


"""simple docstring"""
from abc import ABC, abstractmethod
from typing import Optional, Union

from .. import Dataset, DatasetDict, Features, IterableDataset, IterableDatasetDict, NamedSplit
from ..utils.typing import NestedDataStructureLike, PathLike




class 	lowercase__				(					A_				):





   def __init__(							self      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = False      ,   SCREAMING_SNAKE_CASE = False      ,   SCREAMING_SNAKE_CASE = None      ,   **SCREAMING_SNAKE_CASE      ,   )  ->  str:
      _lowerCamelCase	:					str   =		path_or_paths
      _lowerCamelCase	:					Optional[Any]   =		split if split or isinstance(SCREAMING_SNAKE_CASE      ,   SCREAMING_SNAKE_CASE) else """train"""
      _lowerCamelCase	:					int   =		features
      _lowerCamelCase	:					Any   =		cache_dir
      _lowerCamelCase	:					Optional[Any]   =		keep_in_memory
      _lowerCamelCase	:					Optional[int]   =		streaming
      _lowerCamelCase	:					Union[str, Any]   =		num_proc
      _lowerCamelCase	:					Union[str, Any]   =		kwargs





   @abstractmethod
   def 		UpperCamelCase_  (							self)  ->  Union[Dataset, DatasetDict, IterableDataset, IterableDatasetDict]:
      pass







class 	lowercase__				(					A_				):





   def __init__(							self      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = None      ,   SCREAMING_SNAKE_CASE = False      ,   SCREAMING_SNAKE_CASE = False      ,   SCREAMING_SNAKE_CASE = None      ,   **SCREAMING_SNAKE_CASE      ,   )  ->  Tuple:
      _lowerCamelCase	:					Tuple   =		features
      _lowerCamelCase	:					Any   =		cache_dir
      _lowerCamelCase	:					int   =		keep_in_memory
      _lowerCamelCase	:					Dict   =		streaming
      _lowerCamelCase	:					List[str]   =		num_proc
      _lowerCamelCase	:					List[Any]   =		kwargs





   @abstractmethod
   def 		UpperCamelCase_  (							self)  ->  Union[Dataset, IterableDataset]:
      pass





"""simple docstring"""
from math import isqrt, loga

def 				_snake_case      (   __snake_case							:      int   ):




   """simple docstring"""







   _lowerCamelCase	:					List[str]   =		[True] * max_number
   for i in range(2						, isqrt(max_number - 1   ) + 1   ):
      if is_prime[i]:
         for j in range(i**2						, __snake_case						, __snake_case   ):
            _lowerCamelCase	:					Optional[int]   =		False

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

def 				_snake_case      (   __snake_case							:      int = 800800						, __snake_case							:      int = 800800   ):




   """simple docstring"""







   _lowerCamelCase	:					Union[str, Any]   =		degree * loga(__snake_case   )
   _lowerCamelCase	:					Union[str, Any]   =		int(__snake_case   )
   _lowerCamelCase	:					Dict   =		calculate_prime_numbers(__snake_case   )

   _lowerCamelCase	:					Optional[int]   =		0
   _lowerCamelCase	:					Any   =		0
   _lowerCamelCase	:					Any   =		len(__snake_case   ) - 1
   while left < right:
      while (
          prime_numbers[right] * loga(prime_numbers[left]   )
          + prime_numbers[left] * loga(prime_numbers[right]   )
          > upper_bound
      ):
         right -= 1
      hybrid_integers_count += right - left
      left += 1

   return hybrid_integers_count


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

