code: import posixpath
  from pathlib import Path
  from unittest.mock import patch
  
  import pytest
  from fsspec.implementations.local import AbstractFileSystem, LocalFileSystem, stringify_path
  from fsspec.registry import _registry as _fsspec_registry
  
  class 				_lowercase						(    UpperCAmelCase__ ):
  
  
  
  
  
  
      '''simple docstring'''
      SCREAMING_SNAKE_CASE:							int        =						'mock'
  
  
  
  
      def __init__(						self					,	*lowerCamelCase__					,	lowerCamelCase__					,	**lowerCamelCase__   ):
         super().__init__()
         lowerCAmelCase_:       Tuple         =  LocalFileSystem(*lowerCamelCase__					,	**lowerCamelCase__   )
         lowerCAmelCase_:       Tuple         =  Path(lowerCamelCase__   ).resolve().as_posix() + "/"
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       Optional[int]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.mkdir(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.makedirs(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         lowerCAmelCase_:       str         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.rmdir(lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	lowerCamelCase__=True					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       Any         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         lowerCAmelCase_:       Dict         =  self._fs.ls(lowerCamelCase__					,	detail=lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
         if detail:
            return [{**info, "name": info["name"][len(self.local_root_dir   ) :]} for info in out]
         else:
            return [name[len(self.local_root_dir   ) :] for name in out]
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       Optional[int]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         lowerCAmelCase_:       Dict         =  dict(self._fs.info(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )   )
         lowerCAmelCase_:       Any         =  out["name"][len(self.local_root_dir   ) :]
         return out
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       Optional[int]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         lowerCAmelCase_:       Optional[Any]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.cp_file(lowerCamelCase__					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.rm_file(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       Union[str, Any]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.rm(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         lowerCAmelCase_:       List[str]         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs._open(lowerCamelCase__					,	*lowerCamelCase__					,	**lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         lowerCAmelCase_:       Dict         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.created(lowerCamelCase__   )
  
  
  
  
      def     _a						(						self					,	lowerCamelCase__   ):
         lowerCAmelCase_:       Tuple         =  posixpath.join(self.local_root_dir					,	self._strip_protocol(lowerCamelCase__   )   )
         return self._fs.modified(lowerCamelCase__   )
  
  
  
  
      @classmethod
      def     _a						(						cls					,	lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  stringify_path(lowerCamelCase__   )
         if path.startswith("mock://"   ):
            lowerCAmelCase_:       int         =  path[7:]
         return path
  
  
  
  
  
  class 				_lowercase						(    UpperCAmelCase__ ):
  
  
  
  
  
  
      '''simple docstring'''
      SCREAMING_SNAKE_CASE:							int        =						'tmp'
      SCREAMING_SNAKE_CASE:							Dict        =						None
  
  
  
  
      def __init__(						self					,	*lowerCamelCase__					,	**lowerCamelCase__   ):
         assert self.tmp_dir is not None, "TmpDirFileSystem.tmp_dir is not set"
         super().__init__(*lowerCamelCase__					,	**lowerCamelCase__					,	local_root_dir=self.tmp_dir					,	auto_mkdir=lowerCamelCase__   )
  
  
  
  
      @classmethod
      def     _a						(						cls					,	lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  stringify_path(lowerCamelCase__   )
         if path.startswith("tmp://"   ):
            lowerCAmelCase_:       Union[str, Any]         =  path[6:]
         return path
  
  
  
  
  
  @pytest.fixture
  def 		snake_case__  (		):
     lowerCAmelCase_:       Optional[Any]         =  MockFileSystem
     lowerCAmelCase_:       Union[str, Any]         =  TmpDirFileSystem
     yield
     del _fsspec_registry["mock"]
     del _fsspec_registry["tmp"]
  @pytest.fixture
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       str         =  tmp_path_factory.mktemp("mockfs"				)
     return MockFileSystem(local_root_dir=lowercase       ,							auto_mkdir=lowercase				)
  
  
  
  
  
  
  
  @pytest.fixture
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       Union[str, Any]         =  tmp_path_factory.mktemp("tmpfs"				)
     with patch.object(lowercase       ,							"tmp_dir"       ,							lowercase				):
        yield TmpDirFileSystem()
  
  
  
  
style_context: import itertools
  def 		snake_case__  (		lowercase				):
     return (
         int("".join(combination[0:2]				)				) * int("".join(combination[2:5]				)				)
         == int("".join(combination[5:9]				)				)
     ) or (
         int("".join(combination[0]				)				) * int("".join(combination[1:5]				)				)
         == int("".join(combination[5:9]				)				)
     )
  def 		snake_case__  (		):
     return sum(
         {
             int("".join(pandigital[5:9]				)				)
             for pandigital in itertools.permutations("123456789"				)
             if is_combination_valid(lowercase				)
         }				)
  
  
  if __name__ == "__main__":
   print(solution())