





from __future__ import annotations



def        __lowercase       (				_SCREAMING_SNAKE_CASE     )			->       list[int]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						[True] * limit
      SCREAMING_SNAKE_CASE		=						False
      SCREAMING_SNAKE_CASE		=						False
      SCREAMING_SNAKE_CASE		=						True

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

      SCREAMING_SNAKE_CASE		=						[2]

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

      return primes



def        __lowercase       (				_SCREAMING_SNAKE_CASE = 1_00_00_00     )			->       int:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						prime_sieve(_SCREAMING_SNAKE_CASE     )
      SCREAMING_SNAKE_CASE		=						0
      SCREAMING_SNAKE_CASE		=						0

      for i in range(len(_SCREAMING_SNAKE_CASE     )     ):
            for j in range(i + length			,						len(_SCREAMING_SNAKE_CASE     )     ):
                  SCREAMING_SNAKE_CASE		=						sum(primes[i:j]     )
                  if sol >= ceiling:
                        break

                  if sol in primes:
                        SCREAMING_SNAKE_CASE		=						j - i
                        SCREAMING_SNAKE_CASE		=						sol

      return largest


if __name__ == "__main__":
      print(F'''{solution() = }''')









from typing import List, Optional, TypeVar

from .arrow_dataset import Dataset, _concatenate_map_style_datasets, _interleave_map_style_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .info import DatasetInfo
from .iterable_dataset import IterableDataset, _concatenate_iterable_datasets, _interleave_iterable_datasets
from .splits import NamedSplit
from .utils import logging
from .utils.py_utils import Literal


SCREAMING_SNAKE_CASE_						       =	logging.get_logger(__name__)


SCREAMING_SNAKE_CASE_						       =	TypeVar("""DatasetType""", Dataset, IterableDataset)



def        __lowercase       (				_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = "first_exhausted"			,						)			->       DatasetType:


      '''simple docstring'''


      from .arrow_dataset import Dataset
      from .iterable_dataset import IterableDataset

      if not datasets:
            raise ValueError("""Unable to interleave an empty list of datasets."""     )
      for i, dataset in enumerate(_SCREAMING_SNAKE_CASE     ):
            if not isinstance(_SCREAMING_SNAKE_CASE			,						(Dataset, IterableDataset)     ):
                  if isinstance(_SCREAMING_SNAKE_CASE			,						(DatasetDict, IterableDatasetDict)     ):
                        if not dataset:
                              raise ValueError(
                                  F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                                  """is an empty dataset dictionary."""     )
                        raise ValueError(
                            F"""Dataset at position {i} has at least one split: {list(_SCREAMING_SNAKE_CASE     )}\n"""
                            F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(_SCREAMING_SNAKE_CASE     )     )}']"""     )
                  raise ValueError(
                      F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(_SCREAMING_SNAKE_CASE     ).__name__}."""     )
            if i == 0:
                  SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						(
                      (Dataset, IterableDataset) if isinstance(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     ) else (IterableDataset, Dataset)
                  )
            elif not isinstance(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     ):
                  raise ValueError(
                      F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""     )
      if stopping_strategy not in ["first_exhausted", "all_exhausted"]:
            raise ValueError(F"""{stopping_strategy} is not supported. Please enter a valid stopping_strategy."""     )
      if dataset_type is Dataset:
            return _interleave_map_style_datasets(
                _SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						info=_SCREAMING_SNAKE_CASE			,						split=_SCREAMING_SNAKE_CASE			,						stopping_strategy=_SCREAMING_SNAKE_CASE     )
      else:
            return _interleave_iterable_datasets(
                _SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						info=_SCREAMING_SNAKE_CASE			,						split=_SCREAMING_SNAKE_CASE			,						stopping_strategy=_SCREAMING_SNAKE_CASE     )



def        __lowercase       (				_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = None			,						_SCREAMING_SNAKE_CASE = 0			,						)			->       DatasetType:


      '''simple docstring'''


      if not dsets:
            raise ValueError("""Unable to concatenate an empty list of datasets."""     )
      for i, dataset in enumerate(_SCREAMING_SNAKE_CASE     ):
            if not isinstance(_SCREAMING_SNAKE_CASE			,						(Dataset, IterableDataset)     ):
                  if isinstance(_SCREAMING_SNAKE_CASE			,						(DatasetDict, IterableDatasetDict)     ):
                        if not dataset:
                              raise ValueError(
                                  F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} """
                                  """is an empty dataset dictionary."""     )
                        raise ValueError(
                            F"""Dataset at position {i} has at least one split: {list(_SCREAMING_SNAKE_CASE     )}\n"""
                            F"""Please pick one to interleave with the other datasets, for example: dataset['{next(iter(_SCREAMING_SNAKE_CASE     )     )}']"""     )
                  raise ValueError(
                      F"""Expected a list of Dataset objects or a list of IterableDataset objects, but element at position {i} is a {type(_SCREAMING_SNAKE_CASE     ).__name__}."""     )
            if i == 0:
                  SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						(
                      (Dataset, IterableDataset) if isinstance(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     ) else (IterableDataset, Dataset)
                  )
            elif not isinstance(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     ):
                  raise ValueError(
                      F"""Unable to interleave a {dataset_type.__name__} (at position 0) with a {other_type.__name__} (at position {i}). Expected a list of Dataset objects or a list of IterableDataset objects."""     )
      if dataset_type is Dataset:
            return _concatenate_map_style_datasets(_SCREAMING_SNAKE_CASE			,						info=_SCREAMING_SNAKE_CASE			,						split=_SCREAMING_SNAKE_CASE			,						axis=_SCREAMING_SNAKE_CASE     )
      else:
            return _concatenate_iterable_datasets(_SCREAMING_SNAKE_CASE			,						info=_SCREAMING_SNAKE_CASE			,						split=_SCREAMING_SNAKE_CASE			,						axis=_SCREAMING_SNAKE_CASE     )


