


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


__snake_case            =   logging.get_logger(__name__)


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






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		List[DatasetType]       ,  SCREAMING_SNAKE_CASE_   :		Optional[List[float]] = None       ,  SCREAMING_SNAKE_CASE_   :		Optional[int] = None       ,  SCREAMING_SNAKE_CASE_   :		Optional[DatasetInfo] = None       ,  SCREAMING_SNAKE_CASE_   :		Optional[NamedSplit] = None       ,  SCREAMING_SNAKE_CASE_   :		Literal["first_exhausted", "all_exhausted"] = "first_exhausted"       ,  ):





			"""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:
									UpperCamelCase  ,  UpperCamelCase         =					(
									    (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_   :		List[DatasetType]       ,  SCREAMING_SNAKE_CASE_   :		Optional[DatasetInfo] = None       ,  SCREAMING_SNAKE_CASE_   :		Optional[NamedSplit] = None       ,  SCREAMING_SNAKE_CASE_   :		int = 0       ,  ):





			"""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:
									UpperCamelCase  ,  UpperCamelCase         =					(
									    (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_	)








import math






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int	):





			"""simple docstring"""




			UpperCamelCase         =					[True] * n
			UpperCamelCase         =					False
			UpperCamelCase         =					False
			UpperCamelCase         =					True

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

			UpperCamelCase         =					[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_   :		int = 999_966_663_333	):





			"""simple docstring"""




			UpperCamelCase         =					math.floor(math.sqrt(SCREAMING_SNAKE_CASE_	)	) + 100
			UpperCamelCase         =					prime_sieve(SCREAMING_SNAKE_CASE_	)

			UpperCamelCase         =					0
			UpperCamelCase         =					0
			UpperCamelCase         =					primes[prime_index]

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

						UpperCamelCase         =					last_prime**2
						UpperCamelCase         =					next_prime**2

						# Get numbers divisible by lps(current)
						UpperCamelCase         =					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)
						UpperCamelCase         =					upper_bound - next_prime
						while current > lower_bound:
									matches_sum += current
									current -= next_prime

						# Remove the numbers divisible by both ups and lps
						UpperCamelCase         =					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
						UpperCamelCase         =					next_prime
						prime_index += 1

			return matches_sum


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




