"""simple docstring"""




import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

_a   :	Optional[int] 					=     'python tqdm regex requests packaging filelock numpy tokenizers'.split()
if sys.version_info < (3, 7):
     pkgs_to_check_at_runtime.append('dataclasses')
if sys.version_info < (3, 8):
     pkgs_to_check_at_runtime.append('importlib_metadata')

for pkg in pkgs_to_check_at_runtime:
     if pkg in deps:
          if pkg == "tokenizers":
               # must be loaded here, or else tqdm check may fail
               from .utils import is_tokenizers_available

               if not is_tokenizers_available():
                    continue  # not required, check version only if installed

          require_version_core(deps[pkg])
     else:
          raise ValueError(F"""can't find {pkg} in {deps.keys()}, check dependency_versions_table.py""")





def 							SCREAMING_SNAKE_CASE  (    _lowerCamelCase		: Optional[Any]    ,_lowerCamelCase		: Optional[int]=None			) ->   str:
  require_version(deps[pkg]    ,_lowerCamelCase			)





"""simple docstring"""




def 							SCREAMING_SNAKE_CASE  (    _lowerCamelCase		: int = 1000000			) ->   int:
  _lowerCAmelCase		: List[str]						    =  [i - 1 for i in range(limit + 1			)]

  for i in range(2    ,limit + 1			):
    if phi[i] == i - 1:
      for j in range(2 * i    ,limit + 1    ,_lowerCamelCase			):
        phi[j] -= phi[j] // i

  return sum(phi[2 : limit + 1]			)


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




