






'''simple docstring'''







import argparse
import os
import re


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_dummies.py
a__  : Any				=	"src/transformers"

# Matches is_xxx_available()
a__  : Optional[Any]				=	re.compile(R'is\_([a-z_]*)_available()')
# Matches from xxx import bla
a__  : Tuple				=	re.compile(R'\s+from\s+\S*\s+import\s+([^\(\s].*)\n')
a__  : Tuple				=	re.compile(R'^\s+if\s+not\s+\(?is\_[a-z_]*\_available\(\)')


a__  : Optional[int]				=	"\n{0} = None\n"

a__  : Optional[Any]				=	"\nclass {0}(metaclass=DummyObject):\n    _backends = {1}\n\n    def __init__(self, *args, **kwargs):\n        requires_backends(self, {1})\n"


a__  : Any				=	"\ndef {0}(*args, **kwargs):\n    requires_backends({0}, {1})\n"







def _UpperCamelCase	(					__A   )							->		int:


      '''simple docstring'''



      if _re_test_backend.search(UpperCamelCase_   ) is None:
            return None
      UpperCamelCase__  =    [b[0] for b in _re_backend.findall(UpperCamelCase_   )]
      backends.sort()
      return "_and_".join(UpperCamelCase_   )







def _UpperCamelCase	(					)							->		Any:


      '''simple docstring'''



      with open(os.path.join(UpperCamelCase_				,      "__init__.py"   )				,      "r"				,      encoding="utf-8"				,      newline="\n"   ) as f:
            UpperCamelCase__  =    f.readlines()

      # Get to the point we do the actual imports for type checking
      UpperCamelCase__  =    0
      while not lines[line_index].startswith("if TYPE_CHECKING"   ):
            line_index += 1

      UpperCamelCase__  =    {}
      # Go through the end of the file
      while line_index < len(UpperCamelCase_   ):
            # If the line is an if is_backend_available, we grab all objects associated.
            UpperCamelCase__  =    find_backend(lines[line_index]   )
            if backend is not None:
                  while not lines[line_index].startswith("    else:"   ):
                        line_index += 1
                  line_index += 1

                  UpperCamelCase__  =    []
                  # Until we unindent, add backend objects to the list
                  while len(lines[line_index]   ) <= 1 or lines[line_index].startswith(" " * 8   ):
                        UpperCamelCase__  =    lines[line_index]
                        UpperCamelCase__  =    _re_single_line_import.search(UpperCamelCase_   )
                        if single_line_import_search is not None:
                              objects.extend(single_line_import_search.groups()[0].split(", "   )   )
                        elif line.startswith(" " * 12   ):
                              objects.append(line[12:-2]   )
                        line_index += 1

                  UpperCamelCase__  =    objects
            else:
                  line_index += 1

      return backend_specific_objects







def _UpperCamelCase	(					__A				,      __A   )							->		Optional[int]:


      '''simple docstring'''



      if name.isupper():
            return DUMMY_CONSTANT.format(UpperCamelCase_   )
      elif name.islower():
            return DUMMY_FUNCTION.format(UpperCamelCase_				,      UpperCamelCase_   )
      else:
            return DUMMY_CLASS.format(UpperCamelCase_				,      UpperCamelCase_   )







def _UpperCamelCase	(					__A=None   )							->		List[str]:


      '''simple docstring'''



      if backend_specific_objects is None:
            UpperCamelCase__  =    read_init()
      # For special correspondence backend to module name as used in the function requires_modulename
      UpperCamelCase__  =    {}

      for backend, objects in backend_specific_objects.items():
            UpperCamelCase__  =    "[" + ", ".join(F'''\"{b}\"''' for b in backend.split("_and_"   )   ) + "]"
            UpperCamelCase__  =    "# This file is autogenerated by the command `make fix-copies`, do not edit.\n"
            dummy_file += "from ..utils import DummyObject, requires_backends\n\n"
            dummy_file += "\n".join([create_dummy_object(UpperCamelCase_				,      UpperCamelCase_   ) for o in objects]   )
            UpperCamelCase__  =    dummy_file

      return dummy_files







def _UpperCamelCase	(					__A=False   )							->		Union[str, Any]:


      '''simple docstring'''



      UpperCamelCase__  =    create_dummy_files()
      # For special correspondence backend to shortcut as used in utils/dummy_xxx_objects.py
      UpperCamelCase__  =    {"torch": "pt"}

      # Locate actual dummy modules and read their content.
      UpperCamelCase__  =    os.path.join(UpperCamelCase_				,      "utils"   )
      UpperCamelCase__  =    {
          backend: os.path.join(UpperCamelCase_				,      F'''dummy_{short_names.get(UpperCamelCase_				,      UpperCamelCase_   )}_objects.py'''   )
          for backend in dummy_files.keys()
      }

      UpperCamelCase__  =    {}
      for backend, file_path in dummy_file_paths.items():
            if os.path.isfile(UpperCamelCase_   ):
                  with open(UpperCamelCase_				,      "r"				,      encoding="utf-8"				,      newline="\n"   ) as f:
                        UpperCamelCase__  =    f.read()
            else:
                  UpperCamelCase__  =    ""

      for backend in dummy_files.keys():
            if dummy_files[backend] != actual_dummies[backend]:
                  if overwrite:
                        print(
                            F'''Updating transformers.utils.dummy_{short_names.get(UpperCamelCase_				,      UpperCamelCase_   )}_objects.py as the main '''
                            "__init__ has new objects."   )
                        with open(dummy_file_paths[backend]				,      "w"				,      encoding="utf-8"				,      newline="\n"   ) as f:
                              f.write(dummy_files[backend]   )
                  else:
                        raise ValueError(
                            "The main __init__ has objects that are not present in "
                            F'''transformers.utils.dummy_{short_names.get(UpperCamelCase_				,      UpperCamelCase_   )}_objects.py. Run `make fix-copies` '''
                            "to fix this."   )


if __name__ == "__main__":
  a__  : Union[str, Any]				=	argparse.ArgumentParser()
  parser.add_argument('--fix_and_overwrite', action='store_true', help='Whether to fix inconsistencies.')
  a__  : str				=	parser.parse_args()

  check_dummies(args.fix_and_overwrite)









'''simple docstring'''







import math







def _UpperCamelCase	(					__A   )							->		bool:


      '''simple docstring'''



      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5				,      int(math.sqrt(__A   ) + 1   )				,      6   ):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True







def _UpperCamelCase	(					__A = 1000				,      __A = 1000   )							->		int:


      '''simple docstring'''



      UpperCamelCase__  =    [0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1				,      __A   ):
            for b in range(2				,      __A   ):
                  if is_prime(__A   ):
                        UpperCamelCase__  =    0
                        UpperCamelCase__  =    0
                        while is_prime((n**2) + (a * n) + b   ):
                              count += 1
                              n += 1
                        if count > longest[0]:
                              UpperCamelCase__  =    [count, a, b]
      UpperCamelCase__  =    longest[1] * longest[2]
      return ans


if __name__ == "__main__":
  print(solution(1_0_0_0, 1_0_0_0))





