import math



def A__  (			lowercase:     int					)				->		list:
       A						:     Optional[Any]         =[True] * n
       A						:     Tuple         =False
       A						:     List[Any]         =False
       A						:     Dict         =True

       for i in range(3,		int(n**0.5 + 1					),		2					):
              A						:     Dict         =i * 2
              while index < n:
                     A						:     Dict         =False
                     A						:     Dict         =index + i

       A						:     Tuple         =[2]

       for i in range(3,		lowercase,		2					):
              if is_prime[i]:
                     primes.append(lowercase					)

       return primes



def A__  (			lowercase:     int = 999_966_663_333					)				->		int:
       A						:     Optional[int]         =math.floor(math.sqrt(lowercase					)					) + 100
       A						:     Optional[int]         =prime_sieve(lowercase					)

       A						:     Optional[Any]         =0
       A						:     List[Any]         =0
       A						:     Union[str, Any]         =primes[prime_index]

       while (last_prime**2) <= limit:
              A						:     Tuple         =primes[prime_index + 1]

              A						:     Optional[int]         =last_prime**2
              A						:     Tuple         =next_prime**2

              # Get numbers divisible by lps(current)
              A						:     int         =lower_bound + last_prime
              while upper_bound > current <= limit:
                     matches_sum += current
                     current += last_prime

              # Reset the upper_bound
              while (upper_bound - next_prime) > limit:
                     upper_bound -= next_prime

              # Add the numbers divisible by ups(current)
              A						:     List[Any]         =upper_bound - next_prime
              while current > lower_bound:
                     matches_sum += current
                     current -= next_prime

              # Remove the numbers divisible by both ups and lps
              A						:     Any         =0
              while upper_bound > current <= limit:
                     if current <= lower_bound:
                            # Increment the current number
                            current += last_prime * next_prime
                            continue

                     if current > limit:
                            break

                     # Remove twice since it was added by both ups and lps
                     matches_sum -= current * 2

                     # Increment the current number
                     current += last_prime * next_prime

              # Setup for next pair
              A						:     List[str]         =next_prime
              prime_index += 1

       return matches_sum


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







import collections
import importlib.util
import os
import re
from pathlib import Path


_lowercase							:      List[str]      							='''src/transformers'''


# Matches is_xxx_available()
_lowercase							:      Dict      							=re.compile(R'''is\_([a-z_]*)_available()''')
# Catches a one-line _import_struct = {xxx}
_lowercase							:      List[Any]      							=re.compile(R'''^_import_structure\s+=\s+\{([^\}]+)\}''')
# Catches a line with a key-values pattern: "bla": ["foo", "bar"]
_lowercase							:      Tuple      							=re.compile(R'''\s+"\S*":\s+\[([^\]]*)\]''')
# Catches a line if not is_foo_available
_lowercase							:      Dict      							=re.compile(R'''^\s*if\s+not\s+is\_[a-z_]*\_available\(\)''')
# Catches a line _import_struct["bla"].append("foo")
_lowercase							:      List[Any]      							=re.compile(R'''^\s*_import_structure\["\S*"\]\.append\("(\S*)"\)''')
# Catches a line _import_struct["bla"].extend(["foo", "bar"]) or _import_struct["bla"] = ["foo", "bar"]
_lowercase							:      str      							=re.compile(R'''^\s*_import_structure\[\S*\](?:\.extend\(|\s*=\s+)\[([^\]]*)\]''')
# Catches a line with an object between quotes and a comma:     "MyModel",
_lowercase							:      Optional[int]      							=re.compile('''^\s+"([^"]+)",''')
# Catches a line with objects between brackets only:    ["foo", "bar"],
_lowercase							:      Any      							=re.compile('''^\s+\[([^\]]+)\]''')
# Catches a line with from foo import bar, bla, boo
_lowercase							:      List[Any]      							=re.compile(R'''\s+from\s+\S*\s+import\s+([^\(\s].*)\n''')
# Catches a line with try:
_lowercase							:      Optional[Any]      							=re.compile(R'''^\s*try:''')
# Catches a line with else:
_lowercase							:      List[Any]      							=re.compile(R'''^\s*else:''')



def A__  (			lowercase:     Dict					)				->		int:
       if _re_test_backend.search(lowercase					) is None:
              return None
       A						:     Any         =[b[0] for b in _re_backend.findall(lowercase					)]
       backends.sort()
       return "_and_".join(lowercase					)



def A__  (			lowercase:     Any					)				->		List[Any]:
       with open(lowercase,		'r',		encoding='utf-8',		newline='\n'					) as f:
              A						:     Optional[Any]         =f.readlines()

       A						:     Dict         =0
       while line_index < len(lowercase					) and not lines[line_index].startswith('_import_structure = {'					):
              line_index += 1

       # If this is a traditional init, just return.
       if line_index >= len(lowercase					):
              return None

       # First grab the objects without a specific backend in _import_structure
       A						:     Optional[int]         =[]
       while not lines[line_index].startswith('if TYPE_CHECKING'					) and find_backend(lines[line_index]					) is None:
              A						:     int         =lines[line_index]
              # If we have everything on a single line, let's deal with it.
              if _re_one_line_import_struct.search(lowercase					):
                     A						:     int         =_re_one_line_import_struct.search(lowercase					).groups()[0]
                     A						:     int         =re.findall('\[([^\]]+)\]',		lowercase					)
                     for imp in imports:
                            objects.extend([obj[1:-1] for obj in imp.split(', '					)]					)
                     line_index += 1
                     continue
              A						:     Optional[int]         =_re_import_struct_key_value.search(lowercase					)
              if single_line_import_search is not None:
                     A						:     Dict         =[obj[1:-1] for obj in single_line_import_search.groups()[0].split(', '					) if len(lowercase					) > 0]
                     objects.extend(lowercase					)
              elif line.startswith(' ' * 8 + '"'					):
                     objects.append(line[9:-3]					)
              line_index += 1

       A						:     str         ={'none': objects}
       # Let's continue with backend-specific objects in _import_structure
       while not lines[line_index].startswith('if TYPE_CHECKING'					):
              # If the line is an if not is_backend_available, we grab all objects associated.
              A						:     Optional[int]         =find_backend(lines[line_index]					)
              # Check if the backend declaration is inside a try block:
              if _re_try.search(lines[line_index - 1]					) is None:
                     A						:     str         =None

              if backend is not None:
                     line_index += 1

                     # Scroll until we hit the else block of try-except-else
                     while _re_else.search(lines[line_index]					) is None:
                            line_index += 1

                     line_index += 1

                     A						:     List[str]         =[]
                     # Until we unindent, add backend objects to the list
                     while len(lines[line_index]					) <= 1 or lines[line_index].startswith(' ' * 4					):
                            A						:     Optional[Any]         =lines[line_index]
                            if _re_import_struct_add_one.search(lowercase					) is not None:
                                   objects.append(_re_import_struct_add_one.search(lowercase					).groups()[0]					)
                            elif _re_import_struct_add_many.search(lowercase					) is not None:
                                   A						:     Optional[Any]         =_re_import_struct_add_many.search(lowercase					).groups()[0].split(', '					)
                                   A						:     int         =[obj[1:-1] for obj in imports if len(lowercase					) > 0]
                                   objects.extend(lowercase					)
                            elif _re_between_brackets.search(lowercase					) is not None:
                                   A						:     Optional[int]         =_re_between_brackets.search(lowercase					).groups()[0].split(', '					)
                                   A						:     Optional[int]         =[obj[1:-1] for obj in imports if len(lowercase					) > 0]
                                   objects.extend(lowercase					)
                            elif _re_quote_object.search(lowercase					) is not None:
                                   objects.append(_re_quote_object.search(lowercase					).groups()[0]					)
                            elif line.startswith(' ' * 8 + '"'					):
                                   objects.append(line[9:-3]					)
                            elif line.startswith(' ' * 12 + '"'					):
                                   objects.append(line[13:-3]					)
                            line_index += 1

                     A						:     Optional[Any]         =objects
              else:
                     line_index += 1

    # At this stage we are in the TYPE_CHECKING part, first grab the objects without a specific backend
       A						:     Optional[Any]         =[]
       while (
           line_index < len(lowercase					)
           and find_backend(lines[line_index]					) is None
           and not lines[line_index].startswith('else'					)
       ):
              A						:     Any         =lines[line_index]
              A						:     Optional[int]         =_re_import.search(lowercase					)
              if single_line_import_search is not None:
                     objects.extend(single_line_import_search.groups()[0].split(', '					)					)
              elif line.startswith(' ' * 8					):
                     objects.append(line[8:-2]					)
              line_index += 1

       A						:     Optional[Any]         ={'none': objects}
       # Let's continue with backend-specific objects
       while line_index < len(lowercase					):
              # If the line is an if is_backend_available, we grab all objects associated.
              A						:     str         =find_backend(lines[line_index]					)
              # Check if the backend declaration is inside a try block:
              if _re_try.search(lines[line_index - 1]					) is None:
                     A						:     Optional[Any]         =None

              if backend is not None:
                     line_index += 1

                     # Scroll until we hit the else block of try-except-else
                     while _re_else.search(lines[line_index]					) is None:
                            line_index += 1

                     line_index += 1

                     A						:     List[str]         =[]
                     # Until we unindent, add backend objects to the list
                     while len(lines[line_index]					) <= 1 or lines[line_index].startswith(' ' * 8					):
                            A						:     Any         =lines[line_index]
                            A						:     Any         =_re_import.search(lowercase					)
                            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

                     A						:     Dict         =objects
              else:
                     line_index += 1

       return import_dict_objects, type_hint_objects



def A__  (			lowercase:     Any,		lowercase:     int					)				->		Dict:

       def find_duplicates(lowercase:     List[str]					):
              return [k for k, v in collections.Counter(lowercase					).items() if v > 1]

       if list(import_dict_objects.keys()					) != list(type_hint_objects.keys()					):
              return ["Both sides of the init do not have the same backends!"]

       A						:     List[Any]         =[]
       for key in import_dict_objects.keys():
              A						:     List[Any]         =find_duplicates(import_dict_objects[key]					)
              if duplicate_imports:
                     errors.append(F'Duplicate _import_structure definitions for: {duplicate_imports}'					)
              A						:     Tuple         =find_duplicates(type_hint_objects[key]					)
              if duplicate_type_hints:
                     errors.append(F'Duplicate TYPE_CHECKING objects for: {duplicate_type_hints}'					)

              if sorted(set(import_dict_objects[key]					)					) != sorted(set(type_hint_objects[key]					)					):
                     A						:     Tuple         ='base imports' if key == 'none' else F'{key} backend'
                     errors.append(F'Differences for {name}:'					)
                     for a in type_hint_objects[key]:
                            if a not in import_dict_objects[key]:
                                   errors.append(F'  {a} in TYPE_HINT but not in _import_structure.'					)
                     for a in import_dict_objects[key]:
                            if a not in type_hint_objects[key]:
                                   errors.append(F'  {a} in _import_structure but not in TYPE_HINT.'					)
       return errors



def A__  (			)				->		List[str]:
       A						:     Dict         =[]
       for root, _, files in os.walk(lowercase					):
              if "__init__.py" in files:
                     A						:     Any         =os.path.join(lowercase,		'__init__.py'					)
                     A						:     Union[str, Any]         =parse_init(lowercase					)
                     if objects is not None:
                            A						:     str         =analyze_results(*lowercase					)
                            if len(lowercase					) > 0:
                                   A						:     Any         =F'Problem in {fname}, both halves do not define the same objects.\n{errors[0]}'
                                   failures.append('\n'.join(lowercase					)					)
       if len(lowercase					) > 0:
              raise ValueError('\n\n'.join(lowercase					)					)



def A__  (			)				->		int:
       A						:     List[str]         =[]
       for path, directories, files in os.walk(lowercase					):
              for folder in directories:
                     # Ignore private modules
                     if folder.startswith('_'					):
                            directories.remove(lowercase					)
                            continue
                     # Ignore leftovers from branches (empty folders apart from pycache)
                     if len(list((Path(lowercase					) / folder).glob('*.py'					)					)					) == 0:
                            continue
                     A						:     Any         =str((Path(lowercase					) / folder).relative_to(lowercase					)					)
                     A						:     List[str]         =short_path.replace(os.path.sep,		'.'					)
                     submodules.append(lowercase					)
              for fname in files:
                     if fname == "__init__.py":
                            continue
                     A						:     Optional[Any]         =str((Path(lowercase					) / fname).relative_to(lowercase					)					)
                     A						:     Dict         =short_path.replace('.py',		''					).replace(os.path.sep,		'.'					)
                     if len(submodule.split('.'					)					) == 1:
                            submodules.append(lowercase					)
       return submodules


_lowercase							:      Tuple      							=[
    '''convert_pytorch_checkpoint_to_tf2''',
    '''modeling_flax_pytorch_utils''',
]



def A__  (			)				->		Tuple:
       # This is to make sure the transformers module imported is the one in the repo.
       A						:     str         =importlib.util.spec_from_file_location(
           'transformers',		os.path.join(lowercase,		'__init__.py'					),		submodule_search_locations=[PATH_TO_TRANSFORMERS],		)
       A						:     Any         =spec.loader.load_module()

       A						:     Any         =[
           module
           for module in get_transformers_submodules()
           if module not in IGNORE_SUBMODULES and module not in transformers._import_structure.keys()
       ]
       if len(lowercase					) > 0:
              A						:     Dict         ='\n'.join(F'- {module}' for module in module_not_registered					)
              raise ValueError(
                  'The following submodules are not properly registered in the main init of Transformers:\n'
                  F'{list_of_modules}\n'
                  'Make sure they appear somewhere in the keys of `_import_structure` with an empty list as value.'					)


if __name__ == "__main__":
    check_all_inits()
    check_submodules()






