



'''simple docstring'''
from math import isqrt






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						Optional[Any]												=  [True] * max_number
						for i in range(2    ,    isqrt(max_number - 1				) + 1				):
												if is_prime[i]:
																		for j in range(i**2    ,    UpperCAmelCase_    ,    UpperCAmelCase_				):
																								_UpperCamelCase   :						Any												=  False

						return [i for i in range(2    ,    UpperCAmelCase_				) if is_prime[i]]






def A__       (	UpperCAmelCase_ = 1_0**8				):
						_UpperCamelCase   :						Tuple												=  calculate_prime_numbers(max_number // 2				)

						_UpperCamelCase   :						Union[str, Any]												=  0
						_UpperCamelCase   :						List[Any]												=  0
						_UpperCamelCase   :						Optional[int]												=  len(UpperCAmelCase_				) - 1
						while left <= right:
												while prime_numbers[left] * prime_numbers[right] >= max_number:
																		right -= 1
												semiprimes_count += right - left + 1
												left += 1

						return semiprimes_count


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







'''simple docstring'''
from typing import List

import numpy as np






def A__       (	UpperCAmelCase_				):
						_UpperCamelCase   :						Any												=  {key: len(UpperCAmelCase_				) for key, value in gen_kwargs.items() if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)}
						if len(set(lists_lengths.values()				)				) > 1:
												raise RuntimeError(
												    (
												        'Sharding is ambiguous for this dataset: '
												        + 'we found several data sources lists of different lengths, and we don\'t know over which list we should parallelize:\n'
												        + '\n'.join(f'\t- key {key} has length {length}' for key, length in lists_lengths.items()				)
												        + '\nTo fix this, check the \'gen_kwargs\' and make sure to use lists only for data sources, '
												        + 'and use tuples otherwise. In the end there should only be one single list, or several lists with the same length.'
												    )				)
						_UpperCamelCase   :						Tuple												=  max(lists_lengths.values()    ,    default=0				)
						return max(1    ,    UpperCAmelCase_				)






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						Dict												=  []
						for group_idx in range(UpperCAmelCase_				):
												_UpperCamelCase   :						int												=  num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
												if num_shards_to_add == 0:
																		break
												_UpperCamelCase   :						Tuple												=  shards_indices_per_group[-1].stop if shards_indices_per_group else 0
												_UpperCamelCase   :						Tuple												=  range(UpperCAmelCase_    ,    start + num_shards_to_add				)
												shards_indices_per_group.append(UpperCAmelCase_				)
						return shards_indices_per_group






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						Tuple												=  _number_of_shards_in_gen_kwargs(UpperCAmelCase_				)
						if num_shards == 1:
												return [dict(UpperCAmelCase_				)]
						else:
												_UpperCamelCase   :						str												=  _distribute_shards(num_shards=UpperCAmelCase_    ,    max_num_jobs=UpperCAmelCase_				)
												return [
												    {
												        key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
												        if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)
												        else value
												        for key, value in gen_kwargs.items()
												    }
												    for group_idx in range(len(UpperCAmelCase_				)				)
												]






def A__       (	UpperCAmelCase_				):
						return {
						    key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
						    if isinstance(gen_kwargs_list[0][key]    ,    UpperCAmelCase_				)
						    else gen_kwargs_list[0][key]
						    for key in gen_kwargs_list[0]
						}






def A__       (	UpperCAmelCase_    ,    UpperCAmelCase_				):
						_UpperCamelCase   :						int												=  {len(UpperCAmelCase_				) for value in gen_kwargs.values() if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				)}
						_UpperCamelCase   :						Union[str, Any]												=  {}
						for size in list_sizes:
												_UpperCamelCase   :						str												=  list(range(UpperCAmelCase_				)				)
												rng.shuffle(indices_per_size[size]				)
						# Now let's copy the gen_kwargs and shuffle the lists based on their sizes
						_UpperCamelCase   :						Union[str, Any]												=  dict(UpperCAmelCase_				)
						for key, value in shuffled_kwargs.items():
												if isinstance(UpperCAmelCase_    ,    UpperCAmelCase_				):
																		_UpperCamelCase   :						Dict												=  [value[i] for i in indices_per_size[len(UpperCAmelCase_				)]]
						return shuffled_kwargs


