


"""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() = }''')







import unittest

from transformers import JukeboxTokenizer
from transformers.testing_utils import require_torch


class 							UpperCamelCase_       (					unittest.TestCase	):

    '''simple docstring'''






    UpperCAmelCase__				    = JukeboxTokenizer
    UpperCAmelCase__				    = {
        '''artist''': '''Zac Brown Band''',
        '''genres''': '''Country''',
        '''lyrics''': '''I met a traveller from an antique land,
        Who said "Two vast and trunkless legs of stone
        Stand in the desert. . . . Near them, on the sand,
        Half sunk a shattered visage lies, whose frown,
        And wrinkled lip, and sneer of cold command,
        Tell that its sculptor well those passions read
        Which yet survive, stamped on these lifeless things,
        The hand that mocked them, and the heart that fed;
        And on the pedestal, these words appear:
        My name is Ozymandias, King of Kings;
        Look on my Works, ye Mighty, and despair!
        Nothing beside remains. Round the decay
        Of that colossal Wreck, boundless and bare
        The lone and level sands stretch far away
        ''',
    }


    @require_torch
    def 			SCREAMING_SNAKE_CASE				(     self :      Dict)		->int:





           '''simple docstring'''

           import torch

           A__ 					=       JukeboxTokenizer.from_pretrained('''openai/jukebox-1b-lyrics''')
           A__ 					=       tokenizer(**self.metas)['''input_ids''']
           # fmt: off
           A__ 					=       [
               torch.tensor([[
                   0, 0, 0, 7_169, 507, 9, 76, 39, 31, 46, 76, 27,
                   76, 46, 44, 27, 48, 31, 38, 38, 31, 44, 76, 32,
                   44, 41, 39, 76, 27, 40, 76, 27, 40, 46, 35, 43,
                   47, 31, 76, 38, 27, 40, 30, 64, 78, 76, 76, 76,
                   76, 76, 76, 76, 76, 23, 34, 41, 76, 45, 27, 35,
                   30, 76, 71, 20, 49, 41, 76, 48, 27, 45, 46, 76,
                   27, 40, 30, 76, 46, 44, 47, 40, 37, 38, 31, 45,
                   45, 76, 38, 31, 33, 45, 76, 41, 32, 76, 45, 46,
                   41, 40, 31, 78, 76, 76, 76, 76, 76, 76, 76, 76,
                   19, 46, 27, 40, 30, 76, 35, 40, 76, 46, 34, 31,
                   76, 30, 31, 45, 31, 44, 46, 63, 76, 63, 76, 63,
                   76, 63, 76, 14, 31, 27, 44, 76, 46, 34, 31, 39,
                   64, 76, 41, 40, 76, 46, 34, 31, 76, 45, 27, 40,
                   30, 64, 78, 76, 76, 76, 76, 76, 76, 76, 76, 8,
                   27, 38, 32, 76, 45, 47, 40, 37, 76, 27, 76, 45,
                   34, 27, 46, 46, 31, 44, 31, 30, 76, 48, 35, 45,
                   27, 33, 31, 76, 38, 35, 31, 45, 64, 76, 49, 34,
                   41, 45, 31, 76, 32, 44, 41, 49, 40, 64, 78, 76,
                   76, 76, 76, 76, 76, 76, 76, 1, 40, 30, 76, 49,
                   44, 35, 40, 37, 38, 31, 30, 76, 38, 35, 42, 64,
                   76, 27, 40, 30, 76, 45, 40, 31, 31, 44, 76, 41,
                   32, 76, 29, 41, 38, 30, 76, 29, 41, 39, 39, 27,
                   40, 30, 64, 78, 76, 76, 76, 76, 76, 76, 76, 76,
                   20, 31, 38, 38, 76, 46, 34, 27, 46, 76, 35, 46,
                   45, 76, 45, 29, 47, 38, 42, 46, 41, 44, 76, 49,
                   31, 38, 38, 76, 46, 34, 41, 45, 31, 76, 42, 27,
                   45, 45, 35, 41, 40, 45, 76, 44, 31, 27, 30, 78,
                   76, 76, 76, 76, 76, 76, 76, 76, 23, 34, 35, 29,
                   34, 76, 51, 31, 46, 76, 45, 47, 44, 48, 35, 48,
                   31, 64, 76, 45, 46, 27, 39, 42, 31, 30, 76, 41,
                   40, 76, 46, 34, 31, 45, 31, 76, 38, 35, 32, 31,
                   38, 31, 45, 45, 76, 46, 34, 35, 40, 33, 45, 64,
                   78, 76, 76, 76, 76, 76, 76, 76, 76, 20, 34, 31,
                   76, 34, 27, 40, 30, 76, 46, 34, 27, 46, 76, 39,
                   41, 29, 37, 31, 30, 76, 46, 34, 31, 39, 64, 76,
                   27, 40, 30, 76, 46, 34, 31, 76, 34, 31, 27, 44,
                   46, 76, 46, 34, 27, 46, 76, 32, 31, 30, 66, 78,
                   76, 76, 76, 76, 76, 76, 76, 76, 1, 40, 30, 76,
                   41, 40, 76, 46, 34, 31, 76, 42, 31, 30, 31, 45,
                   46, 27, 38, 64, 76, 46, 34, 31, 45, 31, 76, 49,
                   41, 44, 30, 45, 76, 27, 42, 42, 31, 27, 44, 65,
                   78, 76, 76, 76, 76, 76, 76, 76, 76, 13, 51, 76,
                   40, 27, 39, 31, 76, 35, 45, 76, 15, 52, 51, 39,
                   27, 40, 30, 35, 27, 45, 64, 76, 11, 35, 40, 33,
                   76, 41, 32, 76, 11, 35, 40, 33, 45, 66, 78, 76,
                   76, 76, 76, 76, 76, 76, 76, 12, 41, 41, 37, 76,
                   41, 40, 76, 39, 51, 76, 23, 41, 44, 37, 45, 64,
                   76, 51, 31, 76, 13, 35, 33, 34, 46, 51, 64, 76,
                   27, 40, 30, 76, 30, 31, 45, 42, 27, 35, 44, 67,
                   78, 76, 76, 76, 76, 76, 76, 76, 76, 14, 41, 46,
                   34, 35, 40, 33, 76, 28, 31, 45, 35, 30, 31, 76,
                   44, 31, 39, 27, 35, 40, 45, 63, 76, 18, 41, 47,
                   40, 30, 76, 46, 34, 31, 76, 30, 31, 29, 27, 51,
                   78, 76, 76, 76, 76, 76, 76, 76, 76, 15, 32, 76,
                   46, 34, 27, 46, 76, 29, 41, 38, 41, 45, 45, 27,
                   38, 76, 23, 44, 31, 29, 37, 64, 76, 28, 41, 47,
                   40, 30, 38, 31, 45, 45, 76, 27, 40, 30, 76, 28,
                   27, 44, 31, 78, 76, 76, 76, 76, 76, 76, 76, 76,
                   20, 34, 31, 76, 38, 41, 40, 31, 76, 27, 40, 30,
                   76, 38, 31, 48, 31, 38, 76, 45, 27, 40, 30, 45,
                   76, 45, 46, 44, 31, 46, 29, 34, 76, 32, 27, 44,
                   76, 27, 49, 27, 51, 78, 76, 76, 76, 76, 76, 76,
                   76, 76]]),
               torch.tensor([[0, 0, 0, 1_069, 11]]),
               torch.tensor([[0, 0, 0, 1_069, 11]]),
           ]
           # fmt: on
           self.assertTrue(torch.allclose(tokens[0]   ,					EXPECTED_OUTPUT[0]))
           self.assertTrue(torch.allclose(tokens[1]   ,					EXPECTED_OUTPUT[1]))
           self.assertTrue(torch.allclose(tokens[2]   ,					EXPECTED_OUTPUT[2]))





    @require_torch
    def 			SCREAMING_SNAKE_CASE				(     self :      List[str])		->Optional[int]:





           '''simple docstring'''

           import torch

           A__ 					=       JukeboxTokenizer.from_pretrained('''openai/jukebox-5b-lyrics''')
           A__ 					=       tokenizer(**self.metas)['''input_ids''']
           # fmt: off
           A__ 					=       [
               torch.tensor([[
                   0, 0, 0, 1_069, 11, -1, -1, -1, -1, 9, 77, 39,
                   31, 46, 77, 27, 77, 46, 44, 27, 48, 31, 38, 38,
                   31, 44, 77, 32, 44, 41, 39, 77, 27, 40, 77, 27,
                   40, 46, 35, 43, 47, 31, 77, 38, 27, 40, 30, 64,
                   79, 77, 77, 77, 77, 77, 77, 77, 77, 23, 34, 41,
                   77, 45, 27, 35, 30, 77, 72, 20, 49, 41, 77, 48,
                   27, 45, 46, 77, 27, 40, 30, 77, 46, 44, 47, 40,
                   37, 38, 31, 45, 45, 77, 38, 31, 33, 45, 77, 41,
                   32, 77, 45, 46, 41, 40, 31, 79, 77, 77, 77, 77,
                   77, 77, 77, 77, 19, 46, 27, 40, 30, 77, 35, 40,
                   77, 46, 34, 31, 77, 30, 31, 45, 31, 44, 46, 63,
                   77, 63, 77, 63, 77, 63, 77, 14, 31, 27, 44, 77,
                   46, 34, 31, 39, 64, 77, 41, 40, 77, 46, 34, 31,
                   77, 45, 27, 40, 30, 64, 79, 77, 77, 77, 77, 77,
                   77, 77, 77, 8, 27, 38, 32, 77, 45, 47, 40, 37,
                   77, 27, 77, 45, 34, 27, 46, 46, 31, 44, 31, 30,
                   77, 48, 35, 45, 27, 33, 31, 77, 38, 35, 31, 45,
                   64, 77, 49, 34, 41, 45, 31, 77, 32, 44, 41, 49,
                   40, 64, 79, 77, 77, 77, 77, 77, 77, 77, 77, 1,
                   40, 30, 77, 49, 44, 35, 40, 37, 38, 31, 30, 77,
                   38, 35, 42, 64, 77, 27, 40, 30, 77, 45, 40, 31,
                   31, 44, 77, 41, 32, 77, 29, 41, 38, 30, 77, 29,
                   41, 39, 39, 27, 40, 30, 64, 79, 77, 77, 77, 77,
                   77, 77, 77, 77, 20, 31, 38, 38, 77, 46, 34, 27,
                   46, 77, 35, 46, 45, 77, 45, 29, 47, 38, 42, 46,
                   41, 44, 77, 49, 31, 38, 38, 77, 46, 34, 41, 45,
                   31, 77, 42, 27, 45, 45, 35, 41, 40, 45, 77, 44,
                   31, 27, 30, 79, 77, 77, 77, 77, 77, 77, 77, 77,
                   23, 34, 35, 29, 34, 77, 51, 31, 46, 77, 45, 47,
                   44, 48, 35, 48, 31, 64, 77, 45, 46, 27, 39, 42,
                   31, 30, 77, 41, 40, 77, 46, 34, 31, 45, 31, 77,
                   38, 35, 32, 31, 38, 31, 45, 45, 77, 46, 34, 35,
                   40, 33, 45, 64, 79, 77, 77, 77, 77, 77, 77, 77,
                   77, 20, 34, 31, 77, 34, 27, 40, 30, 77, 46, 34,
                   27, 46, 77, 39, 41, 29, 37, 31, 30, 77, 46, 34,
                   31, 39, 64, 77, 27, 40, 30, 77, 46, 34, 31, 77,
                   34, 31, 27, 44, 46, 77, 46, 34, 27, 46, 77, 32,
                   31, 30, 66, 79, 77, 77, 77, 77, 77, 77, 77, 77,
                   1, 40, 30, 77, 41, 40, 77, 46, 34, 31, 77, 42,
                   31, 30, 31, 45, 46, 27, 38, 64, 77, 46, 34, 31,
                   45, 31, 77, 49, 41, 44, 30, 45, 77, 27, 42, 42,
                   31, 27, 44, 65, 79, 77, 77, 77, 77, 77, 77, 77,
                   77, 13, 51, 77, 40, 27, 39, 31, 77, 35, 45, 77,
                   15, 52, 51, 39, 27, 40, 30, 35, 27, 45, 64, 77,
                   11, 35, 40, 33, 77, 41, 32, 77, 11, 35, 40, 33,
                   45, 66, 79, 77, 77, 77, 77, 77, 77, 77, 77, 12,
                   41, 41, 37, 77, 41, 40, 77, 39, 51, 77, 23, 41,
                   44, 37, 45, 64, 77, 51, 31, 77, 13, 35, 33, 34,
                   46, 51, 64, 77, 27, 40, 30, 77, 30, 31, 45, 42,
                   27, 35, 44, 67, 79, 77, 77, 77, 77, 77, 77, 77,
                   77, 14, 41, 46, 34, 35, 40, 33, 77, 28, 31, 45,
                   35, 30, 31, 77, 44, 31, 39, 27, 35, 40, 45, 63,
                   77, 18, 41, 47, 40, 30, 77, 46, 34, 31, 77, 30,
                   31, 29, 27, 51, 79, 77, 77, 77, 77, 77, 77, 77,
                   77, 15, 32, 77, 46, 34, 27, 46, 77, 29, 41, 38,
                   41, 45, 45, 27, 38, 77, 23, 44, 31, 29, 37, 64,
                   77, 28, 41, 47, 40, 30, 38, 31, 45, 45, 77, 27,
                   40, 30, 77, 28, 27, 44, 31, 79, 77, 77, 77, 77,
                   77, 77, 77, 77, 20, 34, 31, 77, 38, 41, 40, 31,
                   77, 27, 40, 30, 77, 38, 31, 48, 31, 38, 77, 45,
                   27, 40, 30, 45, 77, 45, 46, 44, 31, 46, 29, 34,
                   77, 32, 27, 44, 77, 27, 49, 27, 51, 79, 77, 77,
                   77, 77, 77, 77, 77, 77]]),
               torch.tensor([[0, 0, 0, 1_069, 11, -1, -1, -1, -1]]),
               torch.tensor([[0, 0, 0, 1_069, 11, -1, -1, -1, -1]]),
           ]
           # fmt: on
           self.assertTrue(torch.allclose(tokens[0]   ,					EXPECTED_OUTPUT[0]))
           self.assertTrue(torch.allclose(tokens[1]   ,					EXPECTED_OUTPUT[1]))
           self.assertTrue(torch.allclose(tokens[2]   ,					EXPECTED_OUTPUT[2]))


