





from math import isqrt, loga
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  list[int]:






   """simple docstring"""







   _UpperCAmelCase           =   [True] * max_number
   for i in range(2				,	isqrt(max_number - 1						) + 1						):
      if is_prime[i]:
         for j in range(i**2				,	SCREAMING_SNAKE_CASE_				,	SCREAMING_SNAKE_CASE_						):
            _UpperCAmelCase           =   False

   return [i for i in range(2				,	SCREAMING_SNAKE_CASE_						) if is_prime[i]]
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 80_08_00				,	SCREAMING_SNAKE_CASE_   :      int = 80_08_00						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   degree * loga(SCREAMING_SNAKE_CASE_						)
   _UpperCAmelCase           =   int(SCREAMING_SNAKE_CASE_						)
   _UpperCAmelCase           =   calculate_prime_numbers(SCREAMING_SNAKE_CASE_						)

   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   0
   _UpperCAmelCase           =   len(SCREAMING_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() = }''')




"""simple docstring"""







# Lint as: python3
import itertools
import os
import re


a_							=    re.compile(r"""([A-Z]+)([A-Z][a-z])""")
a_							=    re.compile(r"""([a-z\d])([A-Z])""")

a_							=    re.compile(r"""(?<!_)_(?!_)""")
a_							=    re.compile(r"""(_{2,})""")

a_							=    r"""^\w+(\.\w+)*$"""

a_							=    r"""<>:/\|?*"""

def     UpperCAmelCase_					(				__a   :			Optional[int]						):




			'''simple docstring'''



			_lowerCamelCase					:					str	       =    _uppercase_uppercase_re.sub(r'\1_\2'      ,							__a						)
			_lowerCamelCase					:					Tuple	       =    _lowercase_uppercase_re.sub(r'\1_\2'      ,							__a						)
			return name.lower()

def     UpperCAmelCase_					(				__a   :			Optional[int]						):




			'''simple docstring'''



			_lowerCamelCase					:					Dict	       =    _single_underscore_re.split(__a						)
			_lowerCamelCase					:					Tuple	       =    [_multiple_underscores_re.split(__a						) for n in name]
			return "".join(n.capitalize() for n in itertools.chain.from_iterable(__a						) if n != ''						)

def     UpperCAmelCase_					(				__a   :			List[Any]						):




			'''simple docstring'''



			if os.path.basename(__a						) != name:
						raise ValueError(f"Should be a dataset name, not a path: {name}"						)
			return camelcase_to_snakecase(__a						)

def     UpperCAmelCase_					(				__a   :			Union[str, Any]      ,							__a   :			Optional[int]						):




			'''simple docstring'''



			if os.path.basename(__a						) != name:
						raise ValueError(f"Should be a dataset name, not a path: {name}"						)
			if not re.match(_split_re      ,							__a						):
						raise ValueError(f"Split name should match '{_split_re}'' but got '{split}'."						)
			return f"{filename_prefix_for_name(__a						)}-{split}"

def     UpperCAmelCase_					(				__a   :			Any      ,							__a   :			Union[str, Any]      ,							__a   :			List[Any]      ,							__a   :			List[str]=None						):




			'''simple docstring'''



			_lowerCamelCase					:					List[Any]	       =    filename_prefix_for_split(__a      ,							__a						)
			if filetype_suffix:
						prefix += f".{filetype_suffix}"
			_lowerCamelCase					:					List[str]	       =    os.path.join(__a      ,							__a						)
			return f"{filepath}*"



def     UpperCAmelCase_					(				__a   :			str      ,							__a   :			List[Any]      ,							__a   :			List[str]      ,							__a   :			Tuple=None      ,							__a   :			Tuple=None						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    filename_prefix_for_split(__a      ,							__a						)
			_lowerCamelCase					:					List[str]	       =    os.path.join(__a      ,							__a						)

			if shard_lengths:
						_lowerCamelCase					:					Union[str, Any]	       =    len(__a						)
						_lowerCamelCase					:					str	       =    [f"{prefix}-{shard_id:05d}-of-{num_shards:05d}" for shard_id in range(__a						)]
						if filetype_suffix:
									_lowerCamelCase					:					int	       =    [filename + f".{filetype_suffix}" for filename in filenames]
						return filenames
			else:
						_lowerCamelCase					:					int	       =    prefix
						if filetype_suffix:
									filename += f".{filetype_suffix}"
						return [filename]





