution())










import importlib
import shutil
import threading
import warnings
from typing import List

import fsspec
import fsspec.asyn

from . import compression
from .hffilesystem import HfFileSystem


A__      :     int       =					importlib.util.find_spec('s3fs') is not None

if _has_safs:
							from .safilesystem import SaFileSystem  # noqa: F401

A__      :     List[compression.BaseCompressedFileFileSystem]       =					[
    compression.BzaFileSystem,
    compression.GzipFileSystem,
    compression.LzaFileSystem,
    compression.XzFileSystem,
    compression.ZstdFileSystem,
]

# Register custom filesystems
for fs_class in COMPRESSION_FILESYSTEMS + [HfFileSystem]:
							if fs_class.protocol in fsspec.registry and fsspec.registry[fs_class.protocol] is not fs_class:
														warnings.warn(F"A filesystem protocol was already set for {fs_class.protocol} and will be overwritten.")
							fsspec.register_implementation(fs_class.protocol, fs_class, clobber=True)






def     a     (		lowerCamelCase_							):






				'''simple docstring'''
				if "://" in dataset_path:
								lowercase__  					=     dataset_path.split('''://'''							)[1]
				return dataset_path






def     a     (		lowerCamelCase_							):






				'''simple docstring'''
				if fs is not None and fs.protocol != "file":
								return True
				else:
								return False






def     a     (		lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				lowercase__  					=     not is_remote_filesystem(lowerCamelCase_							)
				if is_local:
								# LocalFileSystem.mv does copy + rm, it is more efficient to simply move a local directory
								shutil.move(fs._strip_protocol(lowerCamelCase_							)						,  fs._strip_protocol(lowerCamelCase_							)							)
				else:
								fs.mv(lowerCamelCase_						,  lowerCamelCase_						,  recursive=lowerCamelCase_							)






def     a     (		):






				'''simple docstring'''
				if hasattr(fsspec.asyn						,  '''reset_lock'''							):
								# for future fsspec>2022.05.0
								fsspec.asyn.reset_lock()
				else:
								lowercase__  					=     None
								lowercase__  					=     None
								lowercase__  					=     threading.Lock()




